Quantitative structure-activity (QSAR) models have enormous potential for reducing drug discovery and development costs as well as the need for animal testing. Great strides have been made in estimating their overall reliability, but to fully realize that potential, researchers and regulators need to know how confident they can be in individual predictions.Submodels in an ensemble model which have been trained on different subsets of a shared training pool represent multiple samples of the model space, and the degree of agreement among them contains information on the reliability of ensemble predictions. For artificial neural network ensembles (ANNEs) using two different methods for determining ensemble classification – one using vote tallies and the other averaging individual network outputs – we have found that the distribution of predictions across positive vote tallies can be reasonably well-modeled as a beta binomial distribution, as can the distribution of errors. Together, these two distributions can be used to estimate the probability that a given predictive classification will be in error. Large data sets comprised of logP, Ames mutagenicity, and CYP2D6 inhibition data are used to illustrate and validate the method. The distributions of predictions and errors for the training pool accurately predicted the distribution of predictions and errors for large external validation sets, even when the number of positive and negative examples in the training pool were not balanced. Moreover, the likelihood of a given compound being prospectively misclassified as a function of the degree of consensus between networks in the ensemble could in most cases be estimated accurately from the fitted beta binomial distributions for the training pool.Confidence in an individual predictive classification by an ensemble model can be accurately assessed by examining the distributions of predictions and errors as a function of the degree of agreement among the constituent submodels. Further, ensemble uncertainty estimation can often be improved by adjusting the voting or classification threshold based on the parameters of the error distribution. Finally, the profiles for models whose predictive uncertainty estimates are not reliable provide clues to that effect without the need for comparison to an external test set. Considerable work has been done on ways to identify compounds for which predictions are unlikely to be reliable – i.e., on applicability domains [Drug discovery and development is an expensive business and its costs continue to rise. Exploitation of quantitative structure activity relationships (QSARs) and related doing so -3. Consi domains -6 and on domains ,7-13. So domains ,15. To op of misclassifying a compound, the contingent probability P that k of K networks in an ensemble will mistakenly assign a “negative” compound to the “positive” class or a “positive” compound to the “negative class” would be expected to follow a binomial distribution:A key first step on the path to successfully exploiting ensemble variance for classification error analysis was to move away from the traditional truth table assessment of classification performance based on four classes of predictive outcome – true positives, true negatives, false positives and false negatives – and to look instead at distributions of predictions and errors as a function of the level of consensus among the individual submodels making up the ensemble. In particular, we investigated how predictive classification error rates (errors/prediction) relate to the number of positive “votes” obtained from an ensemble model composed of artificial neural networks  – e.g., BB) useful [Such a scheme was explored (data not shown), but proved unsatisfactory. In retrospect, this is not surprising, since the networks are not independent and have different probabilities of making an erroneous prediction for different compounds. When such “overdisperse” distributions are encountered in biometrics problems, researchers have found beta binomial distributions  useful -19:B is the beta function:Here, Γ(n + 1) = n !). Unlike the binomial distribution, the beta binomial can be convex as well as concave. The former is the case for α < 1 and β < 1 whereas the latter holds for α > 1 and β > 1. When α = β = 1, the beta binomial distribution reduces to the discrete uniform distribution on the interval 0 to K.where function , which iK networks making k positive votes for a given compound) directly but the results were not satisfactory. On the other hand, separate beta binomials fit distributions of ensemble predictions and error counts for the training pool reasonably well. This is not altogether surprising, since both distributions result from a series of K events that are related but not independent. There are two possible outcomes in both cases: “the compound in question is a positive or a negative” for predictions and “the prediction is correct or incorrect” for errors. What is somewhat surprising is that the distributions fitted to the training pool match the corresponding distributions seen for large external validation sets as well.We attempted to fit beta binomial distributions to uncertainty profiles  be the probability that a given prediction is in error given that it receives k positive votes, which we equate with the predictive uncertainty of the classification. Let P(k|ϵ) be the probability that a prediction receives k positive votes given that it is erroneous (misclassified). Finally, let P(ϵ) be the overall probability that a prediction is in error and let P(k) represent the probability that a prediction receives k positive votes. Application of Bayes’ theorem yields:The distributions of votes and errors can then be combined to yield an ensemble uncertainty profile using a method rooted in elementary probability theory. Let φ(k) represent our estimate of P(k), the probability distribution of positive vote tallies across all predictions or simply the “prediction distribution”. Let ϵ(k) represent our estimate of P(k|ϵ), the probability distribution of all misclassified predictions as a function of k, which we refer to as the “error distribution”. P(ϵ|k) is the probability of an error in classification  that receives k positive votes; our estimate of it will be represented by u(k) and referred to as the uncertainty profile or distribution.To distinguish between underlying population distributions and estimated distributions fitted to samples, we introduce the following notation. Let P(ϵ) is the overall probability of an error or simply the misclassification rate (MR) of the model. Our estimate of the uncertainty of a prediction receiving k votes is then given by:Finally, MR is obtained from the overall misclassification rate  for the training pool, and ϵ(k) and φ(k) are estimated by fitting beta binomial distributions to the training pool errors and predictions, respectively, as functions of k.Our protocol for vote-based ensemble classifications can be summarized by the following:K submodels.1. Build an ensemble of 2. Establish a classification threshold for each submodel that determines its vote.k for each prediction.3. Tally the number of positive votes 4. Establish a decision rule for the ensemble.5. Classify each ensemble prediction for the training pool as being correct or incorrect.k.6. Count the number of errors for each vote tally 7. Add a continuity correction to the count for each tally by adding 1 to each prediction tally and adding 0.5 to each error count.φ(k), that best matches the cumulative voting distribution as a function of k by minimizing the Kolmogorov-Smirnov (K-S) statistic [8. Find the alpha and beta parameters of a beta binomial distribution, tatistic  between k), that best matches the observed distribution of the errors by similarly minimizing the K-S statistic between the cumulative distributions.9. Find the optimal beta binomial distribution, ϵ(u(k) = MR*ϵ(k)/φ(k).10. Estimate the uncertainty distribution as k) may substantially improve the overall balance between specificity and sensitivity.The remainder of this paper is devoted to showing applications of this protocol to data sets of varying quality and showing the influence of imbalances in class size. Most of the examples described involve models where the ensemble decision is determined by voting: decision thresholds are established independently for each network and the classification “votes” that result are tallied to determine the ensemble classification. For unbalanced data sets, resetting the ensemble voting threshold to match the mean of ϵ(k). Working with large validation sets proved essential to getting good enough sampling of errors to meaningfully assess how well our uncertainty estimation method works. Typically, the numbers of predictions and errors receiving k votes is small for intermediate values of k , which can result in low counts in this region unless the validation set is comprised of thousands of compounds. This is especially true for good models. The desire to maximize the size of the validation set to minimize the effects of noise in assessing the performance of the model led us to use an unusually small fraction of the available data to train the models – 10 to 30% instead of the typical 80 to 90%. It also helped to demonstrate that the methodology does not require large training sets to work.One application makes use of an alternative method in which individual network outputs are averaged and compared to an aggregate classification threshold. In such cases, the model benefits from resetting the threshold to the geometric mean of the averaged threshold and the mean of ϵ, each made up of 33 individual networks. All networks in an ensemble have the same architecture (same number of neurons and descriptor inputs) but are trained with different subsets of the shared training pool. Details of the model construction are provided in the Methods section, but they are unlikely to affect the general phenomena and conclusions discussed herein.false false negative. There will, however, be a similar number of cases in which a compound miscategorized in the data set is misclassified by the model, so the overall uncertainty is close to 0.5 at the threshold itself.Figure The distribution of errors is only roughly symmetrical in this case, in part because the distribution of observed logP values is not quite symmetrical and in part because the positive examples appear to be slightly harder to learn. This is reflected in the difference between the validation set sensitivity (0.849) and specificity (0.882) shown for model logP2-1 in Table k > 16.5), the compound in question is classified as a positive; otherwise, it is classified as a negative. True and false negatives lie to the left of the threshold, whereas true and false positives lie to the right of the threshold. Figure Figure k because the sampling rate is low. The standard error of a rare event count is equal to its square root, so the relative standard error is large for counts below 10. As a result of the noisy data and low sampling counts, all that can be claimed for the training pool is that the uncertainty profile calculated from the training pool prediction and error beta binomials is consistent with what is actually observed. Note, too, that this “calculated uncertainty profile” crosses the ensemble voting threshold just below the theoretical threshold error rate of 0.5 *N) for a particular value of k is low. The error rate when there is only one prediction, for example, is 0.0 if the prediction in question is correct and 1.0 if it is not, and neither proportion is likely to be a good estimate of the uncertainty. Indeed, in the extreme case where there are no training pool predictions at all – erroneous or otherwise – the uncorrected error rate is equal to 0/0, which is indeterminate. This problem is often encountered when estimating frequencies of rare events, and adding a continuity correction of 0.5 is a standard way to deal with it [k for which the training pool contains no predictions at all.Finally, a continuity correction of 0.5  has been with it . A complvalidation set along with the beta binomial distributions and uncertainty profiles generated using the distribution parameters derived from fitting to the training pool results. The deviations observed are small in both figures, remarkably so for the validation set’s error rate profile  represeet al.