Streptococcus pneumoniae was used, identifying the presence of any one of 91 known pneumococcal serotypes from DNA extracts. This microarray incorporated oligonucleotide probes for all known capsular polysaccharide synthesis genes and required a statistical analysis of the microarray intensity data to determine which serotype, or combination of serotypes, were present within a sample based on the combination of genes detected.Microarrays offer great potential as a platform for molecular diagnostics, testing clinical samples for the presence of numerous biomarkers in highly multiplexed assays. In this study applied to infectious diseases, data from a microarray designed for molecular serotyping of We propose an empirical Bayesian model for calculating the probabilities of combinations of serotypes from the microarray data. The model takes into consideration the dependencies between serotypes, induced by genes they have in common, and by homologous genes which, although not identical, are similar to each other in sequence. For serotypes which are very similar in capsular gene composition, extra probes are included on the microarray, providing additional information which is integrated into the Bayesian model. For each serotype combination with high probability, a second model, a Bayesian random effects model is applied to determine the relative abundance of each serotype.S. pneumoniae that were tested as individual samples could be uniquely determined by the Bayesian model. The model also enabled the presence of combinations of serotypes within samples to be determined. Serotypes with very low abundance within a combination of serotypes can be detected (down to 2% abundance in this study). As well as detecting the presence of serotype combinations, an approximate measure of the percentage abundance of the serotypes within the combination can be obtained.To assess the accuracy of the proposed analysis we applied our methods to experimental data from samples containing individual serotypes and samples containing combinations of serotypes with known levels of abundance. All but two of the known serotypes of  Microarrays are an experimental method for detecting the presence or absence of multiple genes within a sample simultaneously, through specific binding to an array of high-density probes. They therefore have a diagnostic potential in a number of areas including that of infectious diseases. A microarray containing probes for genes specific to different strains of an organism can detect the presence of a particular strain of the organism in a clinical sample according to which of the probes have an elevated signal. Diagnostic testing by microarray is potentially quicker, easier and more reliable than established tests -3. It alStreptococcus pneumoniae was designed to detect 91 known serotypes of the pneumococcus from DNA extracts [S. pneumoniae. A key feature of molecular serotyping by microarray, spurring interest in the method, is that rapid detection of multiple serotypes in a clinical sample should be feasible. In addition it should be possible to quantify the relative abundance of each of the serotypes in the sample. Achieving these two goals with established serotyping methods is either prohibitively time consuming or simply not possible. Here we propose a statistical analysis of the S. pneumoniae microarray data that achieves both these objectives, identifying both the serotype(s) and their relative abundance in samples.A microarray for molecular serotyping of the bacterium extracts . ClinicaStreptococcus pneumoniae molecular serotyping microarray was designed with multiple probes representing all the known capsular polysaccharide synthesis genes. In the rest of this paper we refer to these genes as cps genes and these genes' probes as the CPS probes. The cps genes encode the proteins and enzymes that biosynthesise and assemble the capsular polysaccharide. Serotyping was classically established through cross-reactivity with typing antisera which discriminate each serotype due to structural differences in the capsular polysaccharide. The serotype is relevant because the capsular polysaccharide represents the interface between bacterium and host and so is associated with immunity and invasive disease and forms the basis of polyvalent vaccines currently available. Each serotype of the pneumococcus contains a small subset of the cps genes, ranging in number from 1 to 22 [cps genes present.The  1 to 22 -7, whichcps genes have been sequenced for all 91 serotypes. Most of the serotypes are not fully sequenced. The design of probes for the array is therefore essentially limited to these genes. However, a number of serotypes may have very similar or even identical combinations of cps genes present. Therefore additional probes on the microarray test for more subtle genetic differences between key cps genes of such serotypes. In the rest of this paper we refer to these additional probes as STIDs. One problem that the statistical analysis needed to address was the integration of the CPS probe data and the STIDs probe data.For this reason the The technique presents several further analysis problems. Fluorescent intensity signals from microarray probes for genes indicate gene abundance only indirectly. Such signals are disturbed by a variety of random factors which are difficult to control: from variation in the DNA extraction to variation in the binding of the DNA to its oligonucleotide probe. Concerning the identification of genes, it is sometimes difficult to design probes which are entirely specific to a particular gene. Due to gene homology and the overall similarity of their DNA sequences, a probe for one gene may bind to the DNA from a different gene (cross-hybridisation). In addition, the genomic DNA of the organisms of interest can be contaminated by DNA from the host and from other commensal or pathogenic organisms.cps genes. Then, likelihoods of serotype combinations depending on gene binding and incorporating cross-hybridisation effects are described. Further, likelihoods for serotypes depending on log intensities of STID probes are provided. Finally, all these likelihoods are put together to give a likelihood of serotype combinations depending on log intensities from CPS probes and STID probes. Combined with a prior on serotype combinations this allows us to infer a posterior probability for serotype combinations, apart from a normalising constant. Some of the hyperparameters of the model are estimated in an empirical Bayes fashion from the microarray data. Since there are exponentially many combinations of serotypes, we use a heuristic to limit the number of combinations to a subset of serotypes and serotype combinations with a potential for high probabilities.In the following we develop an empirical Bayesian statistical model for calculating the probabilities of serotype combinations based on the data from the serotyping microarrays. We first set up likelihoods for gene binding depending on microarray log intensities for The second objective of the analysis is to quantify the relative abundance of the serotypes in the sample. So in the final part of the methods section we describe a Bayesian random effects model for estimating abundances of serotypes for a fixed combination of serotypes.S. pneumoniae. We refer to these 91 microarrays as reference arrays. In the first assessment of the method the task was to detect the single serotype present in the sample when applied to the 91 reference arrays. Then, in order to assess the capability of the method to detect combinations of more than one serotype, four additional sets of microarray data were produced using a combination of three or five serotypes in known abundance in a sample. The latter microarrays, to which we refer as spike-in experiments, also allow us to assess the accuracy of the Bayesian random effects model in predicting abundances of serotypes.In order to assess the accuracy of our experimental and statistical approach, we analysed microarray data from samples of the 91 known serotypes of the bacterium Streptococcus pneumoniae microarray and the datasets used in this article. In the second part we develop a probabilistic model for calculating the likelihood of a combination of serotypes given the binding intensities measured for CPS probes and STID probes on a microarray. In the third part of the methods we describe a Bayesian random effects model for estimating the abundance of each serotype in a combination.The first part of the methods section describes the data; the μGS SP-CPSv1.1.0 microarray [The Bcroarray  is a cuscroarray , printedThe microarray contains several thousand oligonu-cleotide probes designed to detect a number of different entities:cps genes. On average there are 10 probes per gene. These probes are used for serotyping the sample.1. It contains probes, referred to here as CPS probes, for 432 cps genes alone.2. It contains probes, referred to here as STID probes, designed to identify serotypes that are too closely related to be resolved by the Streptococcus pneumoniae from two sequenced strains of the bacterium (SpTIGR4 and R6), 6824 probes in total, as well as probes for antibiotic resistance genes and for other pathogens commonly found in nasopharyngeal swabs.3. There are further probes on the microarray for the entire genome of S. pneumoniae genome is used to derive priors for the Bayes calculations in the analysis.The serotype analysis only uses the first two types of probes directly, the CPS probes and the STID probes, for calculating the probabilities of combinations of serotypes. Some of the other probes are used indirectly, in that the median of the log intensities of the 6824 probes for the entire S. pneumoniae SpTIGR4+R6 genome is also marked on the figure, as a horizontal dotted line.Figure S. pneumoniae only contains a small subset of the 432 cps genes. In Figure cps genes found in the serotype being tested by this example microarray experiment are marked in black. Some of the cps genes not found in this serotype have elevated intensities. This reflects cross-hybridization of probes; in some cases it is difficult to design probes which are entirely specific to a particular gene, so probes for one gene may bind to the DNA from a different gene.Any particular serotype of S. pneumoniae that have been identified to date, the subsets of cps genes that they contain are known [cps gene composition for a selection of nine of the 91 known serotypes are shown in table cps genes present in a serotype varies from as few as 1 to as many as 22, with an average of 13. In general any two serotypes will have some cps genes in common. And some serotypes may have very similar sets of characteristic cps genes, which makes differentiating between them more difficult.For the 91 serotypes of re known ,9. As ancps genes found in the five serotypes are shown in the figure for clarity. It can be seen that some of the cps genes are found in two or more of the serotypes contained in this sample. One gene  is found in all five serotypes. The effect of cross-hybridisation can also be seen in Figure In practice a clinical sample may contain more than one serotype. Figure S. pneumoniae molecular serotyping microarray is that eighteen sets of closely related serotypes have identical, or nearly identical, sets of cps genes. An example can be seen in table A further complexity in the design of the Whilst the STIDs are designed to discriminate specific pairs of serotypes, in some cases further serotypes, closely related to the pair in question, will also elevate the