Median percent change: A robust alternative for assessing temporal trends

A typical summary statistic for temporal trends is the average percent change (APC). The APC is estimated by using a generalized linear model, usually under the assumption of linearity on the logarithmic scale. A serious limitation of least-squares type estimators is their sensitivity to outliers. The goal of this study is twofold: firstly, we propose a robust and easy-to-compute measure of the temporal trend based on the median of the rates (median percent change – MPC), rather than their mean, under the hypothesis of constant relative change; secondly, we investigate the performance of several models for estimating the rate of change when some of the most common model assumptions are violated. We provide some guidance on the practices of the estimation of temporal trends when using different models under different circumstances. The robustness property of the median is assessed in a simulation study, which shows that the MPC provides strong reductions in estimation bias and variance in presence of outliers. We also demonstrate how a mathematical property of the median helps addressing the issue of zero counts when estimating trends on the log-scale. Finally, we analyzed an English cancer registration dataset to illustrate the proposed method. We believe that, as a good practice, both APC and MPC should be presented when sensitivity issues arise.