Phasing out fossil fuel dependency to adopt renewable energy technologies is pertinent for both ensuring energy security and for safeguarding the well-being of the environment. However, financial constraints often restrict the developing countries, in particular, from undergoing the renewable energy transition that is necessary for easing the environmental hardships. Against this background, this study makes a novel attempt to evaluate the impacts of FDI inflows on enhancing renewable energy use and attaining environmental sustainability in Bangladesh between 1972 and 2015. Using the autoregressive distributed lags with structural break approach to estimate the short- and long-run elasticities, it is found that FDI inflows enhance the share of renewable electricity output in the total electricity output levels of the country. Besides, FDI inflows are also evidenced to directly hamper environmental quality by boosting the ecological footprints figures of Bangladesh. Hence, it can be said that FDI promotes renewable electricity generation in Bangladesh but transforms the nation into a pollution haven. However, although FDI inflows cannot directly reduce the ecological footprints, a joint ecological footprint mitigation impact of FDI inflows and renewable electricity generation is evidenced. Besides, the findings also verify the authenticity of the Environmental Kuznets Curve hypothesis in Bangladesh’s context. Therefore, economic growth can be referred to as being both the cause and the panacea to the environmental problems faced by Bangladesh. These results, in a nutshell, calls for effective measures to be undertaken for attracting the relatively cleaner FDI in Bangladesh whereby the objectives of renewable energy transition and environmental sustainability can be achieved in tandem. In line with these findings, several appropriate financial globalization policies are recommended. As an economy grows, it is expected that its overall energy demand would increase in tandem  levels can be embodied in multidimensional forms. For instance, the employment of renewable electricity within the manufacturing industries is anticipated to bridge the acute power shortages that are responsible for below-par levels of industrial outputs  phenomenon due to several limitations  inflows into the energy sectors of the underdeveloped nations can depict noteworthy implications for facilitating the RET phenomenon Rahman, . LinkingAgainst this milieu, this study aims to evaluate the impacts of FDI inflow on Bangladesh’s REO share in the aggregate electricity production figures and environmental quality between 1972 and 2015. Bangladesh is a fast-emerging South Asian economy that has registered tremendous growth achievements over the years. The nation has recently eclipsed the criteria of twin graduation to be classified as a lower-middle-income and developing country. Bangladesh is also a member of the Next Eleven countries whereby the nation is expected to experience robust degrees of economic growth in the years to come. As a result, meeting the future energy demand is a major challenge for the government. At the same time, the nation’s traditional reliance on fossil fuels-based electricity generation strategies to meet its energy demand could also go on to jeopardize environmental sustainability in Bangladesh. Thus, keeping Bangladesh’s energy security and environmental sustainability into cognizance, evaluating the macroeconomic factors which can facilitate RET in Bangladesh is extremely important. Besides, the outcomes from this study can be expected to assist in efficient policymaking concerning the nation’s achievement of the SDG by 2030. Furthermore, this study is also relevant from the perspective that Bangladesh has not succeeded in achieving its national target of generating at least 10% of the total electricity output from renewable sources by 2020. On the other hand, Bangladesh is also one of the countries under China’s Belt and Road Initiative (BRI). As a result, the nation can expect to receive hefty amounts of Chinese outward-FDI which, in turn, can be anticipated to have a sizeable impact on the prospects of enhancing renewable power generation figures of Bangladesh. Most importantly, this study can be a standpoint for Bangladesh to phase out its traditional fossil fuel-dependency issues to develop the renewable energy sector. Moreover, this current study is also timely from the perspective that the Asian Development Bank has forecasted Bangladesh to outperform the other South Asian economies in respect of economic recovery following the Covid-19 pandemic  emissions to proxy for environmental quality in Bangladesh, this study considers the ecological footprints to measure the changes in the quality of the environment in response to incoming FDI. Compared to CO2 emissions, the ecological footprint is a more comprehensive measure of environmental quality  countries, Abdouli and Hammami  represent the elasticity parameters to be estimated and ε is the random error term. All the variables are transformed into their natural logarithms for the ease of estimating the conditional bivariate elasticities. The dependent variable REO refers to the percentage shares of electricity generated from renewable resources in the aggregate electricity outputs of Bangladesh. FDI is the principal regressor of interest which denotes the total volume of FDI flowing into Bangladesh, measured in terms of constant 2010 US dollars. Besides, the econometric model is also controlled for the technological advancement within the Bangladesh economy. In this regard, a change in the level of technological advancement is proxied by the energy intensity level (denoted by lnEI) which is measured in terms of energy use  per unit of real GDP. A decline in the energy intensity level can be interpreted as an improvement in energy efficiency which, in turn, can be credited to advancement in technology and vice-versa. Technological innovation is said to enhance the stock of technology within the economy which can be expected to facilitate the integration of renewable energy in the national energy-mix of Bangladesh  are the elasticity parameters to be predicted. The variable EFP refers to the ecological footprints measured in terms of global hectares of land per capita. A rise in the total ecological footprints figures implicates environmental degradation while lower levels of ecological footprints indicate betterment of environmental quality. A positive sign of the elasticity parameter β1 would provide validity to the ‘pollution haven hypothesis.’ In contrast, a negative sign of the elasticity parameter β1 would authenticate the ‘pollution halo hypothesis’. The GDPPC figures and its squared term proxy for the impacts of affluence on the ecological footprints. The squared term is introduced into the model to assess the authenticity of the Environmental Kuznets Curve (EKC) hypothesis which postulates in favor of an inverted-U-shaped relationship between ecological footprints and national income levels  database of the World Bank. WDI provides data for Bangladesh's electricity production from non-renewable energy resources, namely oil, natural gas, and coal sources, as percentages of total electricity production in Bangladesh. Thus, the REO share is calculated by subtracting the share of the non-renewables from 100, which includes electricity generated from hydropower, solar and other sources. Data concerning all the other variables are sourced from WDI as well, except for the world crude oil price which is acquired from the British Petroleum Statistical Review of World Energy 2019 database. Data in the context of the ecological footprints are sourced from the Global Footprint Network GFN, ". The va1Before conducting the regression and causality exercises, it is pertinent to identify the stationarity and cointegrating properties of the variables. Thus, econometric analyses commence by applying appropriate unit root and cointegration techniques.Although most of the preceding empirical studies have suggested the application of the conventional unit root tests, including the Augmented Dickey-Fuller Dickey and Fuller  and Philp values) of individual cointegration tests; EG-J refers to the p values of the Fisher statistic for the combined Engle-Granger (EG) and Johansen (J) tests while EG-J-BO-BD refers to the p values of the Fisher statistic for the combined EG, J, Boswijik  combined test for non-cointegration proposed by Bayer and Hanck . The BH Boswijik  (B) and Boswijik  (BDM) teHowever, the BH method does not take into consideration the SB issues. Hence, this