intensities of the STID probes. This is because in the region of the genome being targeted by the STID probes, they have identical, or nearly identical sequences, as one or other of the pair of serotypes in question. Hence in practice the STID tests are more complex than indicated in the first column of table We used two different experimental datasets in order to validate the probabilistic model described in this article:Reference Arrays: 91 microarrays each testing a sample containing a single serotype.1. Spike-in Experiments: four arrays with samples of more than one serotype. The composition of the combinations are given in table 2. s serotypes is indicated by a binary random variable j S∈ {0,1}, 1≤ j ≤ s. Where s is the number of known serotypes, currently 91. We combine the variables in a binary vector S = . Depending on the context, S will also denote the set of indices of present serotypes. Similarly, whether any gene i of the n genes binds successfully to its CPS probes is indicated by binary random variables iG, 1≤ i ≤ n. Where n is the number of cps genes, currently 432. G denotes the binary vector as well as the set of indices of binding genes. Each serotype j is associated with a subset of cps genes known in advance to characterize this particular serotype  denotes the data sets for all the cps genes on the microarray. This part describes the likelihood of gene i binding depending on its probes iy.1. Likelihood of a serotype combination depending on gene binding. Each serotype is defined by a characteristic subset of cps genes. The subsets of cps genes of different serotypes might partly be identical. In addition genes occurring in the characteristic subsets of genes of two different serotypes may be very similar (homologous) to each other, resulting in cross-hybridisation. These dependencies between serotypes need to be taken into account. This part describes the likelihood of a serotype combination S depending on genes binding and the grouping of genes according to homology.2. Likelihood of a serotype combination depending on STID probes. In order to help with the differentiation between serotypes with identical or very similar sets of cps genes, additional probes are added to the microarrays, the STID probes. Each set ld, 1 ≤ l ≤ L, of STID probes is designed to differentiate between two serotypes . The vector d =  denotes all the STID data from a microarray experiment. This part describes the likelihood of a serotype combination S depending on STID probes d.3. P for a serotype combination S and data y, d. This likelihood can be evaluated for any combination S of the 91 serotypes. Since this is impractical for all 291 possible combinations, we resort to using a heuristic to select a subset of combinations of serotypes. We also suggest a prior P(S) in this section.These three likelihoods are explained in the following three sections. The fourth section, combines the above likelihoods into P(S) and likelihood P for S allow us to calculated the posterior P apart from a normalising constantThe prior cps gene i is represented by a set of about ten CPS probes with log intensities i ris the number of probes on the array for gene i. Assume the true log intensity value for binding of a gene i is iμ, with i G= 1, that is, binding is successful, then i μ>m, where m is the log intensity of the background signal due to unspecific binding. If i G= 0, that is, binding is unsuccessful, then i μ= m. Since we have little information about iμ, m, and P(i y| i G= 0) and P(i y| i G= 1) as follows.Each In general, visual inspection of distributions of log intensities suggests that assumptions of Gaussian distributions on the above parameters might not oversimplify matters too much  is the prior mean for the log intensity signal of the probes when a gene binds, and κ1 is a prior scaling factor for the variance.3. i G= 0 we obtain the likelihoodFor p1 κ1, ν0, ρ0) is a multivariate t distribution as in equation 4 in Additional file μ is solved numerically: the 'int' function of the R [Np is dropped.where 2 for the log signal intensity was set to the median of the data from the 6824 probes on the array for the entire S. pneumoniae SpTIGR4+R6 genome. This genome provides a standard reference level for a binding signal, but is actually independent of the binding of the cps genes in our model. The value of the prior mean for the log signal intensity μ(1) is marked on Figure 2. The prior mean κ1. For increased specificity, that is, less chance of false positives, but with a concomitant increase in false negatives, a value of κ1 = 13 was used, which is the average number of genes of a serotype. For increased sensitivity, that is, fewer false negatives, but possibly more false positives, a value of κ1 = 1 was used.Two values were used for the prior scaling factor for the variance ν0 of the variance prior ρ0 of the variance prior is calculated as 1/4 of the distance between μ0 and μ(1).3. The shape parameter i is present, we expect i G= 1, that is, gene i binds to its probes. We assume that the binding might fail with small probability β for one serotype. The reason may be experimental failure or biological variation. For simplicity we further assume that these failures are independent for each serotype. Hence the probability that a gene i fails to bind is kβ, where i. On the other hand, there might be a small probability α of a spurious binding response. After consultation with experimentalists, these parameters are assumed to be around α = β = 0.01 .If any one of the serotypes cps genes are evolutionarily closely related (homologous) [γ that a gene wrongly appears as present due to the presence of another gene in the same cross-hybridisation group. After consultation with experimentalists we set the value of γ to 0.95. A maximum likelihood estimation of γ is presented in the results section.Some of the ologous) ,7. Theirk Hindicates the presence of a representative gene of cross-hybridisation group k in k) is the index set of genes belonging to group k. When a serotype is present with a gene from the hybridisation group, that group counts as present:For the sake of brevity denote the set of genes present in a set of serotypes by i ∈ ℋ(k) we haveFor k H= 0 means that no member of the cross-hybridisation group ℋ(k) is present, in contradiction to gene i being a member (i ∈ ℋ(k)) and being present Note that in the third condition cps gene complements. In order to distinguish between these serotypes the microarray contains extra oligonucleotide probes which test subtle genetic differences between key cps genes of these serotypes. These extra probes are referred to as STIDs.A number of pairs of serotypes have identical l Tof STID probes is designed to show the presence or absence of any serotype of a set l Tof STIDs we denote the measured differences in log intensities by ld. Similar to equations 1 and 2 we defineSTID probes are different from the CPS probes in that they enable a direct comparison of two specific sets of serotypes: a set where μ2 = 0.5, ν2 = κ2 = 1After inspection of typical differences in log intensities of STID probes we use prior values The likelihood of a given serotype combination is given by combining equations 1, 2, 3, 4, and 5This model is represented schematically in Figure S, currently 91, to calculate P  for all possible 291 combinations. The question is whether we need to test all possible combinations of serotypes. In principle some higher order combination of serotypes might show an unexpectedly high probability, higher than any of its subsets, for example, due to the cross hybridisation effect. However, here we assume that such cases are rare. The observation that in clinical samples a combination containing more than three serotypes is highly unusual provides a further justification for this assumption.In practice there are too many different serotypes P (y | S) for all S with at most two serotypes. We assume it is unlikely that higher order interactions are not visible in at least pairwise interactions. The serotypes from the thirty most probable of these pairwise combinations are pooled and used to calculate P (y | S) for all possible combinations of three or fewer serotypes out of the pool, thus allowing for some high probability three-way interactions that have less probable two-way interactions. Finally, serotypes of the fifteen most probable combinations from this pool are selected to create a final pool of serotypes that is small enough to allow calculation of the probability of combinations of eight or less serotypes from the pool.Therefore we try to catch at least all pairwise interactions by calculating P  from the likelihood we require a prior P (S). Let P(λ) denote the prior probability of being infected by a number of serotypes λ out of a total of s = 91 possible serotypes. Since there are λ serotypes this implies a prior P(S) ofIn order to calculate the posterior λ(S) is the number of serotypes in S. The probability P(λ) is probably declining rapidly with λ. Since the exact distribution is unknown, we assume for simplicity that this probability is constant P(λ) = 1/(s + 1) for all λ (including the possibility that no serotype is present). Prior and likelihood for S allow us to calculated the posterior P apart from a normalising constantwhere PP(S) for a particular set of combinations of serotypes S, using the sum of PP(S) from all the combinations of serotypes chosen according to the above selection heuristic. Since these combinations seem to capture most of the posterior probability mass for S we take these normalised values as approximation to the posterior P.The software implementation of the analysis method normalises If the analysis detects the presence of more than one serotype within a sample then information on the relative abundance of the serotypes is desirable. Each serotype is represented by a selection of genes, whose abundance can be measured. This suggests an ANOVA analysis to estimate abundance of serotypes. Again we opt for a Bayesian treatment which allows us to integrate out nuisance variables such as gene specific effects and to derive credible intervals for the serotype abundance estimates.For the following analysis we work with raw intensities without log transformation since serotype presence and abundance will have an additive effect on gene specific intensities. For obtaining an analytical solution, a linear model with untruncated Gaussian distributions as error and prior distributions is convenient. Since intensities can only be positive such a model can only be considered an approximation. A further problem is that the variance of a variable measuring abundance is often not constant and depends on the size of the variable. This is mitigated to some degree by integrating over variances in the Bayesian model. Despite its shortcomings, the results indicate the model reproduces experimental data reasonably well.b serotypes in the sample. Each serotype is represented by a set of genes as specified in a g × b binary 0/1 matrix G, where g is the number of genes involved. We assume that gene abundance as reflected in its probe intensities is linearly related to the sum of the abundances of serotypes containing the gene. Each gene in turn is represented by a set of probes. From visual inspection  abundances of all serotypes in the sample. As priors we assume A is a b × b matrix, B is a g × g matrix, n Iis the unit matrix, and B cand A care scaling constants. The matrices A and B are fixed in advance, while the scaling constants B cand A care considered hyperparameters. The matrix B is set to B = G'G, that is, the more genes two serotypes have in common the higher their abundance is assumed to correlate. Matrix A is simply set to gI. To enable the calculation of an analytical solution for the posterior θ of via a conjugate analysis and also to make the scaling constants A cand B cidentifiable, we assume χ2 prior with degree ν0 = 10 and expected variance Ac, Bc, ν0 and Where t distribution, see Additional file θ is derived, an estimate of the proportions of serotypes is provided by i πwe draw 10000 samples θk)  of effectively 1, the other 90 serotypes having extremely low probabilities. For a few arrays the serotype being tested had a probability markedly lower than 1. Figure P in the analysis of each of the 91 reference arrays. The lower probabilities of a few of the correct serotypes are due to the existence of another serotype with a very similar cps gene complement, differing by just one gene.For the majority of the reference arrays the particular serotype being tested in the array experiment had a probability Originally the model did not include cross-hybridisation. Without the inclusion of cross-hybridisation the model still gives relatively good results, although three more reference arrays gave incorrect calls. The array testing serotype 24F called a combination of 24F and 24B, whilst the array testing 33A called 33F, and the array testing 7B called a combination of 7B and 7C. The inclusion of cross-hybridisation solved these three problem serotypes.