[Figure et al., but thafalse false negatives. We have found confidence analysis of the sort described here a valuable tool for identifying such potential errors in data sets.Ames-1 does a good job of predicting uncertainties at intermediate vote tallies, but underestimates errors somewhat at the extremes. Having some errors at the extremes is consistent with the rather modest historical accuracy rate of 85% for the Ames assay. The fact that most or all of the networks agree on how these compounds should be classified, however, suggests that some of them may be miscategorized due to mistakes in the literature occurring in the course of publication and subsequent data compilation – i.e., that a number of the misclassifications may in fact be Ames-2 does a better job of matching the observed error rates at the extremes, but consistently underestimates them (and therefore overestimates confidence in the predictions) at intermediate levels of consensus. These may well be compounds that are borderline in their mutagenicity, but the practical outcome with respect to the reliability of confidence estimates is the same: the profile is less useful than it could be for confidence estimation.Fortunately, Ames-2 provides a clue to its weakness even in the absence of any external validation set, in that its calculated uncertainty profile crosses the voting threshold well below 0.5 – below 0.4, in fact Figure  is consiJ[Data sets in which there are many more observations in one class than another are problematic for many classification methods. Rather than trying to balance the training pool , ADMET Modeler addresses such imbalances by scaling the terms in the objective function by class size and by relying on Youden’s index J to set ca. Keeping the same networks as in model logP3-1a, but refining the model by shifting the voting threshold to the beta binomial mean, produces model logP3-1bb. The effect of the shift is shown in Figures Model logP3-1a was built using 33 networks and the naïve majority-voting rule – i.e., with a voting threshold of 16.5. The results are shown in Figures c. That said, the revised uncertainty profile does well enough for most purposes. The count scale in Figure Figure Note that the two predicted uncertainty profiles bracket 0.5 at the refined threshold. The discontinuities near the thresholds arise because Youden’s index is used to set the classification thresholds for the individual networks. For a large training pool and a well-trained model, the density of negative predictions will be high near 0 for each network and fall off as one moves to the right, towards 1. Similarly, the density of positive predictions will be high near 1 and fall off as one moves to the left. In the limit of an infinite training pool, maximizing Youden’s index will place the classification threshold at a point where any shift to the left will increase sensitivity less than it will decrease specificity. Similarly, any increase in specificity achieved by a shift to the right will be more than offset by a decrease in sensitivity.J. Hence the error rate approaching the threshold from the left will be about 1/3 the error rate approaching from the right – once one gets close enough to it. The expected uncertainty exactly at the threshold will still be 0.5, but it will be approached from below that value from the left and from above that value from the right when the number of negatives in the populations (or the ease of their classification) exceeds the number of positives. If this rationale is correct, then the discontinuity should disappear when the network thresholds are set so as to maximize concordance instead of Youden’s index. It does indeed disappear – at the cost of a disproportionate increase in errors for the minor class (details not shown).The discontinuity is exacerbated by the compression of positive (negative) tallies as the threshold is shifted to the right (left), which can be relieved to some extent by increasing the number of networks in the ensemble. This is illustrated in Figure The 3-to-1 imbalance in the logP3 data set results in the classification threshold for each network being set at a point where the density of positive predictions is 1/3 the density of negative predictions; if the relative density were higher than that, a further shift to the left would increase As noted earlier, the logP data sets are somewhat artificial. High-throughput screening data for CYP2D6  inhibitid. The resulting estimates are shown by the dotted gray lines in Figure Increasing the number of networks did not improve the situation in this case (details not shown). One possible alternative strategy for estimating uncertainty is to replace beta binomial profiles with average class uncertainties calculated for the training pool: Jmax threshold”) is used by default. The vote tallies for estimating predictive uncertainty are obtained by comparing each network’s output to the ensemble threshold but are not themselves used for classification.It is perhaps not surprising that the uncertainty estimation method described above works well on ensemble models in which predictive classifications are determined by tallies of independently determined positive votes, since in that case the degree of network consensus reflects the variability of outcomes fairly directly. To explore how broadly applicable the method is, we turned to ANNEs in which classification is determined by averaging the individual network outputs (which are logistic functions ranging from 0 to 1 for classification models) and comparing that average to an ensemble threshold. If the average output lies above the ensemble classification threshold, the compound is classified as a positive; if the average falls below the threshold, the compound is classified as a negative. The ensemble threshold that maximizes Youden’s index across the training pool  the threshold, their average output must do so as well.Jmax threshold for the average output is 0.491, corresponding to a threshold for the sum of 33 × 0.491 = 16.2 and represented by the horizontal dotted red line in Figure r2 = 0.983), they diverge enough to spread the Jmax classification threshold across several tally counts – from 13 to 20 in this case  underestimates the error rates seen in the validation set and thereby overestimates how much confidence one can have in its individual predictions Figure D. This iTallying votes and averaging submodel outputs are both useful ways to assess the degree of consensus within an ensemble. Fitting ensemble misclassification rates to a binomial distribution to assess confidence is intuitively appealing but flounders in practice because predictions by the component submodels are not independent. Using beta binomial distributions to model predictions and errors works well, however, and the ratio of such distributions can be used to estimate the likelihood that a given prediction will be incorrect.The corresponding distributions seen in large, held-out validation sets match those seen for the training pool remarkably well in most cases. Moreover, those cases for which the predicted error rate profile is not reliable provide a good clue to that effect, in that their calculated uncertainty profiles cross the model’s voting threshold  well below the expected value of 0.5. Why this occurs is not clear at this time but it may reflect a lack of diversity in predictions among the networks that make up the ensemble. If consensus is complete across the entire training pool, for example, all predictions and errors will lie at the extremes and no information will be available regarding the distribution of predictions and errors in between.k), helps attenuate that discontinuity. In many cases, the uncertainty profile can still be adequately described by a combination of just two distributions – one fitted to the training pool predictions and another fitted to the training pool errors. In other cases, four sets of distribution parameters and a threshold value are required to create a composite distribution, one pair applying to the left of the threshold  and the other pair to its right . Models built using the averaging method avoid this complication.Models based on voting that are built on unbalanced data sets and use Youden’s index as the criterion for setting individual network classification thresholds tend to have a discontinuity in observed error rates near the ensemble voting threshold. Resetting that threshold to match the mean of the beta binomial for the error, ϵ). Such confidence values can also be generated for classification models created using the ADMET Modeler module of the program.Our approach complements classical overall performance measures based on partitioning predictions into true positive, false positive, true negative and false negative categories; it does not replace them. Implementing it is straightforward: it was originally done using the GAMMALN function and the Solver add-in for Excel  to fit tThe log P data set is diverse and has been heavily curated. It consists of the 12,580 values used to build and test the S + logP model distributed with ADMET Predictor, the bulk of which are derived from the BioByte database . Some enet al.[The Ames mutagenicity data set was taken from the compilation by Hansen et al. and contHigh-throughput screening data on CYP2D6 inhibition comes from PubChem AID 1851 ,34 proviAn indication of titration reliability was provided for each compound and those labeled as reflecting dubious titrations (“activity outcomes” of 3 ) were dia predictions and microstate analysis in ADMET Predictor 7.0.Tautomeric ambiguities for all data set entries were resolved using the pKModels considered here were ensembles of 33 artificial neural networks (except as otherwise noted) constructed in the ADMET Modeler module of a prerelease version of ADMET Predictor 7.0, with all the networks in a given ensemble having an identical architecture, i.e., the same set of descriptor inputs and number of hidden neurons. We do not expect that the conclusions drawn here are limited in applicability by exactly how the particular ensemble models were constructed, but the general procedure followed to build them is described in some detail below.Data remaining after extraction of the external validation set was further divided into a training pool (further divided into “training” and “verification” sets) and an external test set. The latter is used to help identify the ensemble having the “best” architecture but is not used during the model building process itself. A grid of ensemble architectures is trained using a total of 165 networks per architecture from which the best 33 networks are selected. Each architecture uses a different combination of neurons and inputs and each network has its own training and verification set. Two thirds of the training pool was used for training and the remaining third served as a verification set. These training pool splits were made randomly and independently for each network in the ensemble.xi is assigned a weight wij for each neuron j in the single hidden layer such that the output fj for neuron j is a function of the input values as given by:Each input (descriptor) tj is the offset associated with neuron j. Those neural outputs are combined using an output function g defined by:where b is a network offset, and aj is a weight associated with neuron j in the hidden layer. The adjustable parameters wij, tj, aj and b for each network are initialized independently with random values, then adjusted iteratively to minimize the objective function Obj:where “lg” represents the logistic function, q(l) is the class indicator value for observation l (0 for negatives and 1 for positives) and g(l) is the output function evaluated on the input vector xl. The net effect of minimizing Obj is to drive the outputs for observations in the negative and positive classes towards 0 and 1, respectively. The class weights c0 and c1 are the fractions of observations in the positive and negative classes, respectively, resulting in the smaller class having the larger weight.where J for the training set:The verification