A new linear model-based approach for inferences about the mean area under the curve

Outcome versus time data are commonly encountered in biomedical and clinical research. A common strategy adopted in analyzing such longitudinal data is to condense the repeated measurements on each individual into a single summary statistic such as the area under the response versus time curve. Standard parametric or non-parametric methods are then applied to perform inferences on the conditional area under the curve distribution. Disadvantages of this approach include the disregard of the within-subject variation in the longitudinal profile. We propose a general linear model approach, accounting for the within-subject variance, for estimation and hypothesis tests about the mean areas. Inferential properties of our approach are compared with those from standard methods of analysis using Monte Carlo simulation studies. The impact of missing data, within-subject heterogeneity and homogeneity of variance, are also evaluated. A real working example is used to illustrate the methodology. It is seen that the proposed approach is associated with a significant power advantage over traditional methods, especially when missing data are encountered.