κ1 = 13, α = 0.01, β = 0.01, γ = 0.95, were the same as used for the analysis of the reference arrays.Analysis of the four samples in the spike-in experiment gave the correct serotype combinations, with no false positives and no false negatives. The parameter values, Table κ1 = 13, which gives optimal results. In a clinical context, however, not missing a serotype present in a sample in only trace abundance is of importance. We therefore provide a second choice of a high sensitivity setting with κ1 = 1 in the software implementation of the analysis. Figure P probability in the analysis of each of the 91 reference array experiments when κ1 = 1. When κ1 = 1 there are three extra apparent errors.The results for the reference arrays in Figure cps genes in common and five different. The five differences are in cps genes which are closely related. The extra sensitivity of the analysis with κ1 = 1 is detecting the five cps genes of serotype 23B. These have levels slightly elevated from the background due in part to cross-hybridisation from the corresponding five genes in serotype 23F. Refinement of the cross-hybridisation analysis may be able to resolve this problem, although the fact that 23F and 23B are closely related means that from a clinical stand point this false positive is not too critical. In addition the software implementation of the analysis carries out further checks. For each called serotype, the software checks the probabilities of that serotype's genes (P(y | i G= 1)). If any serotype's genes have P(y | i G= 1) < 0.5 that serotype is flagged as such. In this case serotype 23B is flagged as having genes with P(y | i G= 1) < 0.5, alerting users to the need for further investigation.The array calling serotype 23F calls a combination of serotypes 23F and 23B. These two serotypes have thirteen cps gene in common. Similarly serotypes 14 and 19A are also unrelated with only one cps gene in common, so it was thought unlikely that these incorrect calls were due to a problem with the analysis. Further analysis indicates that the genes for 29 and 19A are actually present in very low relative abundance in the samples and we think that these calls are due to contamination of samples 33A and 14 at some stage in the experimental process. Eight microarrays are mounted on a single glass slide. The arrays testing serotypes 14 and 19A were adjacent on the glass slide so contamination of the sample containing serotype 14 with serotype 19A at this stage of the experiment is plausible. If the assumption of contamination is correct, the setting of κ1 = 1 seems to be able to detect the presence of contaminating serotypes at very low abundance levels.The array testing serotype 33A now calls a combination of serotypes 33A & 29, and the array testing serotype 14 calls a combination of 14 & 19A. Serotypes 33A and 29 are not closely related, with only one κ1 = 1 the analysis still identified all the correct serotypes as being present but, due to the higher sensitivity at this set-ting, the analysis also gave some false positives . All the false positives were flagged by the software as having genes with P(y | i G= 1) < 0.5, but none of the true positives were flagged.For the spike-in experiment, with a value of κ1 = 13 will indicate the main serotype or serotypes present in the sample. A second run with κ1 = 1 will indicate if there may also be extra low abundance serotypes present. If any of these serotypes have genes with P(y | i G= 1) < 0.5 they will be flagged, to alert the user that they may warrant further investigation.We recommend that users of the software implementation of the algorithm run the analysis twice. An initial run with α, β and γ will vary with serotype being studied, so general values of the three priors that work well for all serotypes were chosen, based on expert estimates of expected true and false response rates of probes, namely α = 0.01, β = 0.01, γ = 0.95. The suitability of the chosen values was investigated further. Each reference array was analysed in turn. The values of α, β and γ that gave the highest value of P(i S| y) for the serotype that the array was testing were found by numerical optimisation. Figure α, β and γ for the 91 reference arrays. Whilst there are some outliers the optimum values for α, β and γ for most serotypes cluster in the region of the chosen values α = 0.01, β = 0.01, 1 -γ = 0.05.The optimum values of α, β and γ was also investigated. The 91 reference arrays were analysed in turn. Each array was analysed with all combinations of eight different values of α and β  and γ . The effect of the prior values that we are most interested in is not so much the absolute value of P for the serotype S being tested on the array, but whether this probability is the highest on that array. Therefore for each combination of prior values the fraction of the 91 reference arrays that call the correct serotype as the most probable serotype on the array was recorded.The sensitivity of the results to the values of α and β are presented in Figure α and β . The default values of α = 0.01 and β = 0.01 lie within the optimal range to generate the maximum number of correctly called serotypes.The results for β between 0 and 0.02 give the same results as the default of β = 0.01. β is the false negative rate for binding, allowing for those genes that do not bind to their probes, despite a serotype that contains those genes being present in a sample. For the reference arrays, which test samples containing only one serotype, the intensities of the probes that should be present are sufficiently high for this correction to be less important. The benefit of including β = 0.01, arises when a sample contains a combination of serotypes, some with low percentage abundance. Then the intensities of some of the probes that should be present will be much closer to the background noise , the correct calling of the three serotypes that are influenced by cross-hybridisation  was found to be insensitive to the values of γ tested. As the serotyping array develops in the future, as more closely related serotypes of S. pneumoniae are discovered, and more probes are added to the array, then cross-hybridisation may become a greater problem and it may be necessary to adjust the value of γ to give optimal results.Whereas the value of Streptococcus pneumoniae molecular serotyping microarray combined with an empirical Bayesian data analysis presents two main advantages over conventional methods for serotyping strains. Firstly, it is extremely accurate in identifying the correct serotype in single serotype samples. Secondly, it has the ability to easily detect combinations of serotypes within a sample. Initially we tried a simpler analysis of the array data, based on frequentist methods, in which p-values for individual genes were calculated using t-tests and then combined. On the reference arrays a p-value approach gave thirteen incorrect serotype calls, an unacceptably high error rate, so the current Bayesian model was adopted. The empirical Bayesian data analysis does give two incorrect serotype calls for closely related pairs of serotypes, but these errors have been identified as design problems with the array rather than a problem with the analysis, a de-sign problem that will be addressed in future releases of the array.The The Bayesian approach enables additional information, such as on cross-hybridisation or on STIDs, to be integrated into the main model. The method does not require accurate estimates of prior parameters, working well with general estimates of these values for all serotypes. A few hyperparameters are estimated from the data in an empirical Bayes fashion, but in a way that is independent of knowledge of present serotypes or combinations of serotypes. The prior parameters were chosen to be standardised and repeatable across arrays, where levels of signal or background intensity can change. For the reference arrays the signal in the data is reasonably strong. However, for the low percent-age abundance serotypes in the spike-in arrays the signal to noise ratio is much lower, but the same prior parameter values work well.The spike-in experiment indicates that the method can detect multiple serotypes in samples with as large a number of serotypes as is ever likely to be found in a clinical setting. Serotypes with very low abundance within a combination can be detected by the method. As well as detecting the presence of serotype combinations, an approximate measure of the percentage abundance of the serotypes within the combination can be obtained. Of the 16 estimated abundances in table In this article we have proposed two separate models. The first is for calculating posterior probabilities of combinations of serotypes where only presence or absence of serotypes is considered. The second model estimates the relative abundance of serotypes. In principle the two models could be combined. However, the primary clinical interest is in calling presence or absence of serotypes. Their quantitative assessment is of secondary interest. A model comprising both would be more complex and might compromise the performance as a serotype caller.The linear Gaussian model with constant variances for estimating relative abundances of serotypes makes assumptions which are certainly only approximately correct. For example, abundances are always positive and variances will depend on the abundance values. However, in simulations and in the analysis of the spike-in data this model performed considerably better than simpler models without integration over variances or over the hidden gene abundances. That is, under the constraint of having a model that can be solved analytically, which is important when analysing larger data sets interactively as is currently done with the present software, the current model is an excellent approximation.cps gene content of these samples have been checked by manual data analysis methods which has confirmed that the technique described in this article is a reliable automatic analysis method for the S. pneumoniae molecular serotyping microarray. The inference