Permutation Testing for Treatment-Covariate Interactions and Subgroup Identification

Modern approaches for evaluating treatment effect heterogeneity from clinical trials and observational data

In this paper, we review recent advances in statistical methods for the evaluation of the heterogeneity of treatment effects (HTE), including subgroup identification and estimation of individualized treatment regimens, from randomized clinical trials and observational studies. We identify several types of approaches using the features introduced in Lipkovich et al (Stat Med 2017;36: 136-196) that distinguish the recommended principled methods from basic methods for HTE evaluation that typically rely on rules of thumb and general guidelines (the methods are often referred to as common practices). We discuss the advantages and disadvantages of various principled methods as well as common measures for evaluating their performance. We use simulated data and a case study based on a historical clinical trial to illustrate several new approaches to HTE evaluation.

A permutation procedure to detect heterogeneous treatment effects in randomized clinical trials while controlling the type I error rate

BACKGROUND/AIMS

Secondary analyses of randomized clinical trials often seek to identify subgroups with differential treatment effects. These discoveries can help guide individual treatment decisions based on patient characteristics and identify populations for which additional treatments are needed. Traditional analyses require researchers to pre-specify potential subgroups to reduce the risk of reporting spurious results. There is a need for methods that can detect such subgroups without a priori specification while allowing researchers to control the probability of falsely detecting heterogeneous subgroups when treatment effects are uniform across the study population.

METHODS

We propose a permutation procedure for tuning parameter selection that allows for type I error control when testing for heterogeneous treatment effects framed within the Virtual Twins procedure for subgroup identification. We verify that the type I error rate can be controlled at the nominal rate and investigate the power for detecting heterogeneous effects when present through extensive simulation studies. We apply our method to a secondary analysis of data from a randomized trial of very low nicotine content cigarettes.

RESULTS

In the absence of type I error control, the observed type I error rate for Virtual Twins was between 99% and 100%. In contrast, models tuned via the proposed permutation were able to control the type I error rate and detect heterogeneous effects when present. An application of our approach to a recently completed trial of very low nicotine content cigarettes identified several variables with potentially heterogeneous treatment effects.

CONCLUSIONS

The proposed permutation procedure allows researchers to engage in secondary analyses of clinical trials for treatment effect heterogeneity while maintaining the type I error rate without pre-specifying subgroups.

A permutation test for assessing the presence of individual differences in treatment effects

An important goal of personalized medicine is to identify heterogeneity in treatment effects and then use that heterogeneity to target the intervention to those most likely to benefit. Heterogeneity is assessed using the predicted individual treatment effects framework, and a permutation test is proposed to establish if significant heterogeneity is present given the covariates and predictive model or algorithm used for predicted individual treatment effects. We first show evidence for heterogeneity in the effects of treatment across an illustrative example data set. We then use simulations with two different predictive methods (linear regression model and Random Forests) to show that the permutation test has adequate type-I error control. Next, we use an example dataset as the basis for simulations to demonstrate the ability of the permutation test to find heterogeneity in treatment effects for a predicted individual treatment effects estimate as a function of both effect size and sample size. We find that the proposed test has good power for detecting heterogeneity in treatment effects when the heterogeneity was due primarily to a single predictor, or when it was spread across the predictors. Power was found to be greater for predictions from a linear model than from random forests. This non-parametric permutation test can be used to test for significant differences across individuals in predicted individual treatment effects obtained with a given set of covariates using any predictive method with no additional assumptions.

Developing and testing high‐efficacy patient subgroups within a clinical trial using risk scores

There is the potential for high-dimensional information about patients collected in clinical trials (such as genomic, imaging, and data from wearable technologies) to be informative for the efficacy of a new treatment in situations where only a subset of patients benefits from the treatment. The adaptive signature design (ASD) method has been proposed for developing and testing the efficacy of a treatment in a high-efficacy patient group (the sensitive group) using genetic data. The method requires selection of three tuning parameters which may be highly computationally expensive. We propose a variation to the ASD method, the cross-validated risk scores (CVRS) design method, that does not require selection of any tuning parameters. The method is based on computing a risk score for each patient and dividing them into clusters using a nonparametric clustering procedure.We assess the properties of CVRS against the originally proposed cross-validated ASD using simulation data and a real psychiatry trial. CVRS, as assessed for various sample sizes and response rates, has a substantial reduction in the computational time required. In many simulation scenarios, there is a substantial improvement in the ability to correctly identify the sensitive group and the power of the design to detect a treatment effect in the sensitive group.We illustrate the application of the CVRS method on the psychiatry trial.

Studying treatment-effect heterogeneity in precision medicine through induced subgroups

Precision medicine, in the sense of tailoring the choice of medical treatment to patients' pretreatment characteristics, is nowadays gaining a lot of attention. Preferably, this tailoring should be realized in an evidence-based way, with key evidence in this regard pertaining to subgroups of patients that respond differentially to treatment (i.e., to subgroups involved in treatment-subgroup interactions). Often a-priori hypotheses on subgroups involved in treatment-subgroup interactions are lacking or are incomplete at best. Therefore, methods are needed that can induce such subgroups from empirical data on treatment effectiveness in a post hoc manner. Recently, quite a few such methods have been developed. So far, however, there is little empirical experience in their usage. This may be problematic for medical statisticians and statistically minded medical researchers, as many (nontrivial) choices have to be made during the data-analytic process. The main purpose of this paper is to discuss the major concepts and considerations when using these methods. This discussion will be based on a systematic, conceptual, and technical analysis of the type of research questions at play, and of the type of data that the methods can handle along with the available software, and a review of available empirical evidence. We will illustrate all this with the analysis of a dataset comparing several anti-depressant treatments.

Metabolomics identifies metabolite biomarkers associated with acute rejection after heart transplantation in rats

The aim of this study was to identify metabolite biomarkers associated with acute rejection after heart transplantation in rats using a LC-MS-based metabolomics approach. A model of heterotopic cardiac xenotransplantation was established in rats, with Wistar rats as donors and SD rats as recipients. Blood and cardiac samples were collected from blank control rats (Group A), rats 5 (Group B) and 7 days (Group C) after heart transplantation, and pretreated rats 5 (Group D) and 7 days (Group E) post-transplantation for pathological and metabolomics analyses. We assessed International Society for Heart and Lung Transplantation (ISHLT) grades 0, 3B, 4, 1 and 1 rejection in groups A to E. There were 15 differential metabolites between groups A and B, 14 differential metabolites between groups A and C, and 10 differential metabolites between groups B and C. In addition, four common differential metabolites, including D-tagatose, choline, C16 sphinganine and D-glutamine, were identified between on days 5 and 7 post-transplantation. Our findings demonstrate that the panel of D-tagatose, choline, C16 sphinganine and D-glutamine exhibits a high sensitivity and specificity for the early diagnosis of acute rejection after heart transplantation, and LC-MS-based metabolomics approach has a potential value for screening post-transplantation biomarkers.