Randomization-based nonparametric methods for the analysis of multicentre trials

Abstract

Multicentre trials offer several advantages over single centre trials in clinical research, including the ability to recruit patients at a faster rate over the course of the study, increased generalizability through the use of a broader patient population, and the ability to shed light on the replication of findings at multiple centres in a single study. A nonparametric approach to the analysis of multicentre trial data provides a convenient way for addressing the role of centres as well as baseline covariables during data analysis. With the use of randomization-based nonparametric methods, the strategy for evaluating the null hypothesis of no treatment effect can be prespecified during study planning without requiring a specific structure for the relationship of response criteria (or endpoints) to centres, covariables, or potential interaction terms. Further, the basis of inference for the application of these methods is the randomization mechanism, and the population to which inference can be directly made is the study population itself. No assumptions about underlying distributions, data structures, likelihood functions, or samples from super populations of inference are required. A three-step approach is proposed for handling centres via randomization-based nonparametric methods. In Step 1, a test of overall treatment effect is carried out using data from all centres simultaneously, without any assumption about treatment by centre interaction. In Step 2, the question of treatment by centre interaction is addressed, usually through the use of parametric multiple regression methods. In cases with suggestion of such interaction, Step 3 is conducted to evaluate different weighting schemes in forming pairwise treatment comparisons averaged across centres to assess the robustness of treatment effects observed in Step 1. An attractive inferential feature of this three-step approach is that the Type I error for the test of treatment effect is controlled by requiring statistical significance at each step to proceed to the next step. Extended Mantel-Haenszel methods with stratification adjustment for centre can be used to provide a nonparametric assessment of treatment effect. When adjustment for other covariates, such as baseline values, is desired, the more recent nonparametric analysis of covariance methods are available. Both methods are easy to use, require no assumptions beyond that of a valid randomization mechanism, and can be applied in a similar manner to dichotomous, ordinal, failure time, or continuous response criteria (endpoints). The methods are illustrated using data from a confirmatory clinical trial of a therapeutic agent for the treatment of dry eye disease.

Davunetide in patients with progressive supranuclear palsy: a randomised, double-blind, placebo-controlled phase 2/3 trial

“…Using these ranks, a stratified rank test was performed through the use of a permutation test with strata formed by the randomization strata as described. 22 For the CSF analyses, 52 week change from baseline values were compared between treatment groups using a Wilcoxon test. Since no treatment-related differences were identified, data were combined for Spearman correlations with clinical and imaging variables.…”

Randomization inference for treatment effects on a binary outcome

“…In addition to randomization, this approach relies on one particular key assumption, namely that the effect of treatment is additive, i.e., the same for all individuals. Additivity is a strong assumption that may not hold in many settings, particularly if the outcome is binary [2]. In this paper, two methods are developed for constructing randomization based confidence sets for the average effect of treatment on a binary outcome without assuming additivity.…”

Stratified Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment

“…Since g g g would be expected to be null on the basis of randomization of patients to the two groups, randomization-based covariance adjustment of ξ ξ ξ is possible by fitting the model P P P = [I I I r , 0 0 0 rM ] to f f f by weighted least squares; see Koch et al (1998) andLaVange et al (2005). The resulting adjusted counterpart…”

“…However, the power of the van Elteren test statistic can have limitations when the sample sizes within the strata are relatively small (e.g., < 6), and so the number of factors for stratification usually cannot exceed three. For this reason, other baseline factors for adjustment under minimal assumptions need management by randomization-based covariance methods, as reviewed in LaVange, Durham, and Koch (2005). These methods have essentially no assumptions through the invocation of constraints for no differences between treatments for means of covariables (as an implied consequence of randomization).…”