study also applies the Maki  cointegri,t is the dummy variable that is used to signal the presence of a break in the data. Di,t takes a value of 1, denoting the existence of the SBs at specific break years Tbi , if ti are after the break years Tbi (i.e. ti > Tbi) and a value of 0, denoting no SB at the specific break years Tbi , if ti are before the break years Tbi (i.e. if ti < Tbi). Statistical significance of the test statistics in each of the four models  rejects the null hypothesis of no cointegration to confirm the presence of cointegrating associations between the variables in the respective models. The identified SB from test A, within the Maki cointegration approach, is used to create SB dummy variables and included into the respective empirical models to control for time fixed effects. The regression analysis follows the cointegration exercises.t-1 represents the one-period lagged Error-Correction Term (ECT) which is estimated from the residuals of the long-run equation shown in Eq.  the ARDL model can be expressed as:The short run dynamics for model (2) is observed from the model below:The long-run elasticities for model (2) are sourced from the model below:The stability of the ARDL estimates are checked using the Breusch-Godfrey Lagrange Multiplier test for Autocorrelation (BGodfrey) proposed by Breusch and Godfrey , the Lagt, β0 and ut are vectors with dimension n × 1 and Bi (i > 0) is a parameter matric with a dimension of n × n. The error term ut has no expected value and presumed to be independent and identically distributed with a non-singular covariance matrix  causality estimation technique proposed by Hacker and Hatemi-J . This mementclasspt{minimaThis section begins by analyzing the findings from the unit root and cointegration analyses followed by the discussion on the regression and causality outcomes.The NP and CMR unit root test results are reported in Table Table The ARDL short- and long-run elasticity estimates in the context of model (1) are reported in Table ceteris paribus. Murshed  are reported in Table l et al.  also fouceteris paribus. Therefore, it can be said that the ‘pollution haven hypothesis’ is a long-term problem for the Bangladesh economy. However, it is to be noted that the magnitude of the long-run elasticity is relatively smaller than the corresponding short-run elasticities which, to some extent, implies that FDI inflows tend to have low technological spillover effects whereby the positive impacts on the environment are not so pronounced; rather the damages are slightly less. This is a concerning finding in the context of Bangladesh which warrants restructuring of the nation’s foreign financing and financial globalization policies. The nation is better-off attracting cleaner FDI and restricting the inflows of the relatively dirtier ones. This finding of the adverse environmental impact of FDI inflow in Bangladesh corroborates the conclusions made in the study by Doytch , whereby replacing the conventionally consumed fuels by the renewable alternatives can mitigate environmental deterioration in Bangladesh. Similar conclusions were made by Murshed and Tanha  also depict unidirectional causation, without the feedback, from FDI inflows to ecological footprints in Bangladesh. This finding, along with the positive sign of the corresponding elasticity estimate concerning FDI inflows and ecological footprints, implicates that the quality of the FDI flowing into the Bangladesh economy does not safeguard the environmental goals of the nation. Thus, it is pertinent to restructure the foreign finance policy of the government whereby emphasis must be given to attract the relatively cleaner and renewable energy-intensive forms of FDI. The unidirectional causal finding contradicts the bidirectional association between FDI inflows and ecological footprints reported by Khan et al.  for ChinFollowing the global appeal to undergo RET for ensuring energy security and environmental sustainability, the world economies have reached a consensus to align their respective economic growth strategies with the environmental development welfare-maximizing targets. However, undergoing RET is conditional on overcoming several constraints that have traditionally impeded the RET phenomena, especially across the underdeveloped economies. Among these, technological backwardness and infrastructural underdevelopment are hypothesized to be the major limitations hampering the integration of renewables into the energy sectors of these nations. Against this backdrop, this study evaluated how potential technological spillovers from FDI inflows can overcome these constraints to facilitate RET in Bangladesh. The central focus of this study was to unearth the dynamic associations between FDI inflows and REO shares in Bangladesh and to also investigate the impacts, both direct and indirect, of such FDI on the nation’s environmental quality quantified in terms of the ecological footprints.pollution haven hypothesis’ was validated by the corresponding elasticity estimates. However, interestingly, a joint favorable environmental impact of higher FDI inflows and greater REO shares was also evidenced. Hence, these contrasting findings imply that the nature of the FDI determines its impact on RET and environmental sustainability. Accordingly, several policy recommendations are suggested. Firstly, it is pertinent for the government to channel foreign investments for the development of the renewable energy sector which can simultaneously foster the nation's energy security and environmental sustainability objectives. Besides, it is also necessary for Bangladesh to attract FDIs that have the potential of exerting knowledge spillover impacts for enabling large-scale renewable electricity generation in the country. In this regard, the utilization of foreign finance for the development of the domestic energy infrastructure can also be anticipated to further expedite RET in Bangladesh. At the same time, since FDI inflows were found to degrade the environment by boosting the ecological footprints, it is equally important for the government to restructure the national financial globalization policies to monitor and restrict the inflows of dirty FDI. Thus, it is compulsory for the nation to enhance the stringency of the existing environmental rules and regulations in order for Bangladesh to safeguard its economy from transforming into a pollution haven.The results from the regression and causality analyses, in a nutshell, implied that foreign direct investments in the long-run enhance the REO shares in Bangladesh. On the other hand, FDI inflows were also found to directly attribute to environmental degradation through boosting the nation’s levels of ecological footprints since the ‘Secondly, since the long-run elasticity estimates and the causality findings statistically authenticated the EKC hypothesis in Bangladesh, it is recommended that the nation continues to focus on expanding the size of its economy without being fearful of compromising the environmental attributes in the process. This is because the validation of the EKC hypothesis implies that economic growth is both the cause and the panacea to the environmental hardships faced across Bangladesh. However, the growth strategies are ideally to be themed on the use of renewable energy resources in order to gradually phase out the nation's fossil fuel dependency and simultaneously restore the environmental balance. Additionally, it is extremely important for Bangladesh to establish sustainable consumption and production process which would further facilitate the prospects of having complementarity between economic and environmental well-being. Lastly, since the results portrayed that unplanned urbanization is detrimental to Bangladesh’s environmental sustainability, it is suggested that the government adopts appropriate policies to ease out the nations’ unplanned urbanization woes. In this regard, the relocation of the industrial activities from the urban to the rural areas can be helpful.As part of the future scope of research, this study can be extended to specifically analyze the impacts of China's outward-FDI on the changes in the REO shares and ecological footprint figures of Bangladesh for unearthing key policy implications regarding the efficacies of allowing such foreign investments to take place. Furthermore, the recently introduced quantile ARDL technique for regression and causality analyses can be performed to assess the possible heterogeneity of the findings across different quantiles of the REO shares and ecological footprints levels of Bangladesh.


