Analysis of Covariance: Model-based and Randomization-based

For randomized clinical trials with at least moderate sample size, adjustment of
comparisons between treatments for baseline covariables can be helpful for two
reasons. One is enhancement of power, and the other is the removal of the
influence of baseline imbalances for the covariables. Adjustment for baseline
covariables can either be through generalized linear (or semi-parametric) models
or through a nonparametric extension of Mantel-Haenszel methods. The former
has the limitation of assumptions that may be debatable or unrealistic, although
it can have the advantage of fully describing the relationship of an endpoint to
both treatments and covariables in a general population. The latter has the
advantage of no external assumptions (beyond its intrinsic assumptions of valid
randomization and valid data), although it only enables inference for the
comparison between treatments for the randomized population. The
nonparametric method has invocation by constraining differences between
treatments for means of covariables to 0 in a multivariate vector that additionally
includes the unadjusted treatment effect sizes for the endpoints under
assessment. Such nonparametric randomization based analysis of covariance
(RBANCOVA) is applicable to differences between means for continuous
measurements (or their ranks), differences between proportions, log hazard
ratios for time to event data, log incidence density ratios for counted event data,
and rank measures of association for ordinal data. Also, extensions to account for
stratification factors in the randomization are available as well. Several examples
which illustrate RBANCOVA and model based counterparts have discussion.

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