set is used for early stopping , which rUnless otherwise indicated, 165 networks were trained for each architecture (number of inputs and number of neurons) and the 33 having the best performance (combining training and verification statistics) were retained in the final ANNE for that architecture. A matrix of architectures is trained, varying the numbers of inputs and neurons, and the architecture that provides the best, statistically significant performance is selected as the final model.J for the average. The former is the “voting method”, whereas the latter is the “averaging method”.ADMET Modeler combines outputs from the constituent networks in an ensemble model in one of two ways: one is to tally positive “votes” based on each individual network’s own threshold (see above), whereas the other is to compare the averaged output to an ensemble threshold that maximizes Candidate ensembles are compared on the basis of their performance on the training and test sets that they share. To ensure that the results obtained are qualitatively robust, experiments should be run across a range of training pool/test set splits, a range of architectures and a range of random number seeds – as was done for the present study.f and e of predictions and predictive errors, respectively, are calculated as functions of the number k of positive votes for compounds in the training pool, which ranges from 0 to K . A continuity correction [k to help compensate for undersampling (see above). As a result, the observed contingent error rate is e(k)/f(k) = 0.5 for tallies with no predictions, 0.5/2 = 0.25 for tallies having a single correct prediction, and 1.5/2 = 0.75 for tallies with a single incorrect prediction.The distributions rrection  of 0.5 ek) and φ(k) are fitted to the cumulative observed error and prediction distributions, respectively. Intermediate tallies away from the extremes tend to be sparsely sampled even for quite large data sets, however, which can complicate direct fitting. This is addressed in part by the continuity correction described above and in part by fitting cumulative beta binomials to the respective cumulative observed distributions by minimizing the Kolmogorov-Smirnov statistic [k positive votes is in error (the uncertainty) is then given by:Beta binomial distributions ϵ. In the case where the confidences are the same for all compounds of a given class, this reduces to the positive or negative predictive values for the respective classes.where Of the 366 molecular descriptors generated by default in ADMET Modeler, the analyses presented here used a subset of 221: substructure counts  were omitted to maximize the size of the applicability domain, as were molecular weight, total bond count, number of hydrogens and four other descriptors. The latter group was dropped because they were highly correlated with more informative ones. Other descriptors were set aside for individual analyses if they had a coefficient of variation less than 1%, failed to be nonzero in at least 4 cases, or had absolute correlation coefficients with one or more other descriptors above 0.98. The number of descriptors passing those filters in each case ranged from 172 to 183 and included: counts of common element and bond types, rings and molecular volumes; electrotopological and connectivity indices; topological size measures; molecular and partial atomic charge values; polarizabilities; and topological autocorrelation vectors of various atomic properties such as partial charge and Fukui indices.The ranking of descriptors was determined using the Input Gradient option in ADMET Modeler, wherein candidate descriptors are ranked by analysis of their response gradients. Trial neural networks with a specified number of hidden neurons  are built using all descriptors, then the analytical sensitivity gradient is extracted from that network for each candidate descriptor. Then, a series of ensemble models are built for a given number of neurons in which the number of descriptors is progressively increased, selecting them based on the ranking assigned by the Input Gradient procedure. The resulting Input Gradient descriptor rankings are thus dependent on the number of neurons used.aThe means for the error beta binomials for the logP2 and Hansen data sets are very close to 16.5, and shifting the voting threshold has little effect.bModels whose names differ only by a terminal letter have the same component networks but have different classification criteria at the ensemble level.cTo avoid ties, the actual threshold is calculated from the theoretical threshold set to floor(mean)+0.5.dNote that The authors have no competing interests apart from their institutional affiliation with Simulations Plus, Inc.All authors contributed to the manuscript and helped carry out the extensive testing needed to make application of the method it describes practical and robust. In addition, MW derived the formalism for estimating the contingent uncertainty profile from the observed distributions of predictions and errors and implemented it in Excel. WL refined the Excel implementation and encoded it in C++ for use in ADMET Predictor under RF’s supervision. RDC recognized the suitability of beta binomial distributions and the need to apply continuity corrections. ACL and MSL carried out preliminary analyses demonstrating the usefulness of the log P data set for investigating the distributions of classification error and the suitability of the binomial distribution. All authors read and approved the final manuscript.


We like to make readers aware that Leif Jansson and Nils Welsh contributed as guest editors to the issueRemembering Claes Hellerström and those around him. Unfortunately, this title was not placed on the front cover as it should have beenThe title of the issue should have been In addition to this, a number of the ‘flashes’ were erroneously printed from the previous issue (121-01) on the front cover.In the previous issue of this journal (121-02), a number of errors were made.Taylor & Francis apologises for these errors.


In this paper, we have considered an economic order quantity model for deteriorating items with two-level trade credit policy in which a delay in payment is offered by a supplier to a retailer and also an another delay in payment is offered by the retailer to his/her all customers. Here, it is proposed that the demand function is dependent on the length of the customer’s credit period and also the duration of offering the credit period. In this article, it is considered that the retailer’s ordering cost per order depends on the number of replenishment cycles. The objective of this model is to establish a deterministic EOQ model of deteriorating items for the retailer to decide the position of customers credit period and the number of replenishment cycles in finite time horizon such that the retailer gets the maximum profit. Also, the model is explained with the help of some numerical examples. M and the retailer also provides the trade credit period N I(t): the inventory level at time t.(ii)D(t): the demand function at time t.(iii)H: total planning horizon (in year).(iv)A: retailer’s ordering cost per order.(v)p: retailer’s purchase cost per unit item.(vi)s: retailer’s selling price per unit item .(vii)r: rate of inflation.(viii)(ix)h: retailer’s holding cost per unit per unit time.(x)(xi)(xii)M: the retailer’s trade credit period offered by the supplier in years.(xiii)N: the customers credit period offered by the retailer in years, where (xiv)n: the number of replenishment cycles during the planning horizon (a decision variable).(xv)ith replenishment cycle, (xvi)ith replenishment period.(xvii)TPj: total profit of the retailer, (i)H.The inventory system involves only one item over a finite planning horizon (ii)The replenishment occurs instantaneously at an infinite rate.(iii)Shortages are not allowed.(iv)The items deteriorate at a constant rate of deterioration (v)M) of them is offered by a supplier to the retailer and another one (N) is offered by the retailer to each customer in such a way that each customer must pay within the period of the credit period (M) offered by the supplier to the retailer. It is also assumed that the customer’s credit period is less than or equal to the retailer’s credit period i.e., Here, two credit periods have been considered in each cycle. One ((vi)It is considered that the retailer pay his/her dues at the end of each cycle. So, if the length of the replenishment cycle is greater than the length of the credit period the retailer has to an interest at a rate (vii)N) (decision variable) to each customer in certain duration to increase his/her demand (D(t)). Here, the duration of credit period is proposed in such a way that the last end customer who takes the facility of credit period pay his/her dues at the time of credit period (M) offered by the supplier . Therefore, all end customers having this facility, come during the period N and D(t) has been considered as a exponential function of time in respect of In this model, a retailer intends to offer a credit period ((viii)All replenishment cycles have same size.(ix)A) per cycle has been proposed in the following way: a0 (>0) be the fixed cost per cycle, a1 (>0) be the shipment cost for the total quantity delivered in one time and a2 (>0) be the process cost per cycle. Also, here it is clear that for n cycles the total ordering cost considering fixed ordering cost per cycle must be greater than the variable ordering cost per cycle depending on the processing cost. That is, considering fixed ordering cost per cycle total ordering cost (TFOC) will be greater than the total ordering cost (TVOC) considering variability in the ordering cost provided that In this paper, it is assumed that the ordering cost  in the ith cycle for the retailer is given byIn each cycle,deterioration and demand both effect on the inventory. Hence the differential equation of the inventory level mentclass2pt{minimith cycle is given byThe present value of the holding cost ith replenishment period, denoted by The present value of the purchase cost during the ith replenishment period, denoted by The present value of the sales revenue in the  When In this case, it is assumed that length of the replenishment period is greater than the retailer’s credit period, i.e., here, ith replenishment period, denoted by The present value of the interest earned in the ith replenishment period, denoted by  The present value of interest charge in the So, in this case, retailer’s total profit When In this case, it is assumed that the length of the replenishment period is less than the retailer’s credit period. So no interest is charged from the retailer i.e. N to each customer in such a way that all customers must pay their dues within the retailer’s credit period, so in this case, the following must be hold for ith cycle.Since the retailer offers credit period  Thus the present value of interest earned,denoted by  So, in this case, the retailer’s total profit  When In this case, it is assumed that the length of the replenishment period is less than the retailer’s credit period. So no interest is charged from retailer i.e. ith cycle.Since all customers must pay their dues within the retailer’s credit period, so the following must be hold for To illustrate the above model, the following numerical examples have been considered.N to each customer upto a certain time in such a way that all customers must pay their dues within the retailer’s credit period, after that no credit will be given and the retailer earns interest at a rate of 6 %. The ordering cost of the retailer has been considered according to assumption (ix). Here, the retailer’s objective is to maximize the total profit. Find the optimal number replenishment cycle period and optimal credit period N offered by the retailer.A company supplies one kind of items to a retailer at cost of $35 per unit item and offers a credit period 50/365 to the retailer in such a way that he will enjoy the relaxation on interest charge during this period. In this business policy it has been settled that the retailer pays his dues at the end of each cycle. If the credit period be less than the cycle length then due to late payment the retailer must pay an interest to the supplier at a rate of 8 %. The retailer’s holding cost is $3 per unit item and the items deteriorate at a rate of 1 %. The retailer sales each unit of items at cost of $50 to customers. The retailer also offers same credit  In this problem, Since the model corresponding to this problem is non-linear, it cannot be optimized analytically. So to get the optimal solution, the standard LINGO software has been used of such type of model utilizing the above parameters. Before getting the optimal solution, the concavity of the objective function has been shown by Fig.  