Relative Efficiency of Adjusted and Unadjusted Analyses when Baseline Data are Partially Missing

Abstract

<p> Many medical studies are performed to investigate the effectiveness of new treatments (such as new drugs, new surgery) versus traditional (or placebo) treatments. In many cases, researchers measure a continuous variable at baseline and again as an outcome assessed at follow up. The baseline measurement usually has strong relationship with post treatment measurement. Consequently, the ANCOVA model using baseline as covariate may provide more powerful and precise results than the ANOVA model.</p> <p> However, most epidemiologic studies will encounter the problem of missing covariate data. As a result, the patients with missing baseline measurements will be excluded from the data analysis. Hence, there exists a tradeoff between the ANOVA with full data set and the ANCOVA with partial data set.</p> <p> This study focuses on the variance of the estimator of treatment means difference. In practical situation, the standard error of the estimator obtained from the ANCOVA model with partially missing baseline relative to the standard error obtained form the ANOVA with full data relies on the correlation between baseline and follow-up outcome, the proportion of the missing baseline, and the difference of the group means on the baseline. In moderate sample size studies, it is also affected by the sample size.</p> <p> The theoretically required minimum correlations for the ANCOVA model were calculated to obtain the same precision with the ANOVA model assuming the missing proportion, sample size and difference of group means on covariate are available. The minimum correlation can be obtained through checking the reference table or figures.</p> <p> The figures of asymptotic relative efficiencies provide the asymptotic variance and the length of the confidence intervals of the estimated difference obtained from the ANCOVA model relative to the ANOVA model for all the range of the correlation between baseline and follow up.</p>