When performed in an observational setting, treatment effect modification analyses should account for all confounding, where possible. Often, such studies only consider confounding between the exposure and outcome. However, there is scope for misspecification of the confounding adjustment when estimating moderation as the effects of the confounders may themselves be influenced by the moderator. The aim of this study was to investigate bias in estimates of treatment effect modification resulting from failure to account for an interaction between a binary moderator and a confounder on either treatment receipt or the outcome, and to assess the performance of different approaches to account for such interactions.The theory behind the reason for bias and factors that impact the magnitude of bias is explained. Monte Carlo simulations were used to assess the performance of different propensity scores adjustment methods and regression adjustment where the adjustment 1) did not account for any moderator-confounder interactions, 2) included moderator-confounder interactions, and 3) was estimated separately in each moderator subgroup. A real-world observational dataset was used to demonstrate this issue.Regression adjustment and propensity score covariate adjustment were sensitive to the presence of moderator-confounder interactions on outcome, whilst propensity score weighting and matching were more sensitive to the presence of moderator-confounder interactions on treatment receipt. Including the relevant moderator-confounder interactions in the propensity score (for methods using this) or the outcome model (for regression adjustment) rectified this for all methods except propensity score covariate adjustment. For the latter, subgroup-specific propensity scores were required. Analysis of the real-world dataset showed that accounting for a moderator-confounder interaction can change the estimate of effect modification.When estimating treatment effect modification whilst adjusting for confounders, moderator-confounder interactions on outcome or treatment receipt should be accounted for.The online version contains supplementary material available at 10.1186/s12874-022-01519-7. Treatment effect modification (TEM) occurs when the effect of treatment on an outcome is influenced by a third variable, termed a moderator. Such an analysis can identify patients who are more likely to benefit or be harmed from treatment. In some cases, a moderator may have a strong scientific-rationale and their investigation is pre-specified. For example, in their randomised controlled trial protocol, Kyle et al. hypothesised that age may moderate the effect of cognitive behavioural therapy for insomnia on cognitive functioning outcome . In otheRandomised clinical trials provide the best evidence regarding the causal effects of treatments, and thus also the best evidence for the existence of TEM, although if the causal effect of a moderator is of interest, treatment randomisation does not ensure unbiased estimation of this . ObservaObservational studies attempt to adjust for confounding of the treatment–outcome relationship but often do not consider any additional features required to unbiasedly evaluate TEM . Here, wFigure If the differential effect of the confounder across the moderator is not accounted for, this may introduce bias into the estimate of treatment effect modification. Suppose M is binary and the effect of the confounder is greater in one subgroup of M than the other. Accounting for the overall effect of the confounder will lead to an underestimation of the effect of the confounder in one subgroup and an overestimation of the effect of the confounder in the other subgroup, which will lead to biased estimates of the subgroup treatment effects, and hence treatment effect modification. The magnitude of the bias will depend on the prevalence of the moderator, the relative sizes of the moderator and confounder effects, and the number of confounders which are influenced by the moderator. A more detailed explanation is given in the Failure to account for an interaction that exists between a moderator and confounder is essentially a misspecification problem. Both propensity score methods and regression adjustment are sensitive to model misspecification. Some research has indicated regression adjustment (without PS methods) is more sensitive to model specification than PS methods . FurtherConsideration of differences in treatment assignment across subgroups of a moderator when applying propensity score (PS) methods to estimate subgroup-specific effects has been discussed previously –11, 12. In this paper, we aim to add to this literature by additionally considering 1) PS covariate adjustment and regression adjustment as confounding adjustment methods, 2) situations where the moderator influences the relationship between the confounder and either/both the treatment (or exposure) and outcome, and 3) bias introduced into estimates of both TEM and subgroup-specific treatment effects. Patterns of bias under these different scenarios are explored in a simulation study. We discuss factors that influence the magnitude of bias and compare reduction in bias and precision of different approaches to accounting for moderator-confounder interactions.To investigate the impact of the issues discussed in practice, we compared the estimates of treatment effect modification in a real observational dataset when moderator-confounder interactions were and were not included in the confounding adjustment.  The dataset comprised information from the 2018-19 National Survey for Wales and the interest was in whether the effect of tinnitus on mental well-being was moderated by certain variables. We performed a simulation study to confirm and demonstrate that 1) estimates of subgroup-specific treatment effects and TEM can be biased if the moderator also influences the effect of the confounders and this is unaccounted for, 2) the presence of bias depends on the confounding adjustment method and whether or not the moderator influences the effect of the confounder on treatment receipt or the effect of the confounder on the outcome, and 3) the impact of this bias depends on the prevalence of the moderator and the relative effect sizes of the treatment effect moderation. We compared the accuracy and precision of estimates between methods of accounting for the moderator-confounder interactions.The simulated data comprised the following information on each patient: founding . DatasetThe three continuous confounders An individual’s true probability of treatment was defined to depend on the main effects of the variables mentclass2pt{minimAn individual’s outcome measure was defined to be dependent on the main effects of The chosen values of the mentclass2pt{minimThe simulations considered three different values of the coefficients mentclass2pt{minimmentclass2pt{minimFour methods of confounding adjustment were considered: (1) regression adjustment, (2) PS covariate adjustment (where the estimated PS score is added as a linear term to the outcome model), (3) inverse probability of treatment weighting (IPTW) using the propensity score, and (4) PS nearest neighbour one-to-one matching, with replacement. For each, four confounding adjustment models were considered, the first three being (a) adjusting for the main effects ofThe estimated individual propensity scores were obtained by fitting a logistic regression model, regressing treatment receipt on the set of confounders, including For each confounding model and method combination , estimates of the subgroup-specific treatment effects, 500 simulations were run per scenario (18 combinations of moderation effect sizes). This number of simulations was determined to be a conservative number required to detect a treatment-moderator interaction effect size of 0.3 within an accuracy of 10% when the sample size was 1000 . For eacrd error .To demonstrate the potential impact of accounting for interactions between a moderator and a confounder in practice, we used a dataset comprising information from the 2018–19 National Survey for Wales, a large-scale cross-sectional survey run annually by the Office for National Statistics on behalf of the Welsh Government. Participants are randomly selected from the population of Wales and asked a variety of questions regarding their health, lifestyle and interests. The anonymised data is available from the UK Data Service .The specific example relates to the estimation of experiencing tinnitus on mental well-being. Tinnitus is a self-reported binary measure (experiences tinnitus or does not experience tinnitus) and mental well-being was measured using the Warwick-Edinburgh Mental Well-being Scale, a numerical scale scored between 14–70 where a higher score indicates a higher level of mental well-being. We investigated whether the effect of tinnitus on mental well-being was moderated by three binary variables: gender, ethnicity (White/non-White) or current smoking status (currently smoke/currently do not smoke). Additional potential confounders accounted for were age (in years) and BMI .A series of linear regression models were fitted including interactions between tinnitus and each of the three potential moderators. Confounding was adjusted for via both regression adjustment and IPTW. In the assessment of each of the three moderators, the other two potential moderators were included as potential confounders. Two confounding adjustment models for each method were specified, the first adjusting only for the main effects of each confounder, the second adjusting for the main effects of each confounder and interactions between the moderator and each confounder.The simulation study and analysis for the applied example were performed in Stata version 14 .The forest plots in Figs. entclass1pt{minimaWe first discuss the patterns of bias observed when no moderator-confounder interactions were accounted for in the confounding adjustment (i.e. confounding model (a)). In Fig. In this simulation study, the direction of bias was always positive for When an Including all possible moderator-confounder interactions in the confounding adjustment model, i.e. adjustment model (c), and performing the stratified analysis, i.e. adjustment model (d), also resulted in substantially reduced levels of bias in the subgroup-specific treatment effects and In Fig. entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaWhen mentclass2pt{minimTo more thoroughly compare the accuracy in estimates across all models for each adjustment method, we compared the mean bias in entclass1pt{minimaAs expected, the average bias tended to be highest when no moderator-confounder interactions were adjusted for (adjustment model (a)). Overall, the average bias was still reasonably small in magnitude for adjustment model (a); however, this is the average over all The average bias in the estimation of The precision of the various estimates of entclass1pt{minimaComparing the empirical and average model standard error is a way of assessing bias in the estimation of the model standard error . For regMorris et al. say that the comparison of the empirical standard error and the average model standard error should be interpreted with caution when the methods are known to be biased as the empirical SEs can be small as a result . Howeverrd error , 19. We This analysis did not primarily seek to compare the accuracy and precision of the different confounding adjustment methods overall. In general, estimates obtained via regression adjustment had the smallest bias. However, this is likely to reflect the way in which the data was simulated, and will likely not be true in all applications. Estimates obtained via IPTW had noticeably higher precision than PS matching, but it is possible that a more sophisticated version of PS matching