The same problem in Problem-1 when retailer consider ordering cost as a fixed value, $ 1200 which is same as the ordering cost when replenishment cycle number is 1 for the variable ordering cost. The obtained results for three cases have been shown in Table  The same problem in Problem-1 when constant demand is considered i.e., when The obtained results have been shown in Table From Table mentclass2pt{minimmentclass2pt{minimConsidering constant demand i.e., when entclass1pt{minimaFrom Table θ. From this, it is observed that the optimal total profit decreases with the increase of θ which is normal.Figure M) offered by the supplier to the retailer increases, then the optimum profit of the model also increases along with increasing the customer’s credit period (N) though the number of replenishment cycle is almost same. Thus, the retailer may offer more credit to his/her customer to get more profit.From Table TP1 decreases but offering credit period N remains same and the number of replenishment cycles also decreases. But, it is more profitable than the case when fixed ordering cost is considered according to Lemma 1.In Table From results obtained in Tables Here, we have proposed an EOQ model for deteriorating items considering two level credits where all customers are allowed to take the advantage of credit period from the retailer upto a limited period. The demand function is linked with customer’s credit period and the duration of publicity of such credit period in exponential nature. Here, retailer’s ordering cost per order has been considered as function of replenishment cycle number. Some examples have been provided to illustrate the model. Also, managerial insights have been carried out. The proposed model can be further extended in several ways like different demand structures, quantity discount, deterioration with lifetime, warranty cost and others.


The amplitude of the sensor output voltage signals are adjusted to unit amplitude to minimize the amplitude errors. With the unit amplitude signals three to two phase transformation is done to reduce the three multiples of harmonic components. The final output thus obtained is converted to position data by the use of arctangent function. The measurement accuracy of the new method is analyzed by experiments and compared with the conventional two phase method. Using the same number of sensor modules as the conventional two phase method, the proposed method gives more accurate position information compared to the conventional system where sensors are separated by 90° electrical angles.A new method to detect the mover position of a linear motor is proposed in this paper. This method employs a simple cheap Hall Effect sensor-based magnetic sensor unit to detect the mover position of the linear motor. With the movement of the linear motor, Hall Effect sensor modules electrically separated 120° along with the idea of three phase balanced condition ( Recently, linear motors have been used in many areas of manufacturing and automatic transfer system for flat panel display and factory automation. With the increase in the application of linear motors, the position estimation method has captured a lot of attention. In conventional methods, linear encoders are used as the most common position sensors ,2,3. A lTo achieve an alternative low cost and robust method for position detection, magnetic sensors are widely used nowadays. Linear position sensors with an accuracy of 0.2 mm to 1 mm can be designed using Hall Effect sensors . Hall EfThe concept of the present research is motivated by the distinguishing characteristics between conventional two phase and three phase systems for position detection. The work presented in this paper has a couple of steps to precisely achieve mover position: firstly, the conventional magnetic sensor position detection methods using conventional two phase and three phase systems were investigated and compared under equal amount of errors in amplitude and phase. If the amplitudes of the sensor signals are made a unit reference, the three phase system yields better position results than the two phase system. In addition to this, if three to two phase transformation is done on three phase system signals, the resulting two phase signal shows a reduction of multiple of three order harmonics. a + vb + vcv = 0). Three phase signal is made to two phase signal using three to two phase transformation. The position of the linear motor is achieved by using an arctangent function on the two phase signal obtained. The significance and performance of the proposed method is verified by MATLAB/Simulink. In addition, the experimental verification is also achieved by using magnetic sensor units. The proposed method does not need any extra error compensation methods to minimize the errors individually. Secondly, considering the advantages of the conventional three phase system over two phase systems mentioned above, a new position detection method for accurate position detection of linear motors using Hall Effect-based magnetic sensors is proposed. The new position detection method uses same number of sensors like a conventional two phase system, but gives superior result compared to the conventional two phase system. The proposed position detection method produces three phase signals using two magnetic sensor units electrically separated 120° and three phase balanced condition  can be rewritten as:Similarly for the three phase system, considering the error in amplitude only, Equation (4) is rewritten as:Taking the three phase to two phase transformation of Equation (9):αv and βv will be perfect sine and cosine signals, so in the proposed method, the amplitudes of measured sensor signals are made to unit amplitude to get perfect sine and cosine signals.MATLAB simulation models for two phase and three phase position detection systems are made to observe the deviation of the output signal under 1% error in amplitude for both the conventional systems. The simulation result is shown in Similar to the amplitude error, the error in phase is considered individually for both the conventional two phase and three phase position detection systems as follows:In case of a two phase system:For the three phase system:To check the phase error condition, MATLAB simulation with 1% error in phase for both conventional three phase and two phase system is considered. The variation of the position detected by both the systems and their deviation from the reference under phase error is illustrated in αv and βv obtained as a result of the transformation, shown in Equation (16). Similarly harmonics of 3’s multiples  also disappear in the transformation process:Finally the effect of harmonics on both the systems is investigated. Let us assume the three phase system has third harmonic in Equation (15). During three to two phase transformation, the third harmonic disappear in the quadrature signals aV, bV, cV are made to unit amplitude and three to two phase transformation is carried out on three phase system which ultimately eliminates the third harmonic components, the three phase system gives better results compared to the two phase system. Therefore considering the above results, in this paper a method different from both the conventional methods to detect the position of linear motor is proposed. The proposed method presented in this work, consists of two sensing units electrically separated 120° instead of 90° to produce av and bv, the two phase voltages of three phase system. To obtain the third voltage cv, three phase balanced condition is applied. The amplitudes are made to unit amplitude references to fulfill the minimum amplitude error condition mentioned in It is found that when the amplitudes of the three phase signal output vc, using the three phase balanced condition. Three phase to two phase transformation is done followed by the arctangent function to get the position information.To test the validity of the proposed method, a MATLAB simulation model of the sensor module is made. The MATLAB simulated data obtained from the first two sensing modules are used to obtain the third voltage The simulation result obtained is compared with a conventional two phase system under the same error conditions as that of the proposed model and it is found that the proposed system gives better position detection results compared to the two phase system under same condition.I flows through a conductor thickness z placed in a magnetic field of flux density B, hall voltage is given as:To check the validity of the simulation results obtained in The structure of the sensor module  and its 1, X2, X3 of silicon steel are attached with the magnet. Prototype of the sensor module is shown in 1 and X2. The Hall sensor used to design the sensor module is A1324 linear Hall Effect sensor manufactured by Allegro Microsystem LLC . If the sensor unit moves parallel to the stator’s alternate tooth slot arrangement, a sinusoidal wave signal is generated, because when the sensor moves over the stator, the reluctance path of the magnetic fluxes from the sensor’s permanent magnet changes. As shown in pτ to produce sine waves of 120° phase difference. In The magnetic sensor unit consists of a PM, made of Nd-Fe-B and three other parts Xx direction become zero at A and B respectively. Thus for two pole pitch displacement of the sensor module over the stator, the flux density distribution becomes sinusoidal as shown in To test the effect of the variation of airgap between the stator and the sensor unit on the output sensor signal, the airgap is varied in 1 mm steps. The change in the peak to peak value of the output voltage signal with the variation of airgap is shown in av and bv of the proposed method, phase shifted by 120°. To achieve the third signal, cv, three phase balanced condition (av + bv + cv = 0 or cv = − (av + bv)) is applied.Three sensor modules are used to produce two sets of signals. The first set of signals is phase shifted by 90° and the second set of signals has a phase shift of 120°. The sensor unit outputs are presented in αv and βv. The FFT analysis of the three phase signals, αv and βv is carried out. FFT analysis shows that the amplitude of the 3rd harmonic component of the three phase signal is 0.0024 V. In three to two phase transformed signals αv and βv, third harmonics are reduced to 0.0019 V and 0.0003 V, respectively, shown in The final three phase signal is shown in Finally to obtain position information an arctangent function is applied to both the conventional two phase system and the proposed system. The position data obtained from both the systems is compared with the reference position data obtained by using a linear scale. The position signals are shown in In this study, we have introduced a novel mover position detection method for linear motors, different from the conventional position detection approaches. The position is obtained by using two magnetic sensor modules mounted parallel to the stator and three phase balanced condition. Unlike the conventional methods, the proposed method does not use any complex compensation algorithm to minimize the error. Unit amplitudes of the sensor signals and three to two phase transformation are used to minimize the errors caused by amplitude difference and harmonics. The validity of the proposed method is checked using MATLAB simulation model and experimental results. The output of the proposed method is compared with the output of the conventional two phase position detection method. Even though the proposed method uses the same number of Hall Effect based magnetic position sensors, it produces better position information compared to the conventional two phase system.


