Nonparanormal Adjusted Marginal Inference

Abstract: Although treatment effects can be estimated from observed outcome distributions obtained from proper randomization in clinical trials, covariate adjustment is recommended to increase precision. For important treatment effects, such as odds or hazard ratios, conditioning on covariates in binary logistic or proportional hazards models changes the interpretation of the treatment effect and conditioning on different sets of covariates renders the resulting effect estimates incomparable. We propose a novel nonparanormal model formulation for adjusted marginal inference. This model for the joint distribution of outcome and covariates directly features a marginally defined treatment effect parameter, such as a marginal odds or hazard ratio. Not only the marginal treatment effect of interest can be estimated based on this model, it also provides an overall coefficient of determination and covariate-specific measures of prognostic strength. For the special case of Cohen's standardized mean difference d, we theoretically show that adjusting for an informative prognostic variable improves the precision of the marginal, noncollapsible effect. Empirical results confirm this not only for Cohen's d but also for odds and hazard ratios in simulations and three applications. A reference implementation is available in the R add-on package tram.