Type I Error Rates from Mixed Effects Model Repeated Measures Versus Fixed Effects Anova with Missing Values Imputed Via
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0092-86 1 5/200 I Copyright 0 2001 Drug Information Association Inc.
TYPE I ERROR RATES FROM MIXED EFFECTS MODEL REPEATED MEASURES VERSUS FIXED EFFECTS ANOVA WITH MISSING VALUES IMPUTED VIA LAST OBSERVATION CARRIED FORWARD CRAIGH. MALLINCKRODT, W. Scorn CLARK,AND STACYR. DAVID Eli Lilly & Co., Lilly Corporate Center, Indianapolis, Indiana
Treatment effects are often evaluated by comparing change over time in outcome measures. However, valid analyses of longitudinal data can be problematic when subjects discontinue (dropout)prior to completing the trial. This study compared the Type I error rates from a likelihood-based repeated measures analysis (MMRM) to a fixed-effects analysis of variance where missing values were imputed using the last observation carried forward approach (LOCF). Comparisons were made in 32 scenarios, with 3000 simulated data sets per scenario. The null hypothesis of no difference between treatments in mean change from baseline to endpoint was true in all data sets. Subject dropout was introduced to generate ignorable and nonignorable missingness. Pooled across all scenarios, the Type I error rates for MMRM and LOCF were 5.85% and 10.36%, respectively. Type I error rates in the 32 scenarios ranged from 5.03% to 7.17% for MMRM, and from 4.43% to 36.30% for LOCI.: In 19 of the 32 scenarios, MMRM yielded a Type I error rate that was at least 1.00% closer to the expected rate of 5.00% than the corresponding rate from LOCF Greater inflation of Type I error in LOCF resulted from greater bias in estimates of mean change from baseline to endpoint and unduly small standard errors that were a consequence of failing to account for the uncertainiy of imputation. The superior control of Type I error by MMRM suggested that MMRM should replace LOCF as the default primary analysis for longitudinal clinical trials where dropout bias may exist. Key Words: Missing data; Mixed-effects models; Dropout bias; LOCF
INTRODUCTION Analyzing Longitudinal Data from Clinical Trials TREATMENT EFFECTS ARE often evaluated by comparing change over time in out-
Reprint address: Craig H. Mallinckrodt, Eli Lilly & Co.. Lilly Corporate Center, Department MCYXD, Drop Code-2206, Indianapolis, IN 46285.
come measures. Valid analyses of longitudinal data can be problematic when subjects discontinue (dropout) prior to completing the study, which can bias estimates of treatment effects, especially if the reason for dropping out is related to the outcome (1,2). Missing data can be categorized as: 1. Data missing completely at random (MCAR), 2. Data missing for ignorable nonrandom reasons (MAR), and,
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Craig H. Mallinckrodt, W. Scott Clark, and Stacy R. David
3. Data missing for nonignorable nonrandom reasons (MNAR) (3,4).
If data are MCAR, the missingness does not depend on either the observed or unobserved data. If data are MAR, the missingness depends on (is explained by) the observed data. If data are MNAR, the missingness depends on (is explained by) the unobserved data. Traditional approaches to analyses of data fr
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