The aim of this study was to examine the relationship between improvements in lip asymmetry at rest and while smiling after orthognathic surgery in patients with skeletal class III malocclusion.t test and correlations between measurements at rest and when smiling by regression analyses.This study included 21 patients with skeletal class III malocclusion and facial asymmetry. We used preoperative and postoperative CT data and photographs to measure the vertical distance of the lips when smiling. The photographs were calibrated based on these distances and the CT image. We compared preoperative and postoperative results with the There were significant correlations between the postoperative changes in canting of the mouth corners at rest, canting of the canines, canting of the first molars, the slope of the line connecting the canines, and the slope of the line connecting first molars. The magnitude of the postoperative lip line improvement while smiling was not significantly correlated with changes in the canting and slopes of the canines, molars, and lip lines at rest.It remains difficult to predict lip line changes while smiling compared with at rest after orthognathic surgery in patients with mandibular prognathism, accompanied by facial asymmetry. Patients with craniofacial asymmetry frequently also have lip line asymmetry . AsymmetTherefore, the present study examined the relationship between improvements in lip asymmetry at rest and when smiling after orthognathic surgery in patients with skeletal class III malocclusion and menton deviation.Our institutional review board approved this retrospective study. The subjects were patients with mandibular prognathism accompanied by facial asymmetry. More specifically, the subjects comprised patients with skeletal class III malocclusion, a menton displaced laterally more than 2 mm, and no maxillary retrusion. All of the patients underwent bimaxillary orthognathic surgery, namely a Le Fort I maxillary osteotomy and mandibular vertical ramus osteotomy. Patients were only included if they finished preoperative orthodontic treatment, underwent orthognathic surgery, had preoperative and postoperative CT data, and had clinical photographs of themselves smiling that were taken after the surgery, and postoperative orthodontic treatments had been concluded. Twenty-one patients met the above criteria and were included.We collected the preoperative and postoperative CT data, and 3D images were reconstructed using SIMPLANT® software ver. 14.0 . Then, we used the constructed 3D images and three surface images to measure error. The errors were measured as follows. First, we set reference planes in the cranial area of the data. Then, we measured each point on the reconstructed mandible and on the surgical simulation and compared their distances. We constructed three reference planes: the Frankfort horizontal (FH), midsagittal, and coronal. The FH plane was used to measure vertical error. The FH plane crossed the center of the orbitale―the infraorbital margins―and the two portions of both external auditory canals. The plane that runs parallel to the FH plane and crossed the center of the lateral canthus was set as the intercanthus horizontal plane. The midsagittal plane was used to measure lateral error and was perpendicular to the FH plane and crossed the nasion and internal occipital crest. Finally, we used the coronal plane to measure anteroposterior error. It ran perpendicular to the FH plane and midsagittal plane and crossed the nasion. The shortest distances from each of these three planes were named the vertical distance, lateral distance, and anteroposterior distance  software. The same program was used to measure the patients’ right and left lateral canthus distances . The preoperative photograph was adjusted based on these distances and the lateral intercanthus distance that was measured on the preoperative CT image Fig. a. At secWe measured the vertical distance of the lips during smiling, which is the shortest distance from the lateral intercanthus line to the mouth corner. The difference between the right and left vertical distances was defined as canting. The angle between the line that connects the left and right mouth corners and the lateral intercanthus line was defined as the slope angle while smiling. We acquired preoperative and postoperative data by editing the preoperative and postoperative smile pictures via the same procedure. We also calculated the magnitude of change after surgery.We randomly selected ten patients from the sample of 21 subjects. Their preoperative pictures of mouths at rest were modified using the same calibrating procedure used for the smiling pictures. The revised pictures were used to measure the vertical distances of the lips at rest. We used the V-Ceph ver. 6.0 (OSSTEM IMPLANT Co.) software to measure the right and left lateral canthus distances of the patients’ lips at rest. Then, we adjusted the lateral intercanthus distance of the photograph to that measured on the preoperative CT data.Using the revised picture, we measured the vertical distance from the line that connects the left and right lateral canthus to the right mouth corner. We also measured the vertical distance from the lateral canthus plane to the right mouth corner on the preoperative CT data. Then, we modified the vertical ratio of the resting picture that was adjusted using the lateral intercanthus distance to match the distance from the intercanthus line to the right mouth corner of the picture and the preoperative CT. After these modifications, the lateral intercanthus distance and distance from the lateral intercanthus line to the central incisors were the same as those measured on the preoperative CT data. Then, using the revised picture, we measured the vertical distance from the lateral intercanthus line to the right mouth corner. We also measured the vertical distance from the intercanthus horizontal plane to the right mouth corner on the CT image and defined the absolute values of this difference in distance as the error of the clinical photographs. One time per patient, one observer measured the distance in the image of the patients.We used the ten randomly selected patients for measuring errors for clinical photo adjustment. To measure the intraoperator error, one observer measured the vertical distance from the intercanthus line to the right mouth corner in these pictures and measured the errors in the reference points during each trial one time per patient.The intraoperative error during CT image measurements was measured using preoperative CT images of the same ten patients. The intraoperative error during CT image measurements was defined as the difference in the distances from the intercanthus horizontal plane to the right mouth corner when repeatedly measured in ten patients.We compared preoperative and postoperative results by Wilcoxon signed-rank test. The correlations among preoperative and postoperative canting of the canines, canting of the molars, slope of the canines, slope of the molars, canting of the lips at rest, and slope of the lips at rest were examined by regression analyses. Similarly, the correlations among preoperative and postoperative canting of the canines, canting of the molars, slope of the canines, slope of the molars, and canting and slope angle of the lips while smiling were analyzed by regression analyses. The statistical significances of the results were verified using the IBM SPSS statistics 21  program. The level of significance was set at 0.05.P = <.001). The lateral displacement of the menton was also reduced from a mean of 4.54 mm before surgery to a mean of 1.50 mm after surgery (P = .001).There were 21 subjects, 11 females and 10 males in this study. The mean age (mean ± standard deviation (SD)) was 22.0 ± 5.0 years. The average period of time from the surgery to the completion of the postoperative orthodontic treatments, photographs, and CT scans (mean ± SD) was 19.0 ± 10.2 months. After the surgery, the mandibular position of the patients was displaced to the posterior and the horizontal distance from the coronal plane to point B was reduced from a mean of 91.22 mm before surgery to a mean of 82.41 mm after surgery (P = .048). The canting of the mouth corners while smiling was increased from 1.09 mm  before surgery to 1.30 mm  after surgery.The mean vertical distances at the left and right first molars before surgery were 56.82 and 56.71 mm, respectively, and they were reduced to 54.06 and 54.54 mm, respectively, after surgery. The mean canting of the canines was 1.06 mm  before surgery and  after surgery. The mean canting of the molar areas was 1.40 mm  before surgery and 1.36 mm  after surgery, but the difference was not significant. The canting of the mouth corners at rest was reduced from 1.54 mm  before surgery to 0.94 mm  after surgery . Similarly, there was also a significant correlation between the magnitudes of the postoperative changes in the canting of the mouth corners at rest and in the canting of the first molars (P = .023). In addition, there was a significant correlation between the extent of the postoperative change in the canting of the mouth corners at rest and the change in the slope of the line that connects both canines (P = .010). Similarly, there was a significant correlation between the magnitude of the postoperative change in the canting of the mouth corners at rest and the change in the slope of the line that connects both first molars (P = .017) . The intraoperator error for the CT data, which was measured by comparing the vertical distance measurements of the mouth corners, was 0.27 ± 0.16 mm (mean ± SD). The error induced by photo adjustment, which was measured by comparing the values of the canting of the lips at rest on the CT and clinical pictures, was 0.63 ± 0.53 mm (mean ± SD).As mentioned in the “A previous study that used soft tissue scanners and CT data reported there was a significant relationship between the degree of vertical positional change of the jaws and that of the lips after orthognathic surgery in patients with mandibular prognathism and facial asymmetry . SimilarThe results of the present study show that orthognathic surgery results in different degrees of improvement of lip asymmetry while smiling and at rest. Benson and Laskin reported that lip canting while smiling may be different from the occlusal level in subjects without clinical facial asymmetry . In addiThe present study employed clinical photographs to assess lip line canting while smiling, which is one of the limitations. Smiling is not a static phenomenon. Predictability may be unclear in assessing the smile, as the precise anatomic location of many of their points could be significantly altered on the basis of muscle tone related to smiling and factors such as response to light (photographic flash), time of day, etc. We calibrated the length of the clinical photos based on our CT data by adjusting the distance ratio of the photo in accordance with the CT data. This process may have produced errors. The absolute value of the mean error that occurred during the calibrating process was 0.63 mm. There also may have been an error while measuring the lips during smiling from clinical photographs. Also, calibration method adjusted for