Extensions of nonparametric randomization-based analysis of covariance

Hussey, Michael

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March 19, 2019

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Hussey, Michael
- Affiliation: Gillings School of Global Public Health, Department of Biostatistics

Abstract

Nonparametric Randomization-Based Analysis of Covariance (Koch et. al. (1998)) provides covariate-adjusted estimates of treatment effects for randomized clinical trials. It has application in the regulatory setting where analyses are specified a priori, and any statistical assumptions of parametric methods are not verifiable until after data collection. Using (1) a vector containing differences in means of outcomes and differences in means of baseline covariables between the two randomized groups and (2) an empirical covariance matrix for the vector, weighted least squares is applied to force the difference in means of baseline covariables to zero (as expected with valid randomization) to obtain covariate-adjusted estimates. The covariate-adjusted estimates have a population-averaged interpretation and only require a valid randomization and adequate sample size (for approximate normal distributions). Saville and Koch (2012) have developed methodology combining cross-products of DFBETA residuals from a treatment-only model with covariate information to obtain a covariance matrix for use in the nonparametric covariate adjustment. For this research, the methodology is extended to analysis of matched sets with a dichotomous outcome. In the 1:1 setting with randomization or M:1 setting, methods are provided for obtaining an adjusted difference in proportions and an adjusted odds ratio, including techniques for obtaining an exact p-value (for the difference). Application of the methods to the 1:1 observational matched case-control study is also described. For larger strata, the methods of Saville and Koch are expanded to obtain stratified covariate-adjusted log odds ratios (in the case of dichotomous outcomes) or stratified covariate-adjusted log hazard ratios (in the case of time-to-event outcomes). The methods of Saville and Koch are further developed for randomization to multiple treatment groups. Methodology is provided for creation of the appropriate covariance matrix to use in the nonparametric covariance adjustment, and a strategy for accommodating a time-varying treatment effect is presented. These methods avoid modeling assumptions for the covariates (e.g. proportional hazards, functional form) while providing increased precision for the estimated treatment effects. Their use is intended for primary analysis of a randomized clinical trial, with supportive secondary parametric analyses having application to subgroup analyses or assessment of interactions with treatment.

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