could be affected by the heuristic we employ to reduce the number of combinations tested to a computationally feasible level. Increasing the number of combinations tested does not produce any extra combinations of serotypes that have a non-negligible probability, when applied to the clinical data or the reference and spiked-in arrays, indicating that the current cut-off is quite generous.This algorithm has been applied to over one thousand clinical samples, containing both single serotypes and combinations of serotypes. The S. pneumoniae molecular serotyping microarray the serotype combination with the highest probability is accepted as the answer. Alternatively, probabilities for properties of interest, for example, the co-occurrence of specific serotypes, may be obtained by model averaging, that is, by summing probabilities of the corresponding serotype combinations. The method is also easily extensible as more is learned of the different strains of this important pathogen. The use of diagnostic microarrays is not confined to the field of infectious diseases. For example arrays have been used as potential diagnostic tools in oncology [In this Bayesian method to analyse the oncology  and cytooncology . The stacps gene com-positions of the serotypes. The advantage of our approach is that the invariant biological input to the model, that is the cps gene complements of the serotypes determined experimentally by sequencing is separate from the cross-hybridisation input which is a design issue with the array and may not be invariant. The array is being constantly revised and improved so the Bayesian model keeps separate the information that will not change from the information that may change in the future.An alternative solution to the problem of cross-hybridisation would be to reannotate the The method as it stands works very well. Future work will concentrate on solving problems that may arise as further data sets become available. Adding prior information on gene specific variances and STID specific variances will be investigated as a method for improving the accuracy of the analysis . In geneS. pneumoniae who are unfamiliar with R, a user friendly web interface was created for the R script. This web interface was created using the web application Rwui [The algorithms described in this paper were implemented in the R statistical system . For theion Rwui .LW and RN devised the statistical analysis. JH contributed the experimental data and guided interpretation. All authors read and approved the final manuscript.Distributions and posteriors. Equations and derivations for all distributions used in calculating the probabilities of combinations of serotypes.Click here for fileBayesian Anova. Equations and derivation of the Bayesian Anova.Click here for file


It is widely accepted that influenza transmission dynamics vary by age; however methods to quantify the reproductive number by age group are limited. We introduce a simple method to estimate the reproductive number by modifying the method originally proposed by Wallinga and Teunis and using existing information on contact patterns between age groups. We additionally perform a sensitivity analysis to determine the potential impact of differential healthcare seeking patterns by age. We illustrate this method using data from the 2009 H1N1 Influenza pandemic in Gauteng Province, South Africa.Our results are consistent with others in showing decreased transmission with age. We show that results can change markedly when we make the account for differential healthcare seeking behaviors by age.We show substantial heterogeneity in transmission by age group during the Influenza A H1N1 pandemic in South Africa. This information can greatly assist in targeting interventions and implementing social distancing measures. The importance of the dynamics of influenza transmission between age groups is well-appreciated -6. SeverOne key aspect of this work is to estimate the extent to which people in different age groups interact with one another and to what degree they are in contact. This information can then be used as a surrogate for transmission probabilities between age groups -12. Seveet al.[When determining which groups to target for interventions in an outbreak, one strategy is to target those who potentially carry the greatest burden of disease , which het al. considerTo better understand the utility of targeting the groups with the greatest burden of disease, it is also important to determine when different age groups tend to have their peak incidence of cases. This can also be seen as a surrogate measure for the age group that is driving an outbreak -17. Most0, for adults and children that assume particular forms for a next-generation matrix and estimate the parameters of this matrix, leading to outbreak specific estimates of R0. They estimate R0 to be between 2.8 and 3.6 for children and between 0.2 and 0.7 for adults, depending on the assumptions made. In a later study, Glass et al. [0 from the final size of the epidemic to be 1.6 for kids and less than 1 for adults. Wallinga et al. [A different tactic for determining which groups should be the target of interventions is to select those groups most responsible for transmission . Studiesa et al.  have simIn the present study, we present a new approach to estimating the reproductive number by age group by modifying a method initially proposed by Wallinga and Tuenis . We studWe use de-identified data previously reported in  that inc1,…, NT}, where Nt is the number of cases at time point t, and an estimate of the serial interval, p1,…, pk, where pi describes the probability of a serial interval of length i and the maximum serial interval length is k. We review this method in Appendix 1. The estimator they obtain for the effective reproductive number for individual j on day t’ isWallinga and Teunis   onset date (Appendix 2). We create 50 such datasets and repeat all analyses on these datasets and compare these results to those obtained without jittering the data. The second sensitivity analysis tests the impact of differential healthcare seeking behaviors by age. We smooth the distribution of the proportion of cases that were hospitalized by age group to serve as a surrogate distribution of healthcare seeking behavior and/or reporting patterns by age. This distribution is U-shaped, indicating that the very young and very old are more likely to seek medical care, a finding that has been reported elsewhere . We attaFigure Figure 0, the basic reproductive number, by averaging the estimates of Rt during the epidemic period. In reality this can be viewed as a pseudo-R0 given the prior immunity to this strain of influenza. We will refer to it as R0 throughout the text. We assume that the epidemic period corresponds to the point at which transmission was sustained in Gauteng Province until the overall number of cases peaked. This corresponds to the period between 22 June 2009 and 21 August 2009. Figure 0 across age groups along with the number of individuals in each age group who were reported infected throughout the epidemic. Regardless of the choice of matrix, supercritical values of R0 are obtained for those between the age of 5 and 24, with the highest values being observed for those in the 10–14 age-group (R0 = 1.53 for close contacts).We obtain estimates of R0 across the 10 age groups obtained when using contact patterns from South Africa and the eight European countries in the PolyMod study for all close contacts  (denoted WT method hereafter) proposed a method for the estimation of the effective reproductive number by making use of the epidemic curve, th individual with symptom onset on day t, calculate the probabilities of infection by all those with symptom onset on prior days t2 (t2 < t.) These probabilities equal the serial interval probability for the distance in time between the potential infector, tj2 , and infectee, ti, P (tj' →ti) = 1. For the ii was infected by the jth case on day P (tj' →ti), denoted by 2. Calculate the relative probability that the case tth case on day t', say tj', the reproductive number is calculated as the sum of the expected values of a Bernoulli random variable. The Bernoulli random variable describes the event that tj' infected another individual on day s, s > t', say si, and has probability qs,t'. Then the effective reproductive number for individual tj′is3. Calculate the reproductive number. For the js denotes the number with symptom onset on day s.where nIn this analysis, we choose a single imputed dataset and randomly jitter the onset dates of 10% of the sample within 30 days of their observed (or imputed) onset date. We create 50 such datasets and repeat all analyses on these datasets and compare them to the results on the non-jittered dataset.We assume that the reporting distribution by age follows a U-shaped distribution, implying that the very young and very old are most likely to seek healthcare and have their cases reported. To obtain a distribution that follows this shape, we use the distribution of hospitalized cases by age in our data, rescale it so that the highest proportion is one, and smooth the distribution using a loess smoother , where f (x) is a function of the original age distribution observed in the data, g (x), and the reporting distribution shown in Additional file λ ranges between 0 and 1. We run analyses for λ = 0.0, 0.25, 0.50, 0.75 and 1.0 . Results for all 25 datasets are shown in Additional file Here The authors report no conflicts of interest.LFW and MP conceived the project and developed the methods. LFW performed the analyses. BA provided the data and insight on dynamics in South Africa. LFW drafted the manuscript. All authors read and approved the final manuscript.Results for the sensitivity analysis using the South African based age contact information. Result presented is the estimate obtained from the original dataset and the values in the parentheses represent the range of values obtained over the 50 datasets generated for the sensitivity analysis.Click here for file0 using 25 of the 500 imputations described in the original text. Results shown are the mean and range of estimates across the 25 imputed datasets. λ=1.00 corresponds to the results from the original analysis.Estimates of RClick here for fileSmoothed distribution to reflect potential rates of healthcare seeking behavior and/or case-reporting by age.Click here for file