the degree of relative magnification but would not necessarily adjust for dynamic changes related to muscle tone.We conducted analysis on a mixture of images; one was 3D data and the others were 2D photographs. Measuring lip smile from 2D photographs is inaccurate and does not represent the 3D nature of this facial expression. Standardization is difficult in defining for facial expression before and after surgery; this may be essential to provide the corrected measurements. Canting of the lip corners will depend on the magnitude and extent of the smile; this has to be standardized, and evidence should be provided regarding the reproducibility of this facial expression. The authors agree that this may be a crucial factor in this study; without standardization of facial expressions, it would be almost impossible to measure dynamic soft tissue changes and relate them to the performed surgery.To overcome these limitations of using clinical photographs for measurements, researchers may use facial scanners to acquire 3D images of the facial soft tissues or use two cameras to form a 3D image of the face , 4. ThatThis study only involved the cases of patients with mandibular prognathism accompanied by facial asymmetry. For patients with maxillary or mandibular hypoplasia, orthognathic surgeries may significantly improve the magnitude of their facial expressions , 10, 11.The mean value of lip canting was less than 2 mm, which was another limitation of this study. The mean lip canting value was also reduced from 1.54 mm before surgery to 0.94 mm after surgery. In addition, there were no large differences in the lip slopes before and after surgery (0.70° before surgery and 0.56° after surgery) and the slopes were also less than 1°, which was another limitation of this study. The threshold for the recognition of an occlusal cant was suggested to be 4° in a 2D frontal plane study , 14. MosThe mean intraoperator error for the CT images was 0.27 mm, which was larger than that for the clinical pictures (0.17 mm). This is presumed to be due to a change of the horizontal plane, which was induced by an accumulation of intraoperator errors while setting anatomical structures required for the reference horizontal planes in the 3D CT images. The results of this study indicated that the magnitudes of the postoperative changes in the canting and the slope of the mouth corners at rest were significantly correlated with the changes in the canting and slopes of the canines and the molars. However, the magnitude of the postoperative improvement of the lip lines when smiling was not significantly correlated with the changes in the canting and slopes of the canines, molars, and lip lines at rest. Hence, it is still difficult to predict the changes in lip lines while smiling after an orthognathic surgery in patients with mandibular prognathism accompanied by facial asymmetry.In conclusion, the magnitude of the postoperative lip line improvement while smiling was not significantly correlated with changes in the canting and slopes of the canines, molars, and lip lines at rest. It remains difficult to predict lip line changes while smiling after orthognathic surgery in patients with mandibular prognathism, accompanied by facial asymmetry.Ethical approval was provided by the Institutional Review Board of the NHIS Ilsan Hospital.


MS-2 bacteriophage in each home. After 8 h, the hands of each family member (10 fingers) and 20 frequently touched fomites were sampled to determine baseline contamination without intervention. Within 8 h, MS-2 was detected on all of the family member’s hands and most of the fomites. The intervention consisted of providing the families in all selected homes with bottles of an ABHS, which were placed in the kitchen, bathrooms, and nurseries. Smaller individual bottles were provided for each family member greater than 12 years old to place in purses, pockets, backpacks, etc. The families were instructed to use the ABHS one time or three times during the day. For one and three uses, a statistically significant reduction of virus on un-inoculated and inoculated hands of ~99 % occurred within 8 h. Similar reductions occurred on fomites throughout the households (97–99 %). These results demonstrate that the use of an ABHS can significantly reduce transfer of a virus to the hands, and to the commonly touched surfaces within the household.The objectives of this study were to determine the movement of a virus throughout a household and the impact of an alcohol-based hand sanitizer (ABHS) on reducing the movement and exposure of the virus to household members. Bacterial virus MS-2 was used as the surrogate for human enteric and respiratory viruses. Seven households with families having at least two children in the age range of 2–18 living in the home were used in this study. The hands of one adult family member were contaminated with 1 × 10 Good hand hygiene involving hand washing and/or the use of alcohol-based hand sanitizers (ABHS) has been shown to reduce the risk of infection from both respiratory and enteric viruses  to rhinovirus (common cold), norovirus (most common cause of adult gastroenteritis), and many other enteric viruses. For these reasons, it was selected as a surrogate.The objectives of this study were to study the movement of a virus throughout a household and the impact of an intervention with ABHS on reducing the movement and exposure of the virus to household members and fomites. Bacteriophage MS-2 has similar shape and size to many human disease-causing enteric and respiratory viruses likely to be spread in a home setting. Bacteriophage MS-2 infects the bacteria E. coli ATCC 15597 as the host. The E. coli was grown overnight and transferred to Tryptic Soy Broth (TSB)  in a shaking water bath, and one ml of it was transferred to a new sterile broth for 3 h at 37 °C in a shaking water bath to reach the log growth phase. The virus was produced by collecting it from an infected lawn of E. coli by addition of 6 ml of TSB and then removing it with a pipette after 2 h. The suspension was then centrifuged at low speed to remove bacterial debris filtered through a 0.45-µm pore size membrane filter and finally stored at 4 °C until needed for further use.Bacteriophage MS-2 (ATCC 15597-B1) was assayed by the double-layer agar technique with 8 MS-2 bacteriophage. After 8 h, the hands of each family member (10 fingers) and selected high-touch fomites shown in Table To assess the spread of the MS-2 before the interventions, seven households with families having at least two children in the age range of 2–18 living in the home were selected randomly from a pool of available houses that were recruited. Basic demographic data for all households such as number of people living in the home, ages, sex, number and types of pets were obtained for all houses. The hands of one adult family member in each home were contaminated with 1 × 10In all phases, virus was added to the hands of one adult in the household. All individuals received one mL of a physiological saline suspension onto the palm of their hand; however, the virus was only applied to the hands of one adult member of the household. This was done so the household members did not know whose hand was inoculated. Each individual was then asked to gently rub the palm of one hand together with the other hand and move the hands in an upward motion so that the fingertips of one hand slide onto the palm of the opposite hand to disperse the virus onto the fingertips. The contamination of the adult hand occurred at approximately 8:30 AM in the morning. The family was asked to stay at home during the day and go about normal daily activities in between the sampling times. All studies were done on weekend days when families spent most of the day at home. During the study, family members were not allowed to use any other antimicrobial hand products including wipes, sanitizers, and disinfecting cleansers . All families were asked to practice their normal hand washing routine using soap and water during the course of this study. The study consisted of a baseline phase, and then two intervention phases.Families in all the selected houses were given 354 ml bottles of alcohol-based hand sanitizer  to place in the kitchen, bathrooms, and nurseries (3–5 bottles depending on the household size). This product has an active ingredient of 70 % ethanol. Individual bottles (56 ml) for each family member more than 12 years old were provided to place in purses, pockets, backpacks, etc. Instructions on when and how to use sanitizers were given to the families. They were instructed to use the hand sanitizer three times during the day (8 h) in the first intervention phase, and once per day in the second intervention phase  of each family member and fomites were sampled. The fomites sampled in each household are shown in Table 2 of each fomite was sampled.The hands of the same adult family member in each home were contaminated with 1 × 10Permission for conduct of the study was obtained from the University of Arizona’s Office for Human Subjects Research prior to the study.t statistic  was constructed for the log base 10 reductions with upper and lower limits using student Kabacoff .p < 0.0005) for Phase 1  group. The only sites that were not contaminated in the control (baseline) period were toilet handles in two houses and bedroom light switches in three houses. The highest average virus concentrations for fomites were found in the kitchen and living room areas, as well as on cell phones. Reduction in virus on hands (inoculated and non-inoculated) and fomites with use of the ABHS was statistically significant  and reductions may have been greater if a higher virus concentration had been used to contaminate the hand. This may also explain why the reduction in virus for one use per day was similar to three uses per day; if one use per day lowers the virus concentration to or just above the limit of detection, then the study is unable to detect a greater difference. Also the study was based on a single contamination event which is more representative of a person that contaminated their hands outside the home, and is not sick. It is not representative of the contamination that would occur if there was a sick person in the household, as they would be recontaminating the household continuously. Therefore, there would be a higher overall viral concentration in the household, and it is likely that a difference between one use and three uses per day could be detected. Future studies should evaluate the impact of ABHS in reducing viral concentration on hands and fomites where multiple contamination events occur.8 MS-2 was added to the hands to ensure enough viruses to trace its movement through the household. Although this may be high, this level of virus on the hands may not be unexpected. Norovirus, adenovirus, and rotavirus occur in concentrations up to 1011 to 1012 per g; thus, as little as 0.001–0.0001 g of feces could contain 108 of these viruses (Haas et al. A concentration of 10The results of this study demonstrate that the use of an ABHS can greatly reduce the exposure of family members to viruses in the household. The information generated in this study will be useful to validate models for the spread of viruses within households.