would have performed better.Table Adjusting for interactions between the moderator and confounders in regression adjustment had little difference on the estimates of interaction between tinnitus and each of gender and current smoking status. Although not statistically significant in either case, the interaction effect between tinnitus and white ethnicity roughly tripled in magnitude when moderator-confounder interactions were adjusted for. Further inspection showed that an interaction between White ethnicity and age was present and statistically significant. This implies that the effect of age on mental well-being onset was different for people of White and non-White ethnicity.Again, when IPTW was applied, adjusting for interactions between the moderator and confounders in the propensity score model had little difference on the estimates of interaction between tinnitus and each of gender and current smoking status. interaction effect between tinnitus and White ethnicity increased in magnitude when moderator-confounder interactions were included in the propensity score model. Upon further inspection, none of the interactions between White ethnicity and the confounders were of notable size or were statistically significant, however, the combined effect of their inclusion still had an impact on the overall interaction effect between White ethnicity and tinnitus on mental well-being.We did not aim to provide a robust answer to the clinical question posed as there are limitations regarding unmeasured confounding and the dichotomisation of smoking status and ethnicity. However, this practical application shows that different point estimates of effect modification may be obtained in practice depending on whether interactions between the moderator of interest and the confounders are included in the confounding adjustment. In many cases, the differences may be marginal and the overall conclusions will not change. In some cases however, the differences may lead to different conclusions being made.Our findings confirm that failure to account for any interactions present between the moderator and a confounder on treatment receipt introduced bias into subgroup-specific and TEM estimates when IPTW and PS matching was applied –11, 12. Whilst it is not surprising, to our knowledge it has not been previously clarified that PS covariate adjustment is instead sensitive to failure to account for interactions between the moderator and a confounder on outcome. Hence, inclusion of confounder-moderator interactions in the PS model does not rectify this problem; only when subgroup-specific PS models were estimated did PS covariate adjustment produce accurate estimates. Similarly, regression adjustment produced biased estimates where there existed a moderator-confounder interaction on outcome which was not accounted for.The accuracy and precision of estimates  obtained from regression adjustment were similar when only the one moderator-confounder interaction was accounted for in the confounding model, when all possible moderator-confounder interactions were accounted for and when the stratified analysis was performed. For IPTW, the accuracy and precision was higher when all possible moderator-confounder interactions were accounted for and when the stratified analysis was performed, compared to when just the one moderator-confounder interaction was accounted for. For PS matching, the accuracy and precision was highest in the stratified analysis. However, in the methods using propensity scores, particularly IPTW and PS matching, the average model standard errors tended to overestimate the empirical standard errors which would lead to less precision of the subgroup and moderator effect estimates in practice when these methods were used.If the moderator itself is a confounder, by not accounting for any moderator-confounder interactions that exist on either treatment or outcome, one is essentially misspecifying the propensity score or outcome model. This should in theory induce bias into any estimates obtained from the outcome model and it is already recommended that confounder-confounder interactions be considered  althoughThe applied example demonstrated the potential impact of accounting for moderator-confounder interactions. In many cases, the difference in the estimates of treatment effect modification obtained when moderator-confounder interactions were and were not accounted for was very small. However, a difference was observed for some.Although we did not include these in our simulation studies, doubly robust estimators are an attractive way of estimating the effect of exposures on outcomes in observational studies . Doubly In this study, we considered four different methods of adjusting for confounding. Other methods which could have been considered include stratification by the PS and other versions of PS matching. The aim of this analysis was not however to compare the different methods in terms of accuracy and precision, but to explore the bias within each method. We suspect that, in general, methods based on the PS will always be prone to bias when there are interactions between the moderator and confounder on treatment assignment (the exception being PS covariate adjustment).In the simulations, we only considered situations in which there was a linear interaction between the moderator and confounder when either was continuous. In practice, there may be more complex non-linear interactions between the moderator and confounder which may be insufficiently accounted for with a linear interaction term in the confounding adjustment. If this is the case, this should be incorporated into the confounding adjustment if possible.Additionally, we only considered scenarios with a continuous outcome and a binary moderator. We expect similar patterns of bias to be seen with other outcome and moderator types, but the relative accuracy and precision of the confounding adjustment models within each method may not be the same. We also only simulated data where there were six confounders and only one moderator of interest, but in practice there may be many more confounders and moderators of interest. It may be that a moderator interacts with multiple confounders and, if the bias introduced by each moderator-confounder pair were in the same direction, the overall amount of bias on the estimation of treatment effect modification could be substantial. Alternatively, the different biases could cancel each other out if they acted in different directions.It has been recommended that a propensity score model include not only confounders, but also variables associated with the outcome as this increases precision . It seemHere, we consider a simplistic, although common, approach to assessing treatment effect modification as only one moderator is considered at a time in a parametric model. More sophisticated and flexible approaches exist which allow researchers to assess treatment heterogeneity more generally. Bayesian additive regression trees (BART), for example, avoid the strong parametric assumptions required for the standard linear and logistic regression models and automates the detection of interactions . AdditioIn conclusion, we recommend that the presence of moderator-confounder interactions are considered and accounted for when estimating treatment effect medication whilst adjusting for additional variables. Accounting for moderator-confounder interactions that did not exist did not have a negative impact in our simulation study, hence we suggest that researchers include interactions terms if they are undecided about their presence. However, this approach may be unattractive when using regression adjustment with a smaller sample size. We also recommend that subgroup-specific propensity scores are created and used in a stratified analysis when using propensity score covariate adjustment to assess treatment effect modification by a binary variable.Additional file 1.


When probed at nanometer and picosecond scales, the properties of a liquid present striking analogies with the ones of the corresponding solid, one of the most surprising is the ability of supporting shear wave propagation, as a rigid medium. Although this evidence is being reported by a growing number of terahertz scattering measurements, it remains an open question whether it is universal or rather typical of some liquids only. Furthermore, given its elusive signatures in the scattering signal, the detection of this effect appears as a typical case where an unintentional “bias of confirmation” can mislead experimentalists. We thus decided to use a Bayesian inference approach to achieve a probabilistically grounded and evidence-based lineshape modeling of the inelastic neutron scattering spectra from liquid silver, whose simulated density autocorrelations bear evidence of a shear mode propagation over very short distances. The result of our analysis indicates that the observation of any additional, non-longitudinal, acoustic modes in this simple system goes beyond the accuracy of the used scattering method. In the last decades, growing experimental evidence is being gathered in support of the similarities between the response of liquid and solid systems over short distances and timescales. Advances in the accuracy of available probes have corroborated the overall perception of such similarity while unraveling more subtle aspects of it.In general, the distinction between a solid-like (rigid and elastic) and a liquid-like (viscous and dissipative) response of non-gaseous systems becomes increasingly elusive upon approaching microscopic scales.In fact, in liquids, atoms are so tightly packed that the only movements they can experience are primarily rapid rattling oscillations within their first neighbors cage, which have a direct analogy in the lattice vibrations of an ordered solid. However, it remains an open question to what extent the collective atomic dynamics mirrors this similarity.S, where Q and E can be identified with the amplitude wavevector and energy exchanged in a scattering process7, is far from obvious. Despite having been reported in a wealth of diverse materials, the experimental observation of this “high-frequency rigidity” of liquids poses severe challenges. To begin with, spectroscopic methods best suited to probe it, such as Inelastic Neutron (INS) and X-ray Scattering (IXS), are intrinsically unfit to assess the transverse polarization of an acoustic mode in S, unless sided by a parallel computational effort8 able to determine other, more appropriate, correlation functions inaccessible to experiments. Even so, convincing experimental evidence for this effect is often hampered by its loosely resolved and feeble spectral signatures.For instance, a genuine solid-like aspect of the terahertz acoustic dynamics of some liquids is the onset of a shear mode. However, its appearance in the system response, that is in the spectrum of density fluctuations 10 offers undoubted advantages. The monatomic character of MMs makes them simple benchmarks of possible universal properties of liquid aggregates, also making computer simulations of their microscopic interactions more straightforward. Furthermore the spectrum of density fluctuations of MMs, as opposed to that of other disordered systems, is featured by well-resolved and intense inelastic peaks and often non-preponderant elastic peak11. These are ideal prerequisites to detect weak inelastic features gathering in the low-frequency portion of the spectrum, as is likely the case of transverse acoustic modes in liquids. Yet, literature works reporting the onset of shear modes in the spectrum of MMs13 often entailed some stretch of the model’s predictive capabilities, or, perhaps an excessive reliance on the resolution, spectral contrast, or statistical accuracy of the measurement.In these