Adjusting sample size for anticipated dropouts in clinical trials.

Statistical models for calculating sample sizes for controlled clinical trials often fail to take into account the negative impact that dropouts have on the power of intent-to-treat analyses. Empirically defined dropout correction coefficients are proposed to adjust sample sizes for endpoint analysis of variance (ANOVA) and analysis of covariance (ANCOVA) that have been initially calculated assuming complete data. The implications of type of analysis (change-score ANOVA or ANCOVA), correlational structure of the repeated measurements (compound symmetry or autoregressive), and percentage of dropouts (20% or 30%) are considered, together with other less influential design and data parameters. We recommend the use of ANCOVA to correct for baseline differences and for time-in-study if there is a nonspecific change across time. Given a realistic autoregressive (order 1) correlational structure for the repeated measurements and a proposed endpoint ANCOVA, the empirical results support the common practice of increasing calculated sample size by the anticipated number of dropouts. The previous rationale has been to retain a requisite number of "completers" on which to base statistical inferences. We believe the present results provide the first documentation of the relevance of that strategy for intent-to-treat analyses in which the incomplete data for dropouts must be included. Based on comparative power analyses, the strategy also seems appropriate for maintaining the power of mixed-model regression analyses, simple regression on a normalized time scale, and analyses of trends fitted to imputed scores for dropouts.

Comparative evaluation of two models for estimating sample sizes for tests on trends across repeated measurements.

Two equations for calculating sample sizes that are required for power in testing differences in rates of change in repeated measurement designs have been presented by different authors. One equation provides support for the conclusion that increased frequency of measurements across a treatment period of fixed duration enhances power of the tests. The other equation supports the counterintuitive conclusion that increased frequency of measurements actually tends to decrease power in the presence of realistic serial dependencies in the data. Monte Carlo methods confirm that the equation providing support for the latter conclusion is accurate, whereas the alternative equation tends to underestimate sample sizes required for power in testing differences in slopes of regression lines fitted to changes in the repeated measurements across time when symmetry is absent from the covariance structure.

Random regression with imputed values for dropouts.

The random regression model (RRM) has been advocated as a potential solution to problems of statistical analysis posed by dropouts in clinical trials. However, the power of the RRM tests for differences in rates of change can be seriously attenuated by presence of dropouts. The use of imputed scores and other modifications are examined in an attempt to render a simple growth-curve form of the RRM analysis more robust against dropouts. Methods that extrapolate from an individual's own performance were found effective, although inclusion of time-in-treatment as a covariate was documented to be important under identifiable conditions. Of the methods evaluated, those that used group data to impute missing values for dropouts produced nonconservative bias. The results suggest the importance of careful evaluation of potential bias when integrating any group-based imputation procedure into the RRM analyses.