More data, less information? Potential for nonmonotonic information growth using GEE.

Statistical intuition suggests that increasing the total number of observations available for analysis should increase the precision with which parameters can be estimated. Such monotonic growth of statistical information is of particular importance when data are analyzed sequentially, such as in confirmatory clinical trials. However, monotonic information growth is not always guaranteed, even when using a valid, but inefficient estimator. In this article, we demonstrate the theoretical possibility of nonmonotonic information growth when using generalized estimating equations (GEE) to estimate a slope and provide intuition for why this possibility exists. We use theoretical and simulation-based results to characterize situations that may result in nonmonotonic information growth. Nonmonotonic information growth is most likely to occur when (1) accrual is fast relative to follow-up on each individual, (2) correlation among measurements from the same individual is high, and (3) measurements are becoming more variable further from randomization. In situations that may lead to nonmonotonic information growth, study designers should plan interim analyses to avoid situations most likely to result in nonmonotonic information growth.