respects, dealing with molten metals (MMs)The situation appears even more worrisome when considering that the use of lineshape models containing a disproportionate number of free parameters is becoming widespread in this kind of studies.15 naturally incorporate this principle while providing criteria to rate the plausibility of a given model based on the experimental outcome. As demonstrated by previous works of our group20, Bayesian methods can be successfully implemented to achieve a minimally biased and probabilistically grounded modeling of the scattering signal. In this work, the inferential approach rests on the use of a Markov Chain Monte Carlo (MCMC) algorithm endowed with a Reversible Jump (RJ) option21. The spectra from the sample are modeled by the sum of k Damped Harmonic Oscillator (DHO) profiles and a Lorentzian term, accounting for the inelastic and quasielastic portions of the spectra, respectively. In this description k itself is treated as a free model parameter whose optimal value and related posterior distribution are to be determined by the algorithm conditionally on the experimental outcome. Details on this Bayesian inference algorithm are illustrated in detail in Refs.22.A natural remedy against this slippery slope would be a more strict adherence to the Occam razor principle or “lex parsimoniae”, which states that among two models providing an equally satisfactory account of some evidence, the simpler one, i.e. the one containing fewer parameters, is always preferable. Bayesian inference methods16, the Bayesian inferential method was applied to the modeling of INS spectra of liquid gold and led to an unambiguous and probabilistically well-grounded conclusion: a single longitudinal acoustic mode dominates the inelastic wings of the spectrum of gold. However, the posterior probability of the Q-increase, becoming non-negligible for Q-increase, the spectral modes got increasingly damped, also migrating toward the border of the accessible kinematic range. Second, the limited count statistics of measured spectra raised the legitimate suspicion that the alleged emergence of a second inelastic mode at the highest Q’s could have been an artifact of the low accuracy in the spectral shape definition.In one of our previous works23. Data allowed only a GH modeling, while other more complex models, like the viscoelastic one, gave non-significant values for additional parameters with respect to the GH lineshape. Once again, no spectral signatures were found of low-frequency spectral features to be possibly assigned to a shear wave propagation. However, the close agreement between experiment and ab initio molecular dynamics (AIMD) computations in an overlapping Q-range authorized an analysis of simulations in a larger Q range. The outcome of this analysis disclosed new interesting scenarios. Indeed, the modeling of the Fourier transform of S with an exponential series expansion26, already successfully tested for classical29 and quantum31 fluids, strongly indicated that a transverse dispersion branch emerges in liquid silver for More recently, some of us measured the INS spectrum of liquid silver and modeled its shape with a Generalized Hydrodynamics (GH) profile32.To further elaborate on this interesting result, here we use the mentioned Bayesian methods to rate probabilistically the plausibility of a second, transverse, mode in the INS spectrum of molten silver, previously measured by INS or simulated by ab initio methodsWhile pursuing this well-targeted objective, we could benefit from three complementary assets: the direct probe provided by the measurement, the one inherently free from experimental uncertainties bestowed by the simulation, and their unbiased modeling allowed by the Bayesian inferential approach.In the following, we succinctly describe the various steps of our analysis as:y are the measured scattering data, The experimental data are given by:T = 1273 K being the temperature of the sample), while the term enclosed by the curly brackets is the sum of a central Lorentzian term, characterized by parameters k DHO doublets. The generic j-th DHO is featured by its undamped oscillation frequency The chosen model function is given by:33 how the representation of Brillouin neutron scattering data in terms of DHO doublets is an oversimplified description lacking accuracy and scientific rigor, it is largely employed to model the dynamic structure factor in liquids and, particularly with noisy data, such description can capture the relevant features of a typical spectrum, especially when the energy transfer range explored is limited. Furthermore, for consistency, we deliberately adopted the same model already used for liquid gold.Although it has been shown22.The best-fitting of the model to the experimental spectra of liquid silver was performed in the 4–16 34 and so do all inference results derived from the joint posterior distribution of all model parameters. In this work, we are especially interested in the posterior distribution of the parameter k which is obtained through a marginalization process of the joint posterior distribution The method essentially relies on the Bayes theoremQ’s. This deliberate choice was adopted to let the inferential process be driven uniquely by the experimental evidence without any external bias.Upon assuming, as we did, a uniform prior distribution for each possible model option, i.e. imposing , and the slope of the low Q dispersion leads to estimate a propagation speed close to the speed of sound in silver, i.e. about 2790 m/s.Figure 23), two distinctive aspects of the spectrum of MMs as compared to the one of other liquid systems, i.e. the persistence of a well-defined triplet shape up to Q values approaching the position of the first sharp diffraction maximum, and an inelastic-to-elastic intensity ratio quite larger than in non-metallic liquids. As mentioned in the introductory section, both features seem advantageous when attempting to spot loosely resolved low frequency spectral features, which is how the alleged transverse mode in the spectrum supposedly looks like.Overall, data in Fig. Q in any systematic fashion, not even at the highest Q’s. This partial scrutiny of the measurement outcome urges us to conclude that, albeit AIMD calculated spectral shape bore unquestionable evidence for a double excitation structure, the plausibility of a transverse mode in the measured spectra appears overly slim.As clearly shown by Fig. Figure Q-dependencies of the undamped frequency 23 through a GH modeling of present spectra. The overall agreement between the two curves is more than satisfactory, although absolute values of the excitation frequencies from Ref.23 are slightly larger than those estimated by the MCMC algorithm in the present work, such small difference being very likely due to the current use of the DHO model. A close agreement is also obtained for the halfwidth of the central Lorentzian component  are obviously much larger than those corresponding to a single DHO option, consistently with the low plausibility attributed to the second mode by the Bayesian algorithm.Based on the AIMD simulation outcome, we decided to carry out a double excitation modeling uniquely for the spectra collected in the Q range, at odds with what suggested by the analysis of AIMD spectra, for which the transverse acoustic mode, if present in that range, is so weak to remain below the detectability threshold. This evident inconsistency with the simulation outcome further undermines the plausibility of a double mode hypothesis for the measured spectral shapes.Finally, data in the inset of Fig. l for longitudinal) and t for transverse) posteriors pertaining to either the Q = 16 To get a more complete picture of the Bayesian inference results, it is worth giving a closer look at Fig. It appears that whenever the probabilistically more grounded model is chosen, best-fit lineshape parameters are determined with a smaller uncertainty, i.e. they have a posterior sharp, unimodal and symmetrical with respect to the mean. Conversely, when the sub-optimal solution is considered, the high frequency mode still preserves a sharp character , yet the position, We have here discussed the results of a Bayesian inferential analysis of inelastic neutron scattering measurements on liquid silver, aiming to unravel a possible coupling of density fluctuations with shear mode propagation. As opposed to other, more popular, fitting approaches, the one considered here delivers not only best-fitting values of lineshape parameters, but also the related probability distributions conditional to the measurement at hand. Furthermore, it provides a minimally invasive or biased interpretation of the spectral shape, as the number of inelastic modes contributing to it is treated in itself as a free model parameter to be optimized on the basis of available experimental data. Most importantly, this method incorporates the Occam razor principle, which, among competing models satisfactorily accounting for some experimental evidence, privileges the one containing the least number of free parameters, whenever more complex models are not adequately justifiable by the available data. Briefly, we believe that the inferential method described here possesses all prerequisites to provide a reliable answer to the topical question this work aims at addressing: does the terahertz spectrum of a liquid metal bear evidence for a high frequency sample rigidity, as revealed by the onset of a shear propagation mode? The outcome of our analysis on liquid gold and silver indicates that an affirmative answer to this question would fall far beyond the accuracy of the measurements carried out so far on these systems. We cannot exclude that some of past literature works on molten metals might have had slightly different results if Bayesian inference had endowed the lineshape modeling with a probabilistic ground, while protecting it from the risk of an overparametrization. On the other hand, the mentioned computer simulations leave open the possibility that a shear mode could be observed in the spectrum of density fluctuations, if more advanced experimental probe and a better statistical accuracy would enable to spot its presence.We sincerely hope that elements of wisdom inherent to Bayesian inferential methods will rapidly spread inside our scientific community, hopefully inspiring new powerful and probabilistically grounded lineshape analysis protocols; after all, this is one of the viable scenarios ensuring our field of research a sustainable future.23, to which we address the interested reader. We remind here that correction of the raw data includes the subtraction of background and container scattering signals as determined by ancillary measurements. Moreover, both the incoherent and the multiple scattering must be evaluated at best and subtracted, in order to obtain the correct double-differential cross section and, from this, the final S. The data points with error bars shown in Fig. As already mentioned, the Bayesian analysis described in this paper has been carried out on a set of experimental data that had been previously obtained by INS on a liquid silver sample. The experimental setup and, even more important, the various steps of the data analysis that are required to extract the wanted dynamic structure factor from the detected raw count rates, have been described in full detail in Ref.Q, E) plane with the small-angle scattering setup required for neutron Brillouin scattering, the incident neutron energy was chosen to be We stress that the experiment was carried out using the thermal-neutron Brillouin spectrometer BRISP, which exploits one of the intense neutron beams of the high-flux reactor of the Institute Laue–Langevin . In order to cover an appropriate region of the (Supplementary Informations.