Overweight and obesity are growing public health problems in high income countries and is now growing at a dramatic pace in low and middle income countries, particularly in urban settings. The aim of this trial was to examine the effects of a weight reduction program in adults and to determine whether or not a more extensive intervention was superior to ordinary care.Patients seeking advice for overweight/obesity or illness related to overweight/obesity at eight primary health care centers in Sweden were randomized either to intervention or control care groups with both groups given dietary advice and individualized information on increased regular physical activity. In the intervention group advice was more extensive and follow-up more frequent than in the control group during the study period of two years. Main outcome measure was reduction in body weight of five percent or more from study start.From October 2004 to April 2006, 133 patients, 67 in the intervention group and 66 in the control group, were randomized over a period of 18 months. Target weight was achieved at 12 months by 26.7% of the patients in the intervention group compared with 18.4% in the control group (p = 0.335). There was an average absolute weight loss of 2.5 kg in the intervention group and 0.8 kg in the control group at 12 months as compared with the weight at study entry. There were no significant differences between the groups in quality of life, blood glucose and lipids. At 24 months target weight was achieved in 21.9% versus 15.6%, with an average weight reduction of 1.9 kg and 1.2 kg in the two groups, respectively.Promotion of a diet with limited energy intake, appropriate composition of food and increased physical activity had limited effects on body weight in a Swedish primary care setting. More extensive advice and more frequent visits made no significant difference to the outcome.NCT01606917ClinicalTrial.gov:  Overweight and obesity are growing public health problems in high income countries and is now growing at a dramatic pace in low and middle income countries, particularly in urban settings . OverweiScientific assessments of treatment methods for overweight and obesity have shown modest but not sustained weight reduction over a short period, and the types of weight-loss interventions that contribute most to successful long-term outcomes have not yet been established . Many inThe aim of this two years study was to examine the short and long-term effects of a weight intervention program in adults, seen in a primary care setting. A prerequisite for inclusion was that the patients consulted or were in care for overweight/obesity. The aim was also to compare more extensive advices with appointments and telephone contacts with ordinary care, all done with a pragmatic study design and with limited resources.Adult patients between 18 and 70 years of age who consulted or were in care for overweight/obesity with or without type 2 diabetes, hypertension, CVD, coronary heart disease (CHD), dyslipidemia, gallstone, or musculoskeletal disorders at eight Primary Health Care Centers (PHCC) in Örebro County, Sweden were eligible for the trial.Patients were not eligible if they were already taking part in another weight control program, understood the Swedish language poorly, were mentally ill, or had an alcohol or drug abuse problem. Neither were they eligible if they had a physical disability preventing intensified physical activity or were pregnant at study start.In the waiting room of the PHCCs, information about the study was posted, inviting patients to take part in the trial. At their appointments with the GPs at the centers, patients were invited to participate in the trial if appropriate, irrespective of whether or not the patients asked about the study. After obtaining informed consent, an individualized target weight was formulated. It was also decided over what time period it should be achieved, the same for both groups. Patients were advised that a realistic goal was a weight reduction of at least 5% by one year after study start.The patients were then randomized to the intervention or control group. Figure Patients in the intervention group had regular appointments five times over the first two years with both a study nurse and a study physiotherapist. In addition, the study nurse and the physiotherapist contacted the patient by telephone four times during study months 6, 9, 15 and 21  on the importance of a diet of adequate composition, reducing the total energy intake, and regular physical activity for weight control was given. Food advice was also based on the “plate-model” with the same composition as in the intervention group. The written information on the “plate-model” was given to the patients with no further discussion on the content. Patients in the control group had a check-up with a nurse after one month of compliance with the advice, and a repetition of what had been said at the start. At three months the nurse and the physiotherapist phoned the patients to encourage patients to comply with the advice given. They were also given a diary in which their physical activity was to be recorded and shown to the physiotherapist at the check-ups Figure .The trial was executed only by staff members at the participating PCHCs who all had a short instruction session by a dietitian before study start to describe the “plate model”, and the effects and importance of physical activity according to the metabolic equivalent (MET) intensities model by a physiotherapist . In bothBiannual meetings, lasting half a day, were organized for the staff members by the steering committee. The purpose of the meetings was to discuss problems that had arisen during the study, but it was also an opportunity for the steering committee to motivate the members to keep up their involvement in the study.The primary outcome was the proportion of patients who achieved target weight at two years. Secondary outcomes were weight loss, clinical or laboratory manifestations of their baseline illness  or death of any cause. Further secondary endpoints were quality of life estimated using the SF-36 and EQ-5D forms. The trial was approved by the regional ethics committee in Uppsala, Sweden (204: M-300) and registered in the Current Controlled Trials, NCT01606917.After written informed consent, randomization was carried out using numbered sealed opaque envelopes stratified for each PHCC, BMI >30 and type 2 diabetes. The order of the envelopes was predetermined by the study statistician and kept in a box of 20 numbered envelopes of varying bloc sizes at each PHCC by the study coordinator at each centre. At randomization an envelope was drawn in the predetermined numbered order.SPSS for Windows, version 17.0  was used for all statistical analyses. On the assumption that 50% of the patients in the intervention group and 20% in the control group would achieve their target weight at two years with a power of 90% at a significance level of 0.05, two-sided test, it was determined that 50 patients in each group would have to be included. We estimated that as many as 50% of the patients would have difficulties in fully complying with the study protocol. We therefore aimed to randomize 75 patients to each study group. The analysis was per protocol. Mean with standard deviation (SD), median with quartile range and proportion of individuals was used to summarize different variables. For comparisons between intervention and control groups, chi-square test or Fischer’s exact test when appropriate were assessed for categorical variables, and unpaired and paired t-tests were used for continuous variables with 95% confidence intervals. P-values less than 5% (two-sided) were regarded as statistically significant.From October 2004 to April 2006, 133 patients were randomized, 67 to the intervention group and 66 to the control group. The goal of 150 randomized patients could not be reached because of declining interest at the PHCCs in carrying on with inclusion of patients in the trial. Inclusion was therefore stopped on April 30, 2006. Baseline characteristics of the patients are given in Table There were considerable difficulties for both the primary care organisation and the patients in complying with the study protocol. Therefore only 45 patients in the intervention group and 49 patients in the control group contributed information at 12 months. At that time, 26.7% of the patients in the intervention group had a weight reduction of 5% or more as compared with 18.4% in the control group, Table There was significant weight loss in the intervention group at 12 months as compared within the group . At 24 months this difference was no longer significant , Table There were no effects on plasma glucose, blood lipids or blood pressure between the study start and values at 12 and 24 months (data not shown). Quality of life was assessed using both the SF-36 (data not shown) and the EQ-5D form, Table The main finding of this trial showed that intervention was not superior to ordinary advice to promote weight reduction. Although the difference between the groups was not statistically significant in terms of the primary outcome, patients in both groups had weight loss of between 1.9 and 1.2 kg even after two years of follow-up.The magnitude of weight loss of 2.5 kg at 12 months in the intervention group seems mostly to have been maintained over the next 12 months. The narrowly missing significance (p = 0.07) may be attributed to the smaller than planned sample size owing to high drop-out rates. The weight loss of 3% is comparable to what can be achieved using drugs such as orlistat and sibutramin . The maiScientific assessments of treatment methods for overweight and obesity have only shown modest but not sustained weight reduction over a short period , althougA short study from eight primary care practices in the UK reported a weight loss of 4.0 kg in the intervention group as compared with 1.2 kg in the ordinary care group over 12 weeks in a weight management programme. The conclusions drawn from that study were that it was feasible to follow the NICE guidelines . OverallPhysicians’ recommendations have a strong impact on individual health behaviors  and physThe Swedish Björknäs Study  performeFrom the perspective of most patients with overweight or obesity, a weight reduction of 2.5 kg is disappointing. Bearing in mind that it takes time to become overweight or obese it is not surprising that weight reduction also takes time. This is a considerable challenge to any clinician who sees such patients, especially when bariatric surgery is so successful in reducing weight, both in a short and a long-term perspective . Access The small effects on weight did not impact on any aspects of quality of life as estimated using SF-36 and EQ-5D. This is not surprising, bearing in mind the size of the effect, the difficulties in executing the protocol over time, and that only measurement at 12 months could be analyzed.The strength of our study was that it was an attempt to perform a study in a routine clinical setting with no extra resources. The limitations include the difficulty of carrying out a trial in such a setting in an organization with a staff with high turnover and with shortages of GPs and other professionals. This influences the continuity and the involvement of the staff members. The regular meetings for the staff members held twice a year could not counteract this negative progress. The importance of this is illustrated in the Björknäs study, in which one committed person managed to keep almost all the patients in the study throughout the whole study period . FurtherThe high drop-out rate in our trial is a major drawback to the internal validity of the trial results at two years. However, the results of this trial probably reflect what is achievable in a Swedish primary care setting without extra added resources. The drop-out rate in this study, 56 participants (42%), is higher than in two other two-year studies, 5%, and 14%, respectively ,30. On tA multimodal intervention to promote a diet with limited energy intake and increased physical activity had limited effects on body weight among patients in a Swedish primary care setting. More extensive advice and more frequent visits made no significant difference to the outcome.None of the authors has any conflicts of interest concerning the interventions and performance of this trial. The authors alone are responsible for the content and writing of the paper.The study was conceived and designed by SJ, PE and GL who also wrote the manuscript. SJ, PE, AM and GL analysed and interpreted data. SJ, PE, AM, GeL and GL reviewed and edited the manuscript. All authors read and approved the final manuscript.


