Baselines and Covariate Information

Statistical Issues in Drug Development, 2nd Edition. Stephen Senn 2007 John Wiley Sons, Ltd. ISBN 978-0-470-01877-4 

This particular heading is one under which many (but not all) of the issues are not controversial among statisticians. It is rather that statisticians have not always succeeded in persuading physicians of their point of view. Both statisticians and physicians are generally agreed on the value of such baseline information. The issues are to do with ways of using it. 

It is also possible in an analysis of covariance to adjust outcomes using individual slopes rather than a postulated common slope. This is not my usual habit in analysing trials and unless I state so specifically I shall not include this further refinement under the heading of analysis of covariance. This point is discussed in section 7.2.7 below. Stratification and analysis of covariance, when carried out on strongly prognostic factors, not only adjust for observed imbalances but even where (in fact especially where) such factors are balanced, bring with them a strong reduction in variance of the estimated treatment effect and a consequent increase in power. 

Hardly a statistician of repute can be found to defend the practice common among physicians of comparing the treatment groups in a randomized clinical trial at baseline using hypothesis/significance tests on covariates. The reason for the statistician s dislike is that such a test appears to be used to say something about the adequacy of the given allocation whereas it could only be a test of the allocation procedure the randomization process itself. 

However, randomization is a chance mechanism. Therefore, if at baseline we conclude that the observed difference is greater than we care to believe may be attributed to chance, we shall have to conclude that randomization has not taken place (or that the values have been disturbed since). In fact, trialists are most reluctant to agree this conclusion. Consequently, they accept that when a significant result occurs, it is a type I error. They then go further, however, and take the result as being some comment on the adequacy of the sample. This is an abuse of the procedure (Altman, 1985 Senn, 1994c, 1995a). 

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Allows assessment of prognostic factors. Fitting the ANCOVA model provides coefficients for the covariates and although this is not the primary focus of the analysis, these coefficients and associated confidence intervals provide information on the effect of the baseline covariates on outcome. 

Important features of the analysis, including adjustments for interim analyses, handling of dropouts, and missing data, should be included. Information on the selection and adjustments for covariate or prognostic factors such as baseline measurements, demographics, and concomitant therapy, together with the results of analyses, should be included. 

It is commonly stated that the analysis of extreme values often plays a more important role than that of the average values in clinical trials because it provides more information on the extent of safety concern at the individual level (14). Extreme values can be examined by creating frequency distributions for maximum absolute values as well as maximum increases from baseline (correcting for placebo), using reference limits of 450 and 500 ms on QT or 30 and 60 ms on AAQTc. It is important to account for covariates known to affect the distribution of QT/QTc values... 

Step 1. This involves labeling subjects into two groups based on the distribution of the baseline values of an important covariate, based on some prior information, from all subjects using a given percentile as the division point. Group 1, for instance, would consist of subjects that have baseline values less than the 10th percentile of the baseline values and the rest of the subjects will be denoted as group 2. 

Some statisticians have maintained that it does (Chambless and Roeback, 1993), but this is wrong in the context of the randomized clinical trial (Senn, 1994a,b, 1995b). The randomized trial permits a valid analysis even where no baselines are measured. If we take the Bayesian view, however, that information carmot be ignored, then when we have measured some covariate we have obtained information we must act on. Instead of using an analysis which corresponds to a probability-weighted average over all possible distributions of the covariate, we must replace it with one which corresponds to the particular distribution observed. However, we are only required to condition on what is observed and what we have observed is the observed covariate ... 

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