The marine predators algorithm (MPA) is a novel population-based optimization method that has been widely used in real-world optimization applications. However, MPA can easily fall into a local optimum because of the lack of population diversity in the late stage of optimization. To overcome this shortcoming, this paper proposes an MPA variant with a hybrid estimation distribution algorithm (EDA) and a Gaussian random walk strategy, namely, HEGMPA. The initial population is constructed using cubic mapping to enhance the diversity of individuals in the population. Then, EDA is adapted into MPA to modify the evolutionary direction using the population distribution information, thus improving the convergence performance of the algorithm. In addition, a Gaussian random walk strategy with medium solution is used to help the algorithm get rid of stagnation. The proposed algorithm is verified by simulation using the CEC2014 test suite. Simulation results show that the performance of HEGMPA is more competitive than other comparative algorithms, with significant improvements in terms of convergence accuracy and convergence speed. Solving optimization problems in engineering and scientific research is a common problem. An optimization problem is the process of finding the best value of a decision variable that satisfies the maximum or minimum objective value without violating the constraints. Traditional gradient-based deterministic algorithms show difficulty in solving practical problems . With thOver the past decades, many metaheuristic algorithms have been proposed. These algorithms can be divided into three categories: evolution-based algorithms, physics-based algorithms, and swarm-based algorithms. Evolutionary-based algorithms are a class of algorithms that simulate the laws of evolution in nature. Genetic algorithm (GA)  is a widThe marine predators algorithm (MPA) is a novel population-based natural heuristic optimization algorithm proposed by Faramarzi et al. , which iAlthough MPA has been applied in several fields, there is less analysis and improvement on the shortcomings of MPA. MPA mainly searches near the optimal individuals when performing population position update, without using the effective information of more individuals. The insufficient diversity leads the MPA into a local optimum. The FADs process is designed to enhance the diversity of the population, but it does not determine the superiority of the offspring and the parent, which is not conducive to the optimization and convergence of the algorithm to a certain extent.Currently, there are three main approaches to improve the performance of natural heuristic optimization algorithms. The first is parameter tuning. Tang et al.  used chaThe left part of this paper is organized as follows: A review of the MPA is presented in In this section, the procedure of the basic MPA is presented. MPA is a novel swarm-based metaheuristic algorithm mainly inspired by the different foraging strategies of marine predators and the optimal encounter rate strategy between the predator and prey.Xmin and Xmax denote the upper and lower bounds of the population variables, respectively. r1 ∈  is a random vector obeying a uniform distribution.Similar to most metaheuristics, the initial solution of MPA is distributed as evenly as possible in the search space. The initialization formula is as follows:The MPA search process is divided into three phases based on different speed ratios: (1) a high-speed phase, where the prey speed is faster than the predator speed; (2) a unit speed ratio phase, where the prey speed and the predator speed are similar; and (3) a low-speed phase, where the prey speed is slower than the predator speed. In each stage, the movement of the predator and prey in nature is imitated separately.P is a constant taking the value 5. max denotes the maximum number of iterations.The high-speed phase occurs at the beginning of the iteration, when the prey obeys Brownian motion and the predator performs mainly exploratory behaviour. The mathematical model for this phase is shown as follows:In the second stage, both exploitation and exploration are required, so the stock is divided into two parts. One part is used for exploitation, and the other for exploration. The prey is used for the exploitation process and the predator for the exploration process. The mathematical model of this stage is described as follows:The first part of the population carries out exploitation behaviour.max))max)2 is a uniformly distributed random number. In addition, environmental issues can cause changes in predator behaviour, and fish aggregating devices (FADs) are a factor that affects predator behaviour and are seen as a local optimum in this search area, assuming that the local optimum can be jumped out of by longer steps. The effect of FADs can be expressed mathematically as follows:The basic MPA uses only the best individuals for iterative search, not making full use of valid information from the remaining individuals, resulting in reduced population diversity. The FADs process is performed at each iteration, which increases the computational cost. We use three strategies to improve the performance of the algorithm. Firstly, we take advantage of the good traversal and randomness of chaotic mapping to generate the initial solution of the population and increase the population diversity. Secondly, we use EDA to sample the dominant population information and correct the evolutionary direction. A Gaussian wandering strategy is used to enhance the population diversity when the algorithm stalls, helping the algorithm to jump out of the local optimum. Finally, a greedy strategy is used to ensure that the algorithm converges efficiently.The initial population of most current intelligent optimization algorithms is randomly generated in the search space, and the quality of the initialized population has a great impact on the efficiency of the optimization algorithm. A uniformly distributed population is conducive to expanding the search range and thus improving the convergence speed and accuracy of the algorithm.MPA, like other intelligent algorithms, suffers from a reduction in population diversity late in the iteration when solving complex problems, which can easily fall into local optima leading to premature maturity resulting in poor convergence accuracy. To improve its global search capability and avoid the reduction of population diversity in the postiteration period, the chaos operator is used to initialize the population, considering that it has the characteristics of randomness and regularity and can traverse all states within a certain range without repetition, so the cubic mapping chaos operator is used. The cubic mapping formula is shown as follows:M − 1 individuals using equation (The cubic mapping is used to initialize the prey population by generating a random vector of −1 to 1 in each dimension as the first individual, then iterating over each dimension of the first individual to obtain the remaining equation , and finωi denotes the weight coefficients in the dominant population in the descending order of fitness values. Cov is the weighted covariance matrix of the dominant population.The estimation of distribution algorithm is an algorithm that uses probability models to represent relationships between individuals. EDA has been employed for hybridization with other algorithms and has achieved better results , 46. It A random walk strategy is used to help the algorithm jump out of stagnation and enhance its exploration capabilities when it falls into a local optimum late in the iteration. A stalled algorithm is considered to have stalled if the average fitness of the top half of the dominant population does not change in two consecutive iterations, and the random walk strategy is then used to update the population. The random walk strategy is a probabilistic model that simulates the random movement of organisms in nature and is widely used in the design and improvement of various optimization algorithms. In this paper, we propose a Gaussian random walk strategy for constructing new offspring using a medium population.As the vector of differences between dominant and intermediate populations can improve the diversity of populations, information on intermediate populations is considered in this paper. The sampling points are related to the relative positions of the medium and dominant populations, extending the search range and providing a strong exploration capability. The mathematical model of the strategy is described as follows:At the end of each iteration, HEGMPA used a greedy strategy to retain the best NP individuals in the parent and offspring, thus forming a new population, which facilitated the global convergence ability of HEGMPA. In summary, the flow chart of the improved algorithm proposed in this paper is shown in the following. The pseudo-code for the HEGMPA is shown in To comprehensively validate the performance of the improved algorithms, we first verify the effectiveness of different improvement strategies and then verify the superiority and competitiveness of the improved algorithms by comparing them with recently proposed ones.The CEC2014 test suite contains 30 test functions, which can be divided into four categories of test functions according to different characteristics: F1–F3 for single-peaked functions, F4–F16 for multipeaked functions, F17–F22 for mixed functions, and F23–F30 for combined functions. The definitions and optimal values of the functions are shown in HEGMPA was compared with MPA-1 using cubic mapping to initialize the population, MPA-2 with fused EDA, MPA-3 using a moderately solved Gaussian random wandering strategy, and basic MPA to verify the effectiveness of the different improvement strategies. From To further illustrate the superiority of the improved algorithms, five algorithms, TLMPA, VCS , MMPA 4, CPIJADEThe analysis in To further illustrate the convergence performance of the algorithms, To analyse the distributional properties of the solutions solved by the improved algorithms, box plots were drawn based on the results of 51 independent solutions for each algorithm, as shown in R+” is a positive rank value indicating the extent to which HEGMPA is better than the comparison algorithm and “R−” indicates the opposite result. As can be seen in To avoid chance in testing, this paper uses the Wilcoxon signed-rank test to verify whether the improved algorithms are statistically significantly different from the comparison algorithms. The computational efficiency of the algorithm is also another important aspect in evaluating the performance of the algorithm. In this paper, we propose a variant of MPA, called HEGMPA. The performance of the algorithm is improved using Tent mapping, distribution estimation strategy, and Gaussian random walk. To evaluate the effectiveness of the improved strategy and the superiority of HEGMPA, it was validated using the CEC2014 test suite. It was compared with five state-of-the-art algorithms through numerical analysis, convergence analysis, stability analysis, and statistical tests. The simulation results show that the HEGMPA algorithm balances development and exploration and is competitive with other algorithms. On the other hand, there is still room for improvement in HEGMPA. The effect of initialization of small populations needs to be investigated. The calculation of the covariance matrix increases the computational cost. Therefore, how to reduce the computational cost while maintaining performance is an issue that needs to be further investigated.In future work, we plan to further apply HEGMPA to medical image recognition detection. In addition, we plan to develop a multiobjective version of HEGMPA to address optimization problems in other domains.