Drosophila melanogaster in order to predict possible functions for previously un‐annotated genes. A total of approximately 5043 different genes, or about one‐third of the predicted genes in the D. melanogaster genome, are represented in the dataset and 1854 (or 37%) of these genes are un‐annotated.While the genomes of hundreds of organisms have been sequenced and good approaches exist for finding protein encoding genes, an important remaining challenge is predicting the functions of the large fraction of genes for which there is no annotation. Large gene expression datasets from microarray experiments already exist and many of these can be used to help assign potential functions to these genes. We have applied Support Vector Machines (SVM), a sigmoid fitting function and a stratified cross‐validation approach to analyze a large microarray experiment dataset from D. melanogaster genome.39 Gene Ontology Biological Process (GO‐BP) categories were found with precision value equal or larger than 0.75, when recall was fixed at the 0.4 level. For two of those categories, we have provided additional support for assigning given genes to the category by showing that the majority of transcripts for the genes belonging in a given category have a similar localization pattern during embryogenesis. Additionally, by assessing the predictions using a confidence score, we have been able to provide a putative GO‐BP term for 1422 previously un‐annotated genes or about 77% of the un‐annotated genes represented on the microarray and about 19% of all of the un‐annotated genes in the D. melanogaster genes. The applied probabilistic analysis to SVM output improves the interpretability of the prediction results and the objectivity of the validation procedure.Our study successfully employs a number of SVM classifiers, accompanied by detailed calibration and validation techniques, to generate a number of predictions for new annotations for  Drosophila melanogaster, approximately 28% of the 14,029 predicted genes have no Gene Ontology (GO) term  associated with them (including both curated and electronic annotations) and only 58% have a GO‐BP  term ..7].Saccharomyces cerevisiae[Arabidiopsis thaliana[D. melanogaster[Mus musculus[Saccharomyces cerevisiae[C. elegans[D. melanogaster[Mus musculus[In addition to the clustering analyses of genes in an unsupervised fashion and without annotation information, a number of supervised methods have been proposed for predicting gene functions. These methods make use of available information about the annotations of genes in order to discover gene expression patterns that characterize those annotations. Then, functional predictions for un‐annotated genes are made based on how well their expression profiles are matched with “annotated” patterns. Perhaps the most popular class of supervised methods are the binary classifiers, where first, expression data are separated into two classes either having or not having a particular annotation, and then un‐annotated genes are predicted of having or not having the annotation, based on which class their expression profile falls under. Examples of applications of these methods include Support Vector Machines (SVM) ,9, randoerevisiae,14, Arab thaliana, D. melaanogaster, and Muserevisiae, C. eleg. elegans, D. melaanogaster,18 and M musculus.D. melanogaster gene functions. SVM is a popular machine learning method for classification and regression. Its proven high performance as well as its solid theoretical basis justify its frequent use in many fields, including bioinformatics and predictions of gene functions. As a two‐class classification tool, SVM attempts to separate the data points not in the original feature space but in an “enlarged” higher‐dimensional space instead. The seemingly highly computationally expensive data transformation is not performed but instead, ingeniously, the separation is performed “implicitly” based on their distances measured with the use of a kernel function. The SVM algorithm uses optimization techniques to find the surface that gives the optimal margin between the points of the two classes [In this study we focus on the use of SVM for the prediction of  classes ,21.S. cerevisiae[M. musculus[D. melanogaster. Our study fills this gap, investigating how well this very popular method works for D. melanogaster gene expression data, in particular when the dataset is of a specific structure imposed by the nature of time‐course experiments, as the one we use in our study.Despite its popularity in bioinformatics along with other research areas, SVM has been used for the prediction of GO‐BP annotations for genes of various organisms (such as erevisiae and M. m musculus) but notD. melanogaster[D. melanogaster genes from the Gene Ontology Consortium (GO‐BP) [D. melanogaster genome by using Support Vector Machines and a two‐level data splitting rotation scheme for validation . Our prediction method was evaluated also externally with the use of an independent dataset.Using microarray data from the life cycle of anogaster, and a c (GO‐BP) , in thisD. melanogaster genome helping to bridge the gap for the large number of genes that have little or no annotation. In addition, this SVM approach provides a precision and probability estimate that can help guide users as to the likelihood a given gene belongs to GO annotation class.Using this approach we have been able to provide a putative GO‐BP term for about 77% of the un‐annotated genes represented in the dataset and about 19% of all of the un‐annotated genes in the Drosophila melanogaster[D. melanogaster genome. From those genes, 1854 were not annotated with any GO‐BP term at the time of the analysis. Data were obtained from the Stanford Microarray Database [D. melanogaster genome using annotation available at Flybase [computer gene (CG) numbers were purposely not removed as we were interested in investigating the consistency of the predictions across the duplicates.The microarray data used in this study was obtained from the series of 138 cDNA microarrays spanning the life cycle of anogaster. The micDatabase  and normDatabase , GEO acc Flybase . Biologi Flybase  in Februp‐dimensional vector data xi and their labels yi taking the values {-1,+1}, a linear Support Vector Machine finds the optimal hyperplane that separates the “positive” from the “negative” class. This plane is maximizing the margin between the two classes. According to the mathematical formulation of the problem, the solution refers to a weight vector w and a scalar b that satisfy the optimization problemA Support Vector Machine (SVM) is a classification and regression method originally developed by Vapnik . Given aN is the number of samples.where When classes are overlapping and misclassifications are allowed, the above constraints becomeξi are slack variables and C a constant. Solutions can be generated by using the “Lagrange” formulation of the problem and its “Wolfe dual” problem. Given the solution, the weight vector w, for a new point x, the function f(x)=wTx+b is calculating the discriminant value for x, which can be used for its classification to the positive or negative class. It turns out that only a number of training points are important for the determination of the solution, the support vectors.where non‐linear separation, after mapping the data onto a higher dimensional space, with the use of a mapping Φ. Φ is determined by a kernelK such that K=<Φ(x),Φ(y)>. The optimization problem is similar with the linear separation case, and following the Lagrange formulation and given a solution of Lagrange multipliers αi, the discriminant function is given by xi,i=1,…,Ns are the support vectors. It is important to note here that the solution and discriminant function depend on the data only through the kernel, and also that the explicit expression of the mapping Φ is not needed for the solutions. This is one of the reasons that make SVM computationally attractive. More information on SVM can be found in [This mechanism can be applied to problems of found in .radial basis kernel,It is evident that SVM depends on the choice of the kernel. After performing a small set of experiments with pilot runs evaluating a number of kernel choices, we decided to use a σ a heuristic value equal to the median value of the distances between positive training points and their nearest negative training points. To combat asymmetric classes, a suggestion from [K is augmented by λ·|C|/N where |C| is the size of the class C that x belongs to, and λ a tuning parameter. For our calculations we use λ=m/2, where m is the median value of the diagonal of the kernel matrix. For the implementation of the SVM algorithm we use the publicly available Gist package [where ance, in ,9). We uion from  is imple package .f(x) to posterior probabilities of class membership, p(y=1|x), we use the method proposed in [For the translation of the discriminant values posed in . The auta,b. The estimation of the parameters a,b is done by solving a maximum likelihood problemwith parameters whereandN+,N- are the sizes of the positive and negative class respectively.where For the sigmoid model we use the model fitting algorithm proposed by , which iI is the index set of all these genes participating in the cross‐validation, a partition {I1,I2,I3,I4} is generated, where each Ij has equal size and equal number of positively labelled genes (to the degree that this is achievable). Two of those sets are used as “training set” for the SVM, one set is used for calibration and sigmoid fitting, and the last set is used as “test” set, where probability estimate values are output from SVM and compared with the known annotations of the genes for the evaluation of the method. For each permutation  of {1,2,3,4}, and if gene gi belongs to set Iα, we denote with pβ|γ,δ(i) the probability estimate for gene gi from an SVM classifier that was trained with training set Iγ∪Iδ and calibrated with the set Iβ. Keeping the test set fixed we can have three different ways of constructing the training and calibration sets, and therefore each gene of the test set has three different probability estimate values. For example, for gene gi in I1, we have p2|3,4(i),p4|2,3(i) and p3|4,2(i). Those three values are averaged to produce a unique probability estimate for every gene. For each test set (or fold) the probability estimates and true annotations of the genes are used for the calculation of performance measures such as precision at 20, 30 and 40. The values of those measures are then averaged to produced one final measure for the whole SVM procedure. Note here the distinction between the probability estimate generation for each gene that involves averaging over the three possible arrangements of training and calibration sets, and the calculation of the performance measure that is done independently for each one of the four folds (test sets), using each time only the genes of the test set.For each selected GO‐BP category a set of annotated genes consisting from the positively annotated and a subset of the negatively annotated of size equal to up to four times the size of the positively annotated is participating in the evaluation of the SVM prediction algorithm. If For the calculation of precision and recall and the generation of the precision‐recall plots the R package ROCR  was usedThe prediction of gene functions was performed with the use of a number of SVM classifiers. Annotation predictions were made independently for each of 788 GO‐BP categories selected based on their size (see Microarray data and annotation sources in Methods section), based on the results of an SVM classifier. Each SVM was trained with the use of a training set of data points of known labels  annotation). To remedy any model fitting problem caused by the high imbalance between the positive and negative classes, for every