John W. Robinson, M.D., Ph.D., LLC
Statistical Consulting ▪ Expert Analysis
Design Suggestion: Take Advantage of Within-Subject Correlation in Longitudinal Comparative Effectiveness Studies
In longitudinal studies, the outcome variable is measured repeatedly, at intervals, after a baseline measurement. Important features of such studies are that repeated measurements on a study subject tend to be positively correlated and that subjects often have missing outcome measurements due, for example, to missed follow-up appointments or dropping out of the study. If a subject’s clinical condition contributes causally to the fact that a measurement is missing, the missing data process cannot be regarded as completely random and the loss of outcome information will tend to bias the study’s findings. However, due to the aforementioned within-subject correlation, it is often possible to reduce the impact of such information loss by leveraging what the observed data reveals about each subject’s outcome trajectory.
For comparing longitudinal outcomes between treatment groups, investigators often use methods such as a t-test, chi-square test, or simple analysis of variance (ANOVA) that disregard within-subject correlation and make a distinct, cross-sectional comparison at each measurement time. If any outcome measurement is missing for a reason related to a subject’s clinical condition, these simple approaches are unable to take advantage of within-subject correlation to reduce the bias caused by the missing measurement.
A better approach is to use a method that fully accounts for within-subject correlation, such as a linear mixed model or generalized linear mixed model fitted by maximum likelihood or a Bayesian strategy. These approaches involve development of a model of within-subject correlation that, when combined with the observed data, can be used to infer a probable distribution of values for each missing measurement. These probable distributions can then, in effect, take the place of the missing measurements, to yield outcome comparisons between treatment groups that tend to be less biased than if the missing measurements were simply disregarded.
Examples of Longitudinal Comparative Effectiveness Studies that Take Advantage of Within-Subject Correlation:
Tashkin DP, Celli B, Senn S, et al. A 4-year trial of tiotropium in chronic obstructive pulmonary disease. N Engl J Med 2008;359(15):1543-54.
Weintraub WS, Spertus JA, Kolm P, et al. Effect of PCI on quality of life in patients with stable coronary disease. N Engl J Med 2008;359(7):677-87.
Other Useful References:
Fitzmaurice GM, Laird NM, Ware JH. Applied Longitudinal Analysis, Second Edition. Hoboken, NJ: John Wiley and Sons, 2011.
Molenberghs G, Kenward MG. Missing Data in Clinical Studies. West Sussex, England: John Wiley and Sons, 2007.
Diggle PJ, Heagerty P, Liang K-Y, Zeger SL. Analysis of Longitudinal Data, Second Edition. New York: Oxford University Press, 2002.