Lung cancer is a kind of cancer with high morbidity and mortality which is associated with various gene mutations. Individualized targeted-drug therapy has become the optimized treatment of lung cancer, especially benefit for patients who are not qualified for lung lobectomy. It is crucial to accurately identify mutant genes within tumor region from stained pathological slice. Therefore, we mainly focus on identifying mutant gene of lung cancer by analyzing the pathological images. In this study, we have proposed a method by identifying gene mutations in lung cancer with histopathological stained image and deep learning to predict target-drug therapy, referred to as DeepIMLH. The DeepIMLH algorithm first downloaded 180 hematoxylin-eosin staining (H&E) images of lung cancer from the Cancer Gene Atlas (TCGA). Then deep convolution Gaussian mixture model (DCGMM) was used to perform color normalization. Convolutional neural network (CNN) and residual network (Res-Net) were used to identifying mutated gene from H&E stained imaging and achieved good accuracy. It demonstrated that our method can be used to choose targeted-drug therapy which might be applied to clinical practice. More studies should be conducted though. Lung cancer has the highest morbidity and mortality worldwide, and it became the main cause of death in China, especially for males . AccordiAlthough many techniques are approved to have significant advantages on diagnostic imaging, visual inspection of histological stained slice is still considered as “gold method” for tumor diagnosis. But, the diagnostic accuracy and treatment plan generally on the basis of the results of biopsy study. It requires well-experienced pathologists who can confidently identify the changes of cell morphology and corresponding tumor stage of lung cancer by visual inspection of pathological images , 17. CurDeep learning means have been used in the medical field for lots of years , which cCurrently, there are different types of cancer therapy, which range from the traditional radio-logical and broad spectrum chemotherapy, to targeted-drug therapy. “Target therapy” is to apply advanced technology to accurately deliver drugs to the tumor region in order to specifically eliminate malignant cells without damaging normal tissue cells. The basis of “target therapy” is aiming to design an individualized treatment plan targeting to specific malignant cells by applying current knowledge of cancer biology and pathogenesis at the cellular and molecular levels. Therefore, it is necessary to develop novel machine learning methods for diagnosis and design treatment plan which might increase the efficiency, accuracy, and consistency of diagnosis.This paper aimed to predict the mutated genes which are potential candidates for targeted-drug therapy by developing a novel algorithm according to convolutional neural network for lung cancer. In this study, we used hematoxylin-eosin (H&E) stained pathological slice of lung cancer which were downloaded from the TCGA, thereby, deep convolution Gaussian mixture model DCGMM was used to perform color normalization. Convolutional neural network (CNN) and residual network (Res-Net) were employed for training data. The average probability of the bio-markers of lung cancer was received through the model, with the highest accuracy rate of the MET which was reached 86.3%. It provided an approach to develop effective targeted therapy on basis of mutant genes of lung cancer, however, it need further studies to evaluate the effectiveness and reliability of designed model before applying to clinical practice.https://portal.gdc.cancer.gov/repository/) as our data set. Then we used cBioportal  to download H&E image SNP data, Cancer Genomics Portal provides a visualization tool for analyzing of cancer gene data. cBioPort was used to perform molecular and cytological studies for genetic, epigenetic, gene expression, and proteomics research. The clinical data of H&E image lung cancer patients were downloaded from the International Cancer Genome Collaborative Group (ICGC) (https://dcc.icgc.org/).We downloaded H&E histopathology images of lung cancer from the Cancer Genome Atlas (TCGA)  of lung cancers which were downloaded from the TCGA, as show in H&E staining is a commonly used staining technique which are widely used in the tumor diagnosis and staging. However, this method might subject to inconsistent color fixing due to specimen preparation standard, staining technique, H&E reagents, the thickness of section, etc. The color difference of image is one of the most important factors in the training process of the CNN. Therefore, unsupervised deep convolution Gaussian mixture model (DCGMM) was applied to standardize the color of H&E stained slices.In order to evaluate the efficiency of trained by DCGMM, these images should have consistent colors and unchanged features such as morphology, pixels, and structure after training, as show in In order to identify the bio-markers of lung cancer H&E stains, we used Tensorflow 2.0.0 software package to train the convolutional neural network model. The convolutional neural network can use back propagation to adjust the parameters of the convolutional neural network, extract the features of the image, and classify the images according to the extracted features. This is an effective gradient descent algorithm that can automatically update the weights during training.We first input the processed lung cancer H&E stain slides and bio-markers to the input layer of the deep convolutional neural network, and then output them to the convolutional layer to extract image features. The convolutional layer is composed of 32 n*n convolution kernels. Secondly, enter the excitation layer containing the ReLu excitation function, and then enter the next hidden layers until all the features of the H&E stained slice are extracted. In order to improve the generalization ability of the network and accelerate the training of higher learning rates, we add a batch normalization layer to the convolutional neural network. However, this will increase the depth of the convolutional neural network, and cause the problem of gradient disappearance, which will slow down network training speed and classification accuracy. So we introduced a residual network with jump connections to solve the above problems. In addition, the optimization function and loss function used in the convolutional neural network are “adam” and “sparse categorical cross entropy” respectively. The output in here are slides with characteristics of different lung cancer bio-markers for targeted therapy.In order to generate the heat map, we firstly scanned the whole slide images with 512*512 slicing windows of lung cancer bio-markers. Then the results of each slides were obtained through the CNN + Res-Net model by applying pixels of sliding windows. Moreover all the values of passed pixels were summed and calculate their average as bio-marker probability of targeted therapy for lung cancer. We used probability visualization to convert the probability of targeted therapeutic markers of pixels in to color values. The probability value was mapped in the range of  to RGB color from pure blue color  to pure red color  linearly. Therefore the red color in the heat map indicated the higher the probability of bio-marker appearance, the blue color indicated lower the probability of bio-markers appearance. A WSI has multiple tiles, and each tile can predict corresponding result probability by the model. We integrate the results of all tiles through the fusion algorithm to obtain the final probability result of the corresponding WSI. Define the average probability of the first n windows as the recognition score. Predict the occurrence probability of lung cancer bio-markers by setting critical thresholds. Among them, those higher than the threshold are considered positive, otherwise they are considered negative. We use the highest value as a hyper-parameter and determined by cross-validation. The hyper-parameters of model were determined by providing hyper-parameter dictionary with using the Grid-Search-CV class in scikit-learn. The resulting heat map is shown in In order to calculate the average probability of different bio-markers from lung cancer H&E full slices, we firstly downloaded 180 lung cancer H&E stained whole slide images from TCGA. The clinical characteristics of the patients were shown in By using the DeepIMLH model, we can get the average probability of different bio-markers from 180 lung cancer H&E stained slice. The AUC value of the lung cancer bio-markers in this study was the average probability of each bio-marker on the lung cancer H&E stained full slice image. The ROC curve of each bio-marker was shown in As