GO‐BP category and SVM classifier we limited the negative examples by randomly selecting a subset of them with a ratio of positive to negative examples being 1:4. The trained system was used for the classification of new, unlabelled data (i.e. prediction of functions for un‐annotated genes). The classification was based on the discriminant value of the data point, which is output by the SVM. As the discriminant value measures the “distance” of the data point from the hyperplane that separates the two classes, traditionally points with discriminant value larger than some threshold  are classified as positives and the rest as negatives. Here, we refrain from translating the discriminant values to binary classifications, but, instead, we used a previously published algorithm to estimate the posterior probability of a gene membership to each GO‐BP category. The algorithm fits a sigmoid function to the discriminant values of labeled data and it uses this function to approximate posterior class probabilities for unlabelled data . A flowcWe validated the performance of SVM and sigmoid fitting function with the use of stratified cross‐validation, where the initial set of known data points (positively and selected negatively annotated genes) was randomly partitioned into four equal size sets, with equal number of positively annotated genes . For evept we can calculate the corresponding precision value, defined as the ratio of the number of genes that have average probability estimate equal or larger than pt and belong to the class, divided by the number of genes that have a probability estimate equal or larger than pt (i.e. True Positives / Predicted Positives). Similarly, recall is defined as the proportion of the genes annotated with the term that also have average probability estimate equal or larger than the threshold . While precision gives a measure of the accuracy of the prediction, recall measures the coverage or completeness. The prediction performance of SVM for a specific GO‐BP category was evaluated with the use of a measure equal to the precision value corresponding to a specific recall value . Precision at 20, 30 and 40 were calculated for each fold and averaged over all four folds, and the number of categories with high performance measure values were calculated. More specifically, the method identified 39 high‐precision categories reaching precision at 40 values equal or larger than 0.75. Table For any chosen probability threshold value DNA‐dependent DNA replication and oxidative phosphorylation, were chosen for further analysis. Precision‐recall plots were generated for both categories and presented in Figures Two of the high‐precision GO‐BP categories, Developmental gene expression profiles for the genes in these two categories are shown in Figure One approach of declaring an un‐annotated gene as predicted to be annotated with some GO‐BP term, is to ascertain if its probability estimate output from the SVM specific for this term was larger than some threshold value (e.g. 0.5) and then assign the un‐annotated gene with that term. However, drawbacks to this approach include the arbitrary choice of the threshold and the fact that it ignores the evaluation of the performance of the classifier, as measured by cross‐validation. In this approach, any gene that has probability estimate score larger than 0.5  for two categories A and B, will be predicted to belong to both A and B, regardless how well SVM is performing for these categories. A third problem with this method is that it assumes that probability estimate values are comparable between different GO‐BP categories. Although the purpose of the sigmoid function fit method is to provide with comparable estimates, one cannot be certain that this is necessarily obtained.We have chosen an approach that takes into account the predictive behaviour of SVM for a specific GO‐BP term, when a prediction is made for an un‐annotated gene, as well as it addresses the other issues mentioned above. For each gene‐GO category pair a “gene precision” score is assigned to be equal to the maximum precision that can be achieved using thresholds smaller or equal to the probability estimate of the gene (output from SVM). If the gene is to be included in the “positive” predictions from SVM (and therefore to be assigned the GO‐BP function), the threshold has to be such that it will give a precision value for the classifier not larger than the “gene precision” score for the gene‐GO category pair. This score measures how probable is for the gene to truly belong to GO‐BP, given its probability estimate output from SVM, and also given the precision value of SVM for the particular category. This gene precision score is calculated separately for each one of the four folds  and the four fold‐specific scores are averaged.D. melanogaster genome, are represented in the dataset. 1854 (or 37%) of these genes are un‐annotated and therefore this method is providing gene function predictions for about 77% (1422/1854) of the un‐annotated genes represented on the microarray and about 19% of all of the un‐annotated genes in the D. melanogaster genome. A graphical representation of these results is shown in Figure We can then declare as gene function predictions all the gene‐category pairs that have “gene precision” score equal or larger than some threshold value. More specifically, 9887 new predictions representing 1422 genes (CG numbers) were generated corresponding to a gene precision score larger than 0.75. A total of approximately 5043 different genes, or about one‐third of the predicted genes in the D. melanogaster FISH database [The un‐annotated genes contained in two of the high‐precision GO‐BP categories, DNA‐dependent DNA replication and oxidative phosphorylation are listed in Tables database ,35 to viOne annotated gene from the dataset known to belong to the GO‐BP and one un‐annotated gene from each of the two GO‐BP categories listed in each of Tables Of the un‐annotated genes that are predicted to belong to the DNA‐dependent DNA‐replication GO‐BP genes, 22 had images in the FlyFISH database and 18 out of 22 (82%) had FISH images that were the same or very similar to the known genes belonging to the category Table .D. melanogaster in order to predict possible functions for previously un‐annotated genes. This approach successfully generated a preliminary GO Biological Process annotation for a large number of these genes.We have applied Support Vector Machines (SVM) and a stratified cross‐validation approach to analyze a large microarray experiment dataset from The SVM analysis, employing a sigmoid fitting function, generated annotation probability values for all the genes in the dataset. Using a recall value of 40%, 39 high‐precision GO‐BP categories were identified and 77% of the un‐annotated genes in the dataset have been assigned to one or more of these GO‐BP categories. Assigning new annotations based on gene‐precision scores takes into account both the overall precision of the GO‐BP category, as well as the individual probability of the gene, outcome of SVM and the sigmoid function. In that way, gene predictions of high confidence can be considered even for GO‐BP categories that have an overall poor precision performance.We chose two of the high‐precision GO‐BP categories to validate using an independent data set (the FlyFISH database). These two categories, DNA‐dependent DNA replication and oxidative phosphorylation, were selected for a number of reasons but chiefly because each contained a fairly large number of previously unannotated genes allowing for a larger number of genes that could be cross‐checked in the FlyFISH database and that the GO‐BP description was fairly precise allowing for the potential to examine whether the unannotated genes are actually involved in the biological process they had been assigned to. While it could be argued that the use of FlyFISH data is perhaps too similar of a data type to be useful , our main goal was to use data that: was from a completely independent source; had at least some data that differed in type from the original microarray data ; where the raw data could be inspected independently at the gene level so that any computer or user assigned functional classification of the genes would not bias the validation. Given the high degree of precision that some of the unannotated genes have for belonging to a specific GO‐BP category, especially for the oxidative phosphorylation category, we feel quite confident that a large number of these genes will be shown in the future to be directly or indirectly involved in these biological processes. Gene expression pattern data has been used in the past to uncover the function of a gene. In a study by Hughes and coworkers , a largeIn the original Arbeitman and coworkers study , the autWe attempted to compare our results with those from the study of Yan and co‐workers , who alsWe believe that the methods used in this study can be applied to other microarray and RNA‐seq datasets. Our own experience trying this approach on other data suggests that the robustness of the results is largely dependent on both the number of array experiments that are in the dataset as well as on the type of experiment(s) the data represent. In this case, a developmental time course with numerous time points provided the ability to identify a large number of co‐expressed genes.D. melanogaster genes, using published time‐course gene expression data. We have assessed the predictive ability of the method using an elaborate stratified double cross‐validation procedure, involving the fitting of a sigmoid function on the raw output from SVM. Precision and recall values for each GO‐BP function were calculated, describing in detail the performance of the prediction. On a second level, our results were validated externally using independent data from FlyFISH database. Finally, we applied SVM for the prediction of GO‐BP annotations of un‐annotated genes, providing certainty estimates for those predictions, based on a method that uses the results from the cross‐validation and the predictive performance of SVM for the specific GO‐BP category.In this study we have applied Support Vector Machines for the prediction of GO‐BP annotation terms for D. melanogaster genes and provides a comprehensive list of new annotation predictions that can be further researched experimentally. We believe that our study is of great value to researchers interested in computational annotation of genes, as well as to the community of D. melanogaster researchers.We believe that this is the first study that investigates the performance of SVM for GO‐BP prediction for GO‐BP: Gene Ontology Biological Processes; SVM: Support Vector MachineThe authors declare that they have no competing interests.NM participated in the conception and design of the study, performed the analysis of the data, participated in the creation of the figures and tables and wrote part of the manuscript. ZR pre‐processed the data and participated in the creation of the figures and tables. ME participated in the conception and design of the study and revised the manuscript for critically important content. TW participated in the conception and design of the study, participated in the creation of figures and tables, wrote part of the manuscript and revised the manuscript for critically important content. All authors read and approved the final manuscript.The Parent‐Child Relationship Between Ontology Biological Process Categories. Figure showing a joined Gene Ontology graph providing an overview of the relationship between the 39 Gene Ontology Biological Process (GO‐BP) categories that were identified from the output of the SVM as having a precision‐at‐40 value equal or larger than 0.75, as indicated in the highlighted polygonal nodes.Click here for fileSelected GO‐BP Predictions for Previously Unannotated Genes. Table showing all new predictions with average gene‐precision score equal or larger than 0.75. Detailed information on gene‐precision scores and probability estimates for each one of the four folds is shown.Click here for file


