Adjusted analyses and analysis of covariance

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

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. 

One disadvantage of ANCOVA is that the modelling does involve a number of assumptions and if those assumptions are not valid then the approach could mislead. For example, it is assumed (usually) that the covariates affect outcome in a linear way there is invariably too little information in the data to be able to assess this assumption in any effective way. In contrast, with an adjusted analysis, assumptions about the way in which covariates affect outcome are not made and in that sense it can be seen as a more robust approach. In some regulatory circles adjusted analyses are preferred to ANCOVA for these reasons. 

At both the trial level and the development plan level, statisticians should take time to review the case report forms (CRFs) to make sure, in particular, that the data being collected will be appropriate for the precise, unambiguous and unbiased measurement of primary and secondary endpoints. Other aspects of the data being collected should also be reviewed in light of the way they will be used in the analysis. For example, baseline data will form the basis of covariates to be used in any adjusted analyses, intermediate visit data may be needed for the use of... 

BMDs and BMDLs for four end points (Finger Tapping, CPT Reaction Time, Boston Naming, and CVLT Delayed Recall) based on (1) models that include log(PCB) as an additional covariate and (2) the subset of subjects in the lowest tertile of PCB exposures. Because PCBs were measmed only for children examined in 1993, only about half of the full cohort (approximately 450 children) are used for analysis 1, and only one-sixth (approximately 150 Children) are used for analysis 2. Results were provided for Hg measured in both maternal hair and cord blood (see Table 7-4). The reduced sample sizes in these additional analyses increased the variability among the results. There was no clear pattern with respect to how the PCB-adjusted analyses differed from the original results. 

Details of statistical analyses for potential toxicities that should be explicitly considered for all products and AEs of special interest Aiialyses for these events will in general be more comprehensive than for standard safety parameters. These analyses may include subject-year adjusted rates, Cox proportional hazards analysis of time to first event, and Kaplan-Meier curves. Detailed descriptions of the models would typically be provided. For example, if Cox proportional hazards analysis is specified, a detailed description of the model(s) that will be used should be provided. This would generally include study as a stratification factor, covariates, and model selection techniques. More advanced methods, such as multiple events models or competing risk analyses, should be described if used (as appropriate). It is recommended that graphical methods also be employed, for example, forest plot and risk-over-time plot (Xia et al., 2011). 

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. 

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