With an increasing focus on precision medicine in medical research, numerous studies have been conducted in recent years to clarify the relationship between treatment effects and patient characteristics. The treatment effects for patients with different characteristics are always heterogeneous, and various heterogeneous treatment effect machine learning estimation methods have been proposed owing to their flexibility and high prediction accuracy. However, most machine learning methods rely on black-box models, preventing direct interpretation of the relationship between patient characteristics and treatment effects. Moreover, most of these studies have focused on continuous or binary outcomes, although survival outcomes are also important in medical research. To address these challenges, we propose a heterogeneous treatment effect estimation method for survival data based on RuleFit, an interpretable machine learning method. Numerical simulation results confirmed that the prediction performance of the proposed method was comparable to that of existing methods. We also applied a dataset from an HIV study, the AIDS Clinical Trials Group Protocol 175 dataset, to illustrate the interpretability of the proposed method using real data. Consequently, the proposed method established an interpretable model with sufficient prediction accuracy.
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We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a stabilisation of the sample. While a maximum likelihood estimate (MLE) may not exist or be unique given sample data, it is always unique given a stabilisation. We relate the MLE given a stabilisation to the MLE given original sample data, when one exists, providing necessary and sufficient conditions for the MLE given a stabilisation to be one given the original sample. For linear regression models, we show that the MLE given any stabilisation is the minimal norm choice among the MLEs given an original sample. We show that the MLE has a well-defined limit as the stabilisation of a sample tends to the original sample, and that the limit is an MLE given the original sample, when one exists. Finally, we study which MLEs given a sample can arise as such limits. We reduce this to a question regarding the non-emptiness of certain algebraic varieties.
Batch effects are pervasive in biomedical studies. One approach to address the batch effects is repeatedly measuring a subset of samples in each batch. These remeasured samples are used to estimate and correct the batch effects. However, rigorous statistical methods for batch effect correction with remeasured samples are severely under-developed. In this study, we developed a framework for batch effect correction using remeasured samples in highly confounded case-control studies. We provided theoretical analyses of the proposed procedure, evaluated its power characteristics, and provided a power calculation tool to aid in the study design. We found that the number of samples that need to be remeasured depends strongly on the between-batch correlation. When the correlation is high, remeasuring a small subset of samples is possible to rescue most of the power.
In biomedical applications it is often necessary to estimate a physiological response to a treatment consisting of multiple components, and learn the separate effects of the components in addition to the joint effect. Here, we extend existing probabilistic nonparametric approaches to explicitly address this problem. We also develop a new convolution-based model for composite treatment-response curves that is more biologically interpretable. We validate our models by estimating the impact of carbohydrate and fat in meals on blood glucose. By differentiating treatment components, incorporating their dosages, and sharing statistical information across patients via a hierarchical multi-output Gaussian process, our method improves prediction accuracy over existing approaches, and allows us to interpret the different effects of carbohydrates and fat on the overall glucose response.
Validity problems in clinical machine learning by indirect data labeling using consensus definitions
We demonstrate a validity problem of machine learning in the vital application area of disease diagnosis in medicine. It arises when target labels in training data are determined by an indirect measurement, and the fundamental measurements needed to determine this indirect measurement are included in the input data representation. Machine learning models trained on this data will learn nothing else but to exactly reconstruct the known target definition. Such models show perfect performance on similarly constructed test data but will fail catastrophically on real-world examples where the defining fundamental measurements are not or only incompletely available. We present a general procedure allowing identification of problematic datasets and black-box machine learning models trained on them, and exemplify our detection procedure on the task of early prediction of sepsis.
The use of the non-parametric Restricted Mean Survival Time endpoint (RMST) has grown in popularity as trialists look to analyse time-to-event outcomes without the restrictions of the proportional hazards assumption. In this paper, we evaluate the power and type I error rate of the parametric and non-parametric RMST estimators when treatment effect is explained by multiple covariates, including an interaction term. Utilising the RMST estimator in this way allows the combined treatment effect to be summarised as a one-dimensional estimator, which is evaluated using a one-sided hypothesis Z-test. The estimators are either fully specified or misspecified, both in terms of unaccounted covariates or misspecified knot points (where trials exhibit crossing survival curves). A placebo-controlled trial of Gamma interferon is used as a motivating example to simulate associated survival times. When correctly specified, the parametric RMST estimator has the greatest power, regardless of the time of analysis. The misspecified RMST estimator generally performs similarly when covariates mirror those of the fitted case study dataset. However, as the magnitude of the unaccounted covariate increases, the associated power of the estimator decreases. In all cases, the non-parametric RMST estimator has the lowest power, and power remains very reliant on the time of analysis (with a later analysis time correlated with greater power).