The structure of the layer was studied by scanning and transmission electron microscopy. Microvolumes with tantalum particles distributed in a copper matrix and microvolumes of copper particles in a tantalum matrix were detected. The tantalum particles in copper have a size of 5⋯500 nm, with a predominance of 5⋯50 nm particles. A mechanism for the formation of the finely dispersed heterophase structure in explosive welding is proposed. The microhardness of interlayers with the heterophase structure reaches 280 HV, which far exceeds the microhardness of copper (~130 HV) and tantalum (~160 HV). Many twins of deformation origin were found in the structure of the copper plate. The effect of heating temperature in the range from 100 to 900°C on the microhardness of copper, tantalum, and the Cu-Ta welded joint was studied. Upon heating to 900°C, the microhardness of the intermediate layer decreases from 280 to 150 HV. The reduction in the strength properties of the weld material is mainly due to structural transformations in copper.The structure and microhardness of Cu-Ta joints produced by explosive welding were studied. It was found that, during explosive welding, an intermediate layer 20⋯40  One of the most essential problems of modern materials science is the development of reliable joints of dissimilar metals with significantly different physical and mechanical properties –3. ThereBelow we consider in detail a Cu-Ta system characterized by nearly zero mutual solubility of the components in the solid state , 10 and This paper deals with the structure and microhardness of welds produced by explosive welding of copper and tantalum plates followed by heat treatment.For explosive welding we used plates of technically pure copper (99.98% Cu) and tantalum (99.95% Ta). The materials used are significantly different in structure, density, melting point, and thermal conductivity in . These d3, which was placed directly on the copper plate. The detonation velocity of the explosive was 3800 m·s−1, and the plate collision angle was 17°. Prior the welding the surfaces of the plates were grinded using SiC abrasive paper (320 grit).Explosive welding of copper and tantalum plates arranged in parallel  was perf-6 Pa.The thermal stability of the Cu-Ta joint was determined by annealing samples at temperatures in the range of 100 to 900°C. The dwell time in the furnace was 1 h. A characteristic feature of tantalum is its active interaction with the gases that make up the air. For this reason, the welded joints were annealed in a vacuum furnace at 10Structural studies were performed on transverse sections. For metallographic studies and microhardness measurements, laminated composite specimens were cut along the direction of shock-wave propagation. Metallographic sections were prepared by conventional techniques comprising grinding and polishing. The structure of copper was revealed by etching in an aqueous solution of ferric chloride and hydrochloric acid.μm, dimple grinding using a Gatan Dimple Grinder, and final ion thinning in a Gatan PIPS 659 ion mill. The structure of the sample material in the region of interaction was studied using an EVO 50 XVP scanning electron microscope.Metallographic studies were carried out using a Carl Zeiss Axio Observer Z1m microscope. Subtle structural changes in plastically deformed materials were studied using a Tecnai G2 20 TWIN transmission electron microscope. The objects of study were foils. The foils were prepared by a technique combining cutting of samples with an electric spark machine, mechanical thinning to a thickness of 100 μm intervals.Microhardness of the samples was measured before and after heat treatment with a Wolpert Group 402 MVD microhardness tester. The load on the diamond indenter was 0.245 N. The measurement procedure involved the creation of a track of indentations perpendicular to the weld in the direction from the copper layer to the tantalum layer. The indenter indentation were spaced at 50 μm thick between the copper and tantalum plates. The layer contains the material formed by mixing of the dissimilar materials under dynamic interaction. During the formation of wavy welds, such structure of a mixture of materials is observed only in the vortex zones formed near the crests and troughs of individual waves.The structure and the scheme of the explosively welded Cu-Ta joint in a longitudinal section are shown in Due to the high degree of dispersion of the resulting mixture, it is difficult to determine the size and shape of individual elements of the structure in the layer by scanning electron microscopy. For this reason, a more detailed structural analysis of the mixing regions was performed using transmission electron microscopy. The main factors determining the structural features of the material are the high rates and amounts of strain in the surface layers of the plates, high heating temperatures of tantalum and copper in the contact area, and the presence of a cumulative sheet of fine particles of the interacting materials.In general, the structure of the intermediate heterophase layer can be defined as a mixture of fine copper and tantalum. The matrix material in the layer, characterized by continuity, is predominantly copper. A lot of dark rounded particles of tantalum can be seen against the background of the bright copper matrix. Tantalum particles in copper have sizes of 5 ⋯ 500 nm, with a predominance of 5 ⋯ 50 nm particles Figures . An examIn addition, the heterophase layer was experimentally found to contain microvolumes in which the matrix material is tantalum and copper is in the form of separate islands. A transmission electron micrograph of a structure of this type is shown in The mechanism of formation of the intermediate heterophase layer can be described as follows Figures  and 5. D−1 penetrate into the rough surface layers of the tantalum plate.It should be emphasized that the surface of the joined plates is rough. The size of the majority of particles in the gap between the joined plates (5 ⋯ ~50 nm) is 2 ⋯ 3 orders of magnitude smaller than the roughness values of the metal workpieces. Thus, some of the highly dispersed particles moving faster than the point of contact >3800 m·sThe impact of the jet fragments on the surface layers of the tantalum plate leads to the formation of a mixing zone and a cloud of fine particles of a mixture of copper and tantalum. Most of the tantalum particles in the mixing zone are randomly distributed in copper. Note that the melting points of copper and tantalum differ by almost a factor of three (1084°C and 2996°C). Tantalum particles remain in the solid state under such collisions. At the same time, microvolumes of copper with ordered arrangement of tantalum particles are also observed. The tantalum clusters shown in The thermal stability of the Cu-Ta joint was evaluated by heating the samples with subsequent analysis of structural changes and microhardness of the materials. The heating temperature was in the range of 100 ⋯ 900°C. The exposure at each temperature was 1 h.μm. Dynamic interaction between the plates leads to deformation strengthening of copper in regions directly adjacent to the weld. This is indicated by the formation of microvolumes with increased dislocation density , the grain size was 22  density  and a se density . Figuresμm intervals along the surface of junction of the plates. It should be noted that in the copper layer, strain far exceeding the critical value occurs at a depth of several tens of micrometers. In the rest of the volume of the copper plate, the amount of strain is close to the critical value. For this reason, copper recrystallization is accompanied by a sharp increase in the grain size. After heating to 700°C, the grain size in the recrystallized zones is 440 μm. In the samples exposed at 900°C for 1 h, the grain size increased to 620 μm.The most notable changes in the strength properties of the plastically deformed materials occur upon heating to values close to the recrystallization temperature. After heating to 500°C, the copper plate has no indications of recrystallization. During heating to 600°C, the recrystallization of copper is nonuniform. Recrystallization occurs in islands spaced at 2000 μm on each side of the plane of junction of the plates. The highest microhardness values were recorded for thermally untreated welded joints. After explosive welding, the microhardness of copper was ~130 HV, and that of tantalum as ~160 HV. Maximum microhardness (280 HV) was recorded in the narrow intermediate layer of heterophase structure.Results of microhardness measurements of thermally untreated samples of welded joints and those annealed at various temperatures are presented in Figures The observed effect of hardening of the material is probably due to the formation of a highly dispersed mixture and strain hardening of tantalum. Despite the large amount of plastic strain in the surface layer of the copper plate, strain hardening does not play a significant role in this case. Rapid heating of local microvolumes of the materials leads to melting of copper and eliminates the dislocations structure formed in the zone of dynamic interaction of the plates. The strain hardening effect is eliminated not only by melting but also upon reaching a temperature leading to recrystallization processes. These processes are typical of explosive welding of metallic materials –19. DuriIn samples heated to 500°C, the microhardness in the zone of mixing of tantalum and copper does not change significantly. This indicates that the heterophase structure is thermally stable in this temperature range. Heating to 600°C or above results in a marked decrease in the microhardness of the material. After annealing at 900°C, the microhardness of the intermediate layer with mixed structure becomes equal to the microhardness of the tantalum plate (~150 HV). In contrast to this layer, the temperature dependence corresponding to tantalum shows no changes. This is due to the fact that the recrystallization temperature of tantalum is more than 300°C higher than the maximum temperature of annealing of the welded joint. Increasing the annealing temperature of copper to 900°C leads to an almost twofold decrease in its microhardness (from 130 to 75 HV) due to relaxation processes in dynamically deformed zones and the formation of a more equilibrium structure than that of the initial one .During explosive welding in the joint area of tantalum and copper, plates form an intermediate layer which has a heterophase structure and consist of a mixture of fragments of dissimilar materials. The matrix material is predominantly copper. Tantalum in copper is in the form of isolated particles. Less common are microvolumes in which the matrix is tantalum with copper particles embedded in it. Based on the sizes of the dispersed-phase particles observed in the intermediate layer, the material can be classified as a highly dispersed system. The size of tantalum particles is predominantly in the nanometer range (~5 ⋯ 50 nm), which corresponds to the size range of colloidal particles. A mechanism for the formation of this structure was proposed which involves the formation of a fragmented, mainly copper, cumulative jet ahead of the point of contact of the plates. The jet moves directly on the surface of the tantalum plate and interacts with the roughness of the latter. The Cu-Ta mixing area is thermally stable upon heating to 500°C. Annealing at 900°C leads to a decrease in the microhardness of the intermediate layer with the heterophase structure from 280 HV to 150 HV.