Estimating a Treatment Effect from Multidimensional Longitudinal Data

SUMMARY Multidimensional longitudinal data result when researchers measure an outcome through time that is quantified by many different response variables. These response variables are often defined on different numerical scales. The objective of this paper is to present a method to summarize and estimate an overall treatment effect from this type of longitudinal data. A regression model is proposed that assumes the treatment effect can be parameterized as an acceleration or deceleration of the time scale of each response variable's trajectory. Generalized estimating equations are used to estimate the model parameters. Cognitive and functional ability data from Alzheimer's disease patients and quality of life data from an AIDS clinical trial are used to illustrate the model. Researchers often attempt to quantify outcomes, such as cognitive ability, quality of life, or physical functioning, for which no single measure exists. To effectively capture all aspects of the outcome, a number of measurements are commonly used. For example, cognitive ability in Alzheimer's disease patients is typically measured with a battery of performance-based tests. Quality of life in AIDS patients is often measured with a multi-item self-report questionnaire. Physical functioning in the elderly is measured using an extensive self-report questionnaire and/or multiple performance-based tests. The result of such measurements is the representation of cognitive ability, quality of life, or physical functioning by a numerous set of scores for each individual. When measurements of this type are also collected over time, the result is multidimensional longitudinal data. A common problem is to evaluate a treatment effect from such data. For example, clinical trials have been performed to determine if therapies can slow the rate of cognitive loss among Alzheimer's disease patients. This paper is concerned with the estimation of a treatment effect from multidimensional longitudinal data. Several statistical issues arise in evaluating a treatment effect from this type of data. A main issue is the multidimensionality. There are several response variables, each one measuring a slightly different aspect than the others. Since no single response variable sufficiently acts as a main outcome variable, methods that collectively consider all of the response variables are desired. The main question is how one can use the multiple response variables to obtain a summary measure of the treatment effect that is readily interpretable. The problem is challenging because the multiple response variables may be defined on different numerical scales. Methods that combine information from the different response variables are required. These methods must also account for the autocorrelation that exists across time within each response variable and the cross-correlation that exists between different response variables both across time and at the same time. One frequently used approach is to analyze the treatment effect on each response variable separately. While this approach is simple and easy to implement, it has limitations. Evaluating individual response variables is informative but often fails to provide an overall statement of the treatment