The synthesis of information deriving from complex networks is a topic receiving increasing relevance in ecology and environmental sciences. In particular, the aggregation of multilayer networks, i.e. network structures formed by multiple interacting networks (the layers), constitutes a fast-growing field. In several environmental applications, the layers of a multilayer network are modelled as a collection of similarity matrices describing how similar pairs of biological entities are, based on different types of features (e.g. biological traits). The present paper first discusses two main techniques for combining the multi-layered information into a single network (the so-called monoplex), i.e. Similarity Network Fusion (SNF) and Similarity Matrix Average (SMA). Then, the effectiveness of the two methods is tested on a real-world dataset of the relative abundance of microbial species in the ecosystems of nine glaciers (four glaciers in the Alps and five in the Andes). A preliminary clustering analysis on the monoplexes obtained with different methods shows the emergence of a tightly connected community formed by species that are typical of cryoconite holes worldwide. Moreover, the weights assigned to different layers by the SMA algorithm suggest that two large South American glaciers (Exploradores and Perito Moreno) are structurally different from the smaller glaciers in both Europe and South America. Overall, these results highlight the importance of integration methods in the discovery of the underlying organizational structure of biological entities in multilayer ecological networks.
This paper investigates the multiple testing problem for high-dimensional sparse binary sequences, motivated by the crowdsourcing problem in machine learning. We study the empirical Bayes approach for multiple testing on the high-dimensional Bernoulli model with a conjugate spike and uniform slab prior. We first show that the hard thresholding rule deduced from the posterior distribution is suboptimal. Consequently, the $\ell$-value procedure constructed using this posterior tends to be overly conservative in estimating the false discovery rate (FDR). We then propose two new procedures based on $\adj\ell$-values and $q$-values to correct this issue. Sharp frequentist theoretical results are obtained, demonstrating that both procedures can effectively control the FDR under sparsity. Numerical experiments are conducted to validate our theory in finite samples. To our best knowledge, this work provides the first uniform FDR control result in multiple testing for high-dimensional sparse binary data.
In prediction settings where data are collected over time, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories. These measures can be estimated and the same approaches for inference can be applied regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics, and we illustrate their use by investigating the longitudinal importance of risk factors for suicide attempt.
Individualized treatment rules (ITRs) for treatment recommendation is an important topic for precision medicine as not all beneficial treatments work well for all individuals. Interpretability is a desirable property of ITRs, as it helps practitioners make sense of treatment decisions, yet there is a need for ITRs to be flexible to effectively model complex biomedical data for treatment decision making. Many ITR approaches either focus on linear ITRs, which may perform poorly when true optimal ITRs are nonlinear, or black-box nonlinear ITRs, which may be hard to interpret and can be overly complex. This dilemma indicates a tension between interpretability and accuracy of treatment decisions. Here we propose an additive model-based nonlinear ITR learning method that balances interpretability and flexibility of the ITR. Our approach aims to strike this balance by allowing both linear and nonlinear terms of the covariates in the final ITR. Our approach is parsimonious in that the nonlinear term is included in the final ITR only when it substantially improves the ITR performance. To prevent overfitting, we combine cross-fitting and a specialized information criterion for model selection. Through extensive simulations, we show that our methods are data-adaptive to the degree of nonlinearity and can favorably balance ITR interpretability and flexibility. We further demonstrate the robust performance of our methods with an application to a cancer drug sensitive study.
Evidence of a global trend in dose-response dependencies is commonly used in bio-medicine and epidemiology, especially because this represents a causality criterion. However, conventional trend tests indicate a significant trend even when dependence is in the opposite direction for low doses when the high dose alone has a superior effect. Here we present a trend test for a strictly monotonic increasing (or decreasing) trend, evaluate selected sample data for it, and provide corresponding R code using CRAN packages.
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