Approximate analysis of covariance in trials in rare diseases, in particular rare cancers

‘Adjustments are not expected to be perfect – they are only supposed to help!’ John Tukey (1)

For the general linear model, covariate adjustment through ordinary least squares (OLS) has three consequences on precision of the treatment estimate in a clinical trials (2). A) To the extent that the covariate is predictive, the residual variance is reduced B) To the extent that the covariate is imbalanced, the variance multiplier is increased C) The second order variance, that is to say the variance of the variance is increased through the reduction in degrees of freedom . If, however, the covariate slopes can be approximated using data that are external to the trial, although residual variances will not be as low as if classical OLS had been used, the treatment estimate will be unbiased in the marginal sense and there will be no adverse effect on B) and C). Thus under certain circumstances, this approach can be beneficial.

Given that trials in rare diseases may have few patients but potentially many prognostic covariates such approximate ANCOVA may be attractive. However, for non-linear models, including proportional hazards models commonly used in cancer, models over averages are not the same as averages over models. This make the situation more complex and the additional issues in using such an approach in trial in cancer will also be discussed.


1)      Tukey, J. W. (1993). "Tightening the clinical trial." Control Clin Trials 14(4): 266-285.

2)      Lesaffre, E. and S. Senn (2003). "A note on non-parametric ANCOVA for covariate adjustment in randomized clinical trials." Statistics in Medicine 22(23): 3583-3596.