Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees

Identification of subgroups of patients for whom treatment A is more effective than treatment B, and vice versa, is of key importance to the development of personalized medicine. Tree-based algorithms are helpful tools for the detection of such interactions, but none of the available algorithms allow for taking into account clustered or nested dataset structures, which are particularly common in psychological research. Therefore, we propose the generalized linear mixed-effects model tree (GLMM tree) algorithm, which allows for the detection of treatment-subgroup interactions, while accounting for the clustered structure of a dataset. The algorithm uses model-based recursive partitioning to detect treatment-subgroup interactions, and a GLMM to estimate the random-effects parameters. In a simulation study, GLMM trees show higher accuracy in recovering treatment-subgroup interactions, higher predictive accuracy, and lower type II error rates than linear-model-based recursive partitioning and mixed-effects regression trees. Also, GLMM trees show somewhat higher predictive accuracy than linear mixed-effects models with pre-specified interaction effects, on average. We illustrate the application of GLMM trees on an individual patient-level data meta-analysis on treatments for depression. We conclude that GLMM trees are a promising exploratory tool for the detection of treatment-subgroup interactions in clustered datasets.Article / Letter to editorInstituut Psychologi

Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees

Identification of subgroups of patients for whom treatment A is more effective than treatment B, and vice versa, is of key importance to the development of personalized medicine. Tree-based algorithms are helpful tools for the detection of such interactions, but none of the available algorithms allow for taking into account clustered or nested dataset structures, which are particularly common in psychological research. Therefore, we propose the generalized linear mixed-effects model tree (GLMM tree) algorithm, which allows for the detection of treatment-subgroup interactions, while accounting for the clustered structure of a dataset. The algorithm uses model-based recursive partitioning to detect treatment-subgroup interactions, and a GLMM to estimate the random-effects parameters. In a simulation study, GLMM trees show higher accuracy in recovering treatment-subgroup interactions, higher predictive accuracy, and lower type II error rates than linear-model-based recursive partitioning and mixed-effects regression trees. Also, GLMM trees show somewhat higher predictive accuracy than linear mixed-effects models with pre-specified interaction effects, on average. We illustrate the application of GLMM trees on an individual patient-level data meta-analysis on treatments for depression. We conclude that GLMM trees are a promising exploratory tool for the detection of treatment-subgroup interactions in clustered datasets.Multivariate analysis of psychological dat

Bias in random forest variable importance measures: Illustrations, sources and a solution

BACKGROUND: Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories. RESULTS: Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand. CONCLUSION: We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and documented thoroughly in an application re-analyzing data from a study on RNA editing. Therefore the suggested method can be applied straightforwardly by scientists in bioinformatics research

Conditional variable importance for random forests

Random forests are becoming increasingly popular in many scientific fields because they can cope with ``small n large p'' problems, complex interactions and even highly correlated predictor variables. Their variable importance measures have recently been suggested as screening tools for, e.g., gene expression studies. However, these variable importance measures show a bias towards correlated predictor variables. We identify two mechanisms responsible for this finding: (i) A preference for the selection of correlated predictors in the tree building process and (ii) an additional advantage for correlated predictor variables induced by the unconditional permutation scheme that is employed in the computation of the variable importance measure. Based on these considerations we develop a new, conditional permutation scheme for the computation of the variable importance measure. The resulting conditional variable importance is shown to reflect the true impact of each predictor variable more reliably than the original marginal approach

A rare exception to Haldane's rule: are X chromosomes key to hybrid incompatibilities?

This work was funded by NERC (NE/G014906/1, NE/L011255/1, NE/I027800/1). Additional funding from the Orthopterists’ Society to PM is also gratefully acknowledged.The prevalence of Haldane’s rule suggests that sex chromosomes commonly have a key role in reproductive barriers and speciation. However, the majority of research on Haldane’s rule has been conducted in species with conventional sex determination systems (XY and ZW) and exceptions to the rule have been understudied. Here we test the role of X-linked incompatibilities in a rare exception to Haldane’s rule for female sterility in field cricket sister species (Teleogryllus oceanicus and T. commodus). Both have an XO sex determination system. Using three generations of crosses, we introgressed X chromosomes from each species onto different, mixed genomic backgrounds to test predictions about the fertility and viability of each cross type. We predicted that females with two different species X chromosomes would suffer reduced fertility and viability compared with females with two parental X chromosomes. However, we found no strong support for such X-linked incompatibilities. Our results preclude X–X incompatibilities and instead support an interchromosomal epistatic basis to hybrid female sterility. We discuss the broader implications of these findings, principally whether deviations from Haldane’s rule might be more prevalent in species without dimorphic sex chromosomes.PostprintPeer reviewe

Alumni giving at a small liberal arts college: evidence from consistent and occasional donors

Conditioning on the observed data is an important and flexible design principle for statistical test procedures. Although generally applicable, permutation tests currently in use are limited to the treatment of special cases, such as contingency tables or K-sample problems. A new theoretical framework for permutation tests opens up the way to a unified and generalized view. We argue that the transfer of such a theory to practical data analysis has important implications in many applications and requires tools that enable the data analyst to compute on the theoretical concepts as closely as possible. We re-analyze four data sets by adapting the general conceptual framework to these non-standard inference procedures and utilizing the coin add-on package in the R system for statistical computing to show what one can gain from going beyond the `classical' test procedures.Series: Research Report Series / Department of Statistics and Mathematic

Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees

Identification of subgroups of patients for whom treatment A is more effective than treatment B, and vice versa, is of key importance to the development of personalized medicine. Tree-based algorithms are helpful tools for the detection of such interactions, but none of the available algorithms allow for taking into account clustered or nested dataset structures, which are particularly common in psychological research. Therefore, we propose the generalized linear mixed-effects model tree (GLMM tree) algorithm, which allows for the detection of treatment-subgroup interactions, while accounting for the clustered structure of a dataset. The algorithm uses model-based recursive partitioning to detect treatment-subgroup interactions, and a GLMM to estimate the random-effects parameters. In a simulation study, GLMM trees show higher accuracy in recovering treatment-subgroup interactions, higher predictive accuracy, and lower type II error rates than linear-model-based recursive partitioning and mixed-effects regression trees. Also, GLMM trees show somewhat higher predictive accuracy than linear mixed-effects models with pre-specified interaction effects, on average. We illustrate the application of GLMM trees on an individual patient-level data meta-analysis on treatments for depression. We conclude that GLMM trees are a promising exploratory tool for the detection of treatment-subgroup interactions in clustered datasets