A Note on Postrandomization Adjustment of Covariates
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A Note on Postrandomization Adjustment of Covariates Xra Cbri Clinical Biostatistics, Sanofi-Aventis. Bridgewater, New Jersey
Miazhi Lir Merck & Co., Rahway, New Jersey Ji Zbaag Clinical Biostatistics, Sanofi-Aventis, Bridgewater, New Jersey
Kry Words Causality; Extrapolation; Pos trandomization adjustment; Principle strata; Proportion of treatment effect (PTE); Simple stratification Corrrrpoadracr Addrrrr Xun Chen, Clinical Biostatistics. Sanofi-Aventis, BX2-4OOC, Bridgewater, NJ08807 (email:xun.cfien @sanofi-aventis.com).
The adjustment for postrandomization variables has been widely used in practice to obtain additional information in randomized experiments despite its conceptual and statistical dificulties. To enhance the chance of more appropriate postrandomizationadjustment analyses and interpretation, this paper systematidlysummarizes the potential problems of the conventional regression-based
postrandomization adjustment method with its rdiabiZity, precision, and causaliv. Some available altemative methods that could possi de either more powerful, less biased or more appropriate assessment for causality are outlined. A working example is used to illustrate the application of the &fierent postrandomization adjustment methodg.
INTRODUCTION In randomized clinical trials (RCTs), there is a broad consensus on the technique of adjusting for covariates measured at baseline-to reduce bias due to the imbalance of baseline covariates and maybe more importantly, to increase the precision of estimate (1,2). The adjustment for postrandomization variables-variables that encode both subject and treatment characteristics-is a totally different matter. It has been widely used (and abused) in practice to obtain additional information (3) or throw light on the nature of treatment effect in randomized experiments (4). Examples include adjusting rescue therapies to explore the underlying difference of treatments which would have been observed in the absence of rescue medication (5) adjusting the level of patient compliance to estimate the treatment effect at the same compliance level ( 6 ) adjusting a postrandomization biomarker to evaluate the surrogating status of the biomarker to the clinical endpoint (7), and adjusting an intermediate endpoint or an endpoint other than the primary one to explore the therapeutic mechanism of one intervention (8). The adjustment for postrandomization variables should not be applied unless one desires to assess the treatment effect apart from the differences of the postrandomization covariates for an exploratory evaluation of the treatment (3,5,7,10). The conventional method adjusts for a pos-
trandomization variable by including it as a covariate of a regression model of the primary endpoint on the treatment (eg, 5,7,8,11).The regression model could be a simple linear regression model, a logistic regression model, or a Cox proportional hazard model, depending on the type of response variable one may have. In this paper, we focus on the concerns on the application of the conventiona
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