shown in in vitro and in vivo models with FGFR mutations, moreover, other studies also chose FGFRs as target for anticancer medical therapy. For an example, multiple kinase FGFR/vascular endothelial growth factor receptor (VEGR) inhibitor gained the promising results in breast cancer with FGFR/FGFR3 amplification  is an unsupervised clustering algorithm which is based on the Gaussian mixture algorithm combined with a deep convolution network. The Gaussian mixture algorithm means a probability distribution algorithm with the below form:k is the weight coefficient of each Gaussian distribution function, also known as the mixing coefficient, must satisfy 0≤ αk ≤1 and ϕ(y|θk) is the density of Gaussian distribution, and th sub-model.Here, αGaussian Mixture Model (GMM) is widely used in many cases, moreover the expectation maximization (EM) algorithm is an effective method to learn the parameters in GMM. GMM is divided into two steps similar to K-means:i, the probability generated by the k-th sub-model  isStep E: Estimate the probability which is generated by each sub-model. For each data xStep M: Based on the maximum likelihood estimation.kπ can also be estimated as Nk/N.Where From formula (1), the natural log-likelihood function could be represented as1, y2,…, yM}). Given GMM, the goal is finding targeted parameters . A common approach is using an EM algorithm to iteratively evaluate responsibilities [formula (3)] and re-estimate the parameters.Here M is the total count of pixels in the input picture  combines the Gaussian Mixture Model (GMM) into the color allocation of the image through the high image representation ability of the Convolutional Neural Network (CNN) to perform the color normalization of the image. We use convolutional neural networks to estimate the liability coefficient. Then the parameters of DCGMM are optimized by gradient descent method and log-likelihood function (Equation 5). In fact, DCGMM first replaces the E step in the EM algorithm with a convolutional neural network, and then uses the existing responsibility parameter estimation to estimate the θ and Σ of the multivariate Gaussian distribution like the M step in the EM algorithm. Finally, the training of DCGMM is mainly carried out through gradient descent method and back propagation.Previous studies have shown that Convolutional Neural Networks (CNN) is the leading deep learning method for tumor diagnosis. The earliest application of neural network was a multilayer perceptron (MLP) with multiple levels of conversion. The traditional neural network contains input layer, hidden layers, and the output layer, and if it includes multiple hidden layers, it is known as a “deep neural network” . A complSince the significance of the neural network studying process is to study the data allocation, once the apportion of training data is inconsistent to the test data, the generalization capacity of the network will sharply decrease. In addition, once the apportion of each heap of training data is inconsistent, the network must study to fit the inconsistent allocations in each iteration, that will significantly decrease the training rate of the network. Once the neural network starts training, the parameters will be changed. In addition to the input layer, the input data allocation of every layer of the subsequent network has been changed. During the training process, the updated of the training parameters from the former layer will cause the changes of input data in the latter layer. Although stochastic gradient descent (SGD) is simple and effective for training deep networks, it requires human settings and wastes time to adjust parameters for instance learning rate, weight attenuation coefficient, parameter initialization, dropout ratio, etc. . Moreovek] is supposed to the mean value of every batch of training data neurons xk, and the denominator is the standard deviation of the activation level of every batch of data neurons xk.Where, E. If we add two more layers to initial network, the ultimate output result will be B[l + 2]. The two layers could become a residual module. The ReLU activation function is used throughout the network, and any activation values are bigger than or equal to 0. For big networks, whether the residual block is jointed to the middle or the end of the neural network will not influence the property of the network, and these residual blocks are relatively easy to learn the identity function. Moreover, they could increase the learning efficiency. As the activation function of the neuron, Relu defines the nonlinear output of the neuron after linear transformation wvia plotting the true positive rate (TPR) and false positive rate (FPR) under kinds of threshold putting, which is, the bight generated with FPR as the x axis and TPR as the y axis. The true positive rate (TPR) is also called sensitivity, that is the ratio of all actual positive samples that are exactly recognized as positive. Its expression is the same as expression of recall rate. The false positive rate (FPR) is also called specificity, which is the ratio of negative samples that are falsely identified as positive in actual negative samples. The strict mathematical definition is as follows:There are many ways to calculate the property of the model. Generally, the performance of the model is measured by the accuracy, recall, accuracy and F1 score, and the curve (AUC) under the receiver operating characteristics (ROC). This study used precision measurement receiver operating characteristics (ROC) to estimate the performance of the CNN model. The ROC curve was drawn Here, true positive (TP) is the count of samples that are forecast as positive and actually are positive, false positive (FP) is the count of samples that are forecast as positive and actually are negative. True negative (TN) is the count of samples that are forecast to be negative and really negative. False negative (FN) is the count of samples that are forecast to be negative and really is positive.From the definition of FPR and TPR, it indicates the near the drawn ROC curve is to the upper left, the result is better. From a geometric angle of observe, with the bigger the region under the ROC curve, it indicates better model. Therefore, we used the area under the ROC curve, which is, AUC (Area Under Curve) value to measure performance of the model .In order to conduct the reliable) and stable of CNN model, we used 2-fold cross-validation to increase the accuracy of the CNN algorithm by adjusting the hyper-parameters of the algorithm to gain the best scores. We split the data into two subsets, and one set was used as the training set to train data by CNN algorithm, and the other was used as a test set to predict the trained algorithm, thereby to find the error of the sample prediction, and summarize their squares afterwards. The above process was performed repeatedly until all samples were exactly predicted.The hyper-parameters were adjusted which primarily included the number of filter cores, sample size, number of layers, and loss function of the CNN algorithm. For the adjustment of hyper-parameters, we firstly determined the activated function as Relu according to its mechanism, and determined the type of loss function and weight initialization afterward, and encoded method of the “output layer.” Secondly, according to the “broad strategy,” a simple structure was previously constructed to determine the number of “hidden layers” in the neural network and the number of neurons in each “hidden layer.” Thereby for the remaining hyper-parameters, we randomly selected a possible value, in order to adjust the learning rate without considering the regular terms in the loss function to reach a relatively appropriate threshold for the learning rate, then selected half of the threshold as the initial value. Then determine the size of the small batch of samples through experiments. Use the determined learning rate and verification data to select appropriate regularization parameters, and then return to re-optimize the learning rate. The overall observation of these experiments can determine learning rounds.The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.BL and WZ conceived the concept of the work; KH, YY, and ZM collected or analyzed the data; KH performed literature search and designed the experiments; KH, and ZM wrote the paper; KH and F-XW modified and reviewed the manuscript. All authors contributed to the article and approved the submitted version. This work was supported by the National Nature Science Foundation of China , Natural Science Foundation of Hainan, China (Grant Nos. 119MS036), and 2019 Hainan Province Graduate Innovative Scientific Research Project (Hys2019-265).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.