The childcare environment offers a wide array of developmental opportunities for children. Providing children with a feeling of security to explore this environment is one of the most fundamental goals of childcare.In the current study the effectiveness of Video-feedback Intervention to promote Positive Parenting-Child Care (VIPP-CC) was tested on children’s wellbeing in home-based childcare in a randomized controlled trial.Forty-seven children and their caregivers were randomly assigned to the intervention group or control group. Children’s wellbeing, caregiver sensitivity, and global childcare quality were observed during a pretest and a posttest.We did not find an overall intervention effect on child wellbeing, but a significant interaction effect with months spent with a trusted caregiver was present. Children who were less familiar with the caregiver showed an increase in wellbeing scores in both the intervention and control group, but for the group of children who were more familiar with the caregiver, wellbeing increased only in the intervention group.Although there was no overall effect of the VIPP-CC on children’s wellbeing, the VIPP-CC seems effective in children who have been cared for by the same trusted caregiver for a longer period of time. A feeling of wellbeing is a necessary condition for children to effectively explore their environment and thus encounter developmental opportunities. The childcare environment offers a wide array of such developmental opportunities. Providing children with a feeling of security to explore this environment is one of the most fundamental goals of childcare. The current study matches this goal by focusing on a video-feedback intervention aimed at improving childcare quality and ultimately child wellbeing in home-based childcare.A large number of children are attending childcare nowadays, and home-based childcare has become a commonly used type of care. The NICHD Early Child Care Research Network reported that 24 % of the children in their sample attended home-based childcare at entry in childcare , caregiver interaction skills , and, to a lesser extent, child behavior . Thus, the effect on the child level regarding social-emotional behavior was small, yet significant. The authors conclude that there is a lack of intervention studies using solid designs with sufficient power focusing on social-emotional outcomes in children. Although these studies did not measure ‘wellbeing’ per se, wellbeing is frequently used as an overarching term all of these domains  and infant attachment insecurity (d = 0.20). Interventions with video-feedback were more effective (d = 0.44) than interventions without this method (d = 0.31). Interventions with fewer than five sessions were as effective (d = 0.42) as interventions with 5–16 sessions (d = 0.38), but interventions with more than 16 sessions were less effective (d = 0.21) than interventions with a smaller number of sessions. Based on this meta-analysis, a short-term, behaviorally focused intervention program was developed: the Video-feedback Intervention to promote Positive Parenting and Sensitive Discipline . In addition, although the expected increase in observed sensitivity was not found (d = 0.21), caregivers in the intervention group showed a more positive attitude towards sensitive caregiving and limit setting after the intervention than caregivers in the control group (d = 0.69).The current study uses the same dataset, but also includes child variables in the analyses. As suggested in the meta-analysis by Werner et al. (The adaptation of the VIPP-SD for home-based childcare—the VIPP-ChildCare (VIPP-CC)—was described by Groeneveld et al. . As the r et al. , there rFamiliarity with a caregiver may be an important moderator of this association. In the reported study, we will focus on the amount of months a child has spent with this specific trusted caregiver. It should be noted that the number of weekly hours in childcare, which in the Netherlands is usually between 16 and 24 h, is not taken into account. Thus far, previous studies did not report on the impact of the months spent with a trusted caregiver on intervention effects. If children attend childcare for a longer period of time, and are in the care of the same caregiver for a longer period of time, they may feel more at ease, and thus be more receptive to interventions. In the current study, we will focus on the effect of a video-feedback intervention on the wellbeing of children, taking months spent with the trusted caregiver into account.In the current paper, we will focus on the effect of the VIPP-CC on the wellbeing of the children in the childcare setting. We will also examine whether the intervention effect is moderated by childcare quality and months children spent with their trusted caregiver. We expect the intervention program to be effective in enhancing children’s wellbeing during childcare, especially for children in higher quality settings. In addition, if children, have been in the care of the same caregiver for a longer period of time, they may feel more at ease in childcare and thus be more receptive to the intervention. Following this line of reasoning, we expect children in the intervention group to show a larger increase in wellbeing when they have been in the care of their caregiver for a longer period of time.Caregivers and children in this randomized, controlled study were recruited from 23 home-based childcare organizations in the western region of the Netherlands from both urban and rural areas. Inclusion criteria were: 1) caregivers took care of at least two children under the age of four, (2) caregivers were not biologically related to these children, and (3) caregiving took place in the caregiver’s own home. Invitation letters were sent to approximately 1000 caregivers. In total 157 caregivers refused to participate: at least 20 % refused because they did not meet the inclusion criteria described in the invitation letter. Other frequently mentioned reasons were that caregivers felt uncomfortable with video recordings or were too busy. Registration for the study was closed after agreement to participate was obtained from 120 caregivers. The flow chart . As a result, 66 caregivers were selected for our study. Based on our pilot study we anticipated a refusal rate of about 25 % . Therefore, we included an extra group of caregivers to avoid selective attrition. The 66 caregivers were randomly assigned to either the intervention group (n = 25), the control group (n = 25), or the extra group (n = 16). Because of availability of interveners, the number of participants in the intervention group and the control group was restricted to 25. Following randomization procedures (random numbers), participants were assigned to one of these three groups. The 50 caregivers in the intervention group and the control group received a letter revealing whether they were assigned to the ‘training’ (intervention) or the ‘telephone’ (control) group. Eight caregivers in the intervention group and four caregivers in the control group refused to participate after receiving this letter. Caregivers from the extra group were randomly assigned to the intervention (n = 8) or the control group (n = 4). Of these caregivers, again four caregivers declined from the study, and caregivers from the extra group were again randomly assigned to the intervention (n = 3) or the control group (n = 1). Of this group, only one caregiver (in the intervention group) discontinued, because all the children she was taking care of had left. The caregivers who declined from the study (n = 17) did not differ on caregiver sensitivity from caregivers who remained in the study . In addition, caregivers who declined from the intervention group (n = 12) did not differ on caregiver sensitivity from caregivers who declined from the control group (n = 5) . The allocation phase resulted in two groups of caregivers: 24 caregivers in the intervention group and 25 caregivers in the control group.In the next step, we excluded caregivers who scored high on caregiver sensitivity  of education after primary school entrance, and mothers of children in control group had on average 13.50 years of education after age 6 . For fathers, no differences in level of education between the two types of care were present either . The mean age of the mothers did not differ between the two groups , neither did the mean age of fathers . The family structure across the two groups of children was also similar: All children were raised in two-parent families. The nationality of almost all parents was Dutch . As described in Groeneveld et al. All 49 caregivers received a pretest home visit, followed by the intervention or control period. The posttest took place in May–July 2009, after which the trial was ended. One caregiver in the control group did not complete the posttest because she cancelled all appointments. In addition, one of the target children in the intervention group left childcare, because his parents moved to another region of the Netherlands. Scores on all measures  during baseline and pretest, did not differ from the other caregivers’ and children’s mean scores. The final sample included 47 caregiver–child pairs: 23 pairs in the intervention group and 24 pairs in the control group. Demographic information on the children is summarized in Table All procedures were carried out with the adequate understanding and written informed consent of caregivers and parents. Ethical approval for this study was provided by the Leiden Institute of Education and Child Studies. There was no conflict of interest for any of the authors. The first author takes responsibility for the integrity and the accuracy of the data analysis.During baseline, each setting was visited by an observer who spent a morning in the childcare homes to administer the Caregiver Interaction Scale . Again, the IT-CC-HOME was administered and unstructured and structured play episodes were videotaped. All videotaped episodes were rated afterwards on children’s wellbeing and caregiver sensitivity by coders who were unaware of the experimental condition and who met the criteria to reliably assess these scales. To obtain independency in ratings, observers who visited the childcare setting did not rate children’s wellbeing or caregivers’ sensitivity in this specific setting, and coders who rated the pretest child fragments did not rate caregiver fragments or the fragments from the posttest, and vice versa. For the same reason, observers visited a specific childcare setting only once.Caregivers in the intervention group received six home visits and, parallel in timing, caregivers in the control group received six telephone calls. Post-test visits took place approximately 6 months after baseline  are (S1) exploration versus attachment behavior: showing the difference between the child’s contact seeking behavior and play and explaining the differential responses needed from the caregiver, (S2) ‘speaking for the child’: promoting the accurate perception of children’s signals by verbalizing their facial expressions and nonverbal cues. For discipline (D), the themes for these two sessions are (D1) inductive discipline and distraction: recommending induction and distraction as non-coercive responses to difficult child behavior and (D2) positive reinforcement: praising the child for positive behavior and ignoring negative attention seeking. The second phase focuses at improving caregiver behavior by showing at what moments strategies work. The sensitivity themes of the two sessions in this phase focus on (S3) the sensitivity chain: explaining the relevance of prompt and adequate responding to the child’s signals, and (S4) sharing emotions: showing and encouraging parents’ affective attunement to the emotions of their child. For discipline, these two sessions focus on (D3) the use of a sensitive time-out: a short break to calm down and (D4) empathy: showing understanding for the child. The third phase consists of two booster sessions in which all feedback and information is reviewed. At the end of the intervention program, caregivers receive a brochure with information on key issues discussed during the home visits . In the VIPP-SD, interveners first videotaped structured play sessions  and then subsequently discussed the videotaped episodes from the last visit (for about an hour) based on prepared comments (script). In the VIPP-CC, interveners first videotaped the structured play sessions and then left the home, allowing caregivers and children to have a quiet lunch. After the caregivers put (some of) the children into bed, interveners returned and discussed the videotaped episodes from the last visit. Furthermore, the ‘speaking for the child’ was not only directed to one child at a time, but also to the entire group of children (‘speaking for the children’), emphasizing caregivers’ attention for the signals of all children present. In addition, the toys that were used during structured play situations were adapted for a group setting, for example by using a big box of Duplo bricks and large story books.n = 7) had comparable backgrounds in terms of education. They were all graduate students at the Centre of Child and Family Studies, who were first trained on the VIPP-SD during a full-time week workshop by one of the VIPP-SD experts from the Centre of Child and Family Studies, including home assignments which were provided with feedback from the VIPP-SD expert. After this training, interveners received further training on the adapted VIPP-CC. During the intervention period, four feedback sessions were held, in which video-taped structured play situations and scripts were discussed, as well as how to build and obtain a professional relationship with the caregiver. We found no intervener effects.Interveners  to 4 (very applicable). In a Dutch study  were videotaped to code children’s wellbeing. Coding of videotaped episodes took place by means of the Laevers Wellbeing Scale (2003) that was adapted and validated by the Dutch Consortium for Child Care Research for infants and toddlers in childcare  was .73 (range from .70 to .78). Internal consistency of the intervals was .86.The IT-CC-HOME  and two structured play episodes of each 5 min were videotaped to code caregiver sensitivity. Both structured situations consisted of 10 min play with Duplo bricks or a car rollercoaster. Caregivers were asked to play with the children as they would normally do. Coding of videotaped episodes took place by means of a scale developed and validated by the Dutch Consortium for Child Care Research  were included as covariates into the repeated measures ANOVA to test whether childcare quality influenced the change in wellbeing over time. Missing data were present at item level only: these missing item scores were filled in with the person mean on the other items from that particular scale. To test the effect of months spent with the caregiver, we used a residual variable representing the number of months children attended this particular childcare setting controlled for the age of the children. Seven children had missing data on ‘months spent with the caregiver’. These missing values were imputed using multiple imputation with predictive mean matching in SPSS. Analysis results were pooled using the standard procedure in SPSS, which is based on the rules described by Rubin .M = 4.5. SD = 0.77; control group M = 4.50, SD = 0.42), during the posttest wellbeing ranged from 3.38 to 5.5 in the intervention group  and from 4.08 to 5.67 in the control group . No significant differences were present between the intervention group and the control group during both pre- and posttest (without taking any covariates into account).Descriptive statistics and correlations of the baseline, pretest and posttest measures are shown in Tables r = .41, p < .05). In addition, global quality during baseline was positively associated with caregiver sensitivity during the posttest , and global quality during the posttest was positively associated with caregiver sensitivity during the pretest . In the control group, global quality was positively associated during baseline and posttest . Also, observed sensitivity during pretest and posttest were positively associated .For the intervention group, children’s wellbeing in the posttest was positively associated with caregiver sensitivity in the posttest , and global childcare quality was higher when children spent a longer period of time with that specific caregiver .For months spent with the caregiver, again no difference was present between the intervention group and the control group. Prior to the intervention, there were two significant associations between months spent with the caregiver and quality of care: caregivers were more sensitive to children who were in their care for a shorter period of time  = 7.75, p < .01, ηp2 = .15], indicating an overall increase in children’s wellbeing from the pretest to the posttest in both the intervention group and the control group. No significant main effect was present for group . In addition, no significant interaction effect was found .To test whether the wellbeing of the children improved in the intervention group as compared to the control group, repeated measures ANOVA’s were conducted. A main effect was present for time .To test whether caregiver sensitivity and/or global quality moderated the change in wellbeing over time, the quality measures were added to the repeated measures ANOVA and the interactions between quality and time were investigated. We found no significant interaction effects . In the control condition, these groups were similar .To illustrate the interaction between the intervention and time spent with the trusted caregiver, we dichotomized time in childcare by using a median-split procedure . Four groups are presented in Fig. ηp2 = 0.76; Groeneveld et al. Previous studies in families have shown the effectiveness of the VIPP-SD in changing children’s behavior, especially in decreasing children’s externalizing behavior problems in high risk samples ; Groeneveld et al. The fact that we did not find a stronger increase in wellbeing in the total intervention group compared to the control group may be explained by the timing of our posttest. Effects of interventions may lie dormant directly after the intervention (sleeper effect), but may become noticeable later on. In the current study, the posttest took place 2 weeks after the last intervention session. Although global childcare quality did improve in the intervention group . The current study attempts to stay close to such “at risk” situations by focusing on caregivers scoring relatively low on sensitivity (CIS score < 3.0). However, there might have been a ceiling effect, since the average wellbeing and sensitivity score of the included children and caregivers was still quite high, compared to previous Dutch childcare studies . This difference in global childcare quality might be due to caregivers being more able to adjust the childcare environment  to children they are more familiar with. In addition, an interaction effect with (the intervention or control) group was present. Wellbeing scores of children who visited the caregiver for a shorter period of time increased from pretest to posttest in both the intervention and the control group, but a different pattern of wellbeing scores was present in the group of children who visited the caregiver for a longer period of time. While in the control group these children showed stable scores in wellbeing from pretest to posttest, children in the intervention group showed an increase in wellbeing over time. Thus, the VIPP-CC seems most effective in children who have been cared for by a caregiver for a longer period of time. A possible explanation is that the familiarity of the childcare setting is the first step in order to profit from the intervention. The childcare context is different from the children’s home situation, with another adult taking care of them in a new environment, with an unfamiliar group of children, and without the presence of their parents. A change in childcare quality might not have a large impact on the wellbeing of these children, since they are still trying to get used to the childcare environment with an unfamiliar caregiver and unfamiliar children. When children are accustomed to the childcare environment, subtle changes in childcare quality of this environment might have more effect on their wellbeing compared to their peers who are not accustomed to the childcare environment. Thus, our results indicate that the VIPP-CC seems most effective when it is implemented in childcare settings where children are accustomed to the childcare environment. It should be noted however that this interaction effect needs to be confirmed in larger samples, and preferably in childcare centers as well.The sample size of this study is relatively small, which may have resulted in a lack of statistical power to detect moderation effects. As a result, we were limited in the number of moderators we could include in the study. We selected one target child per caregiver, which reduced our sample size, but had the advantage that all caregivers and children in our sample were from different childcare settings. Since the children were randomly selected prior to the intervention, we do not expect that we only selected children who would have shown more or less improvement than the other children in that setting. Besides sample size, another limitation of the study is the relatively high level of childcare quality and wellbeing scores prior to the intervention. Although caregivers with very high scores on caregiver sensitivity were excluded, scores on childcare quality and children’s wellbeing were still relatively high. A ceiling effect is possible and might have decreased the intervention effects.Furthermore, not all caregivers responded positively to our invitation to participate in our research, which might have resulted in a selection bias. In addition, 17 caregivers (26 %) dropped out after the selection phase. However, attrition seems unavoidable in intervention studies in childcare, even during the intervention phase. For example in the Family-to-Family study, 27 % of the caregivers dropped out during the intervention phase (Kontos et al. In addition, the non-inclusion of a follow-up is a limitation of this study. We do not know whether children’s wellbeing in the intervention will improve in the long run, nor do we know whether the reported interaction effect will remain over time.The current study revealed that children’s wellbeing scores in home-based childcare increase over time. For children who have been cared for by the same trusted caregiver for a longer period of time, the VIPP-CC was effective in enhancing their wellbeing.