A comparison of different ways of including baseline counts in negative binomial models for data from falls prevention trials. Issue 1 (25th October 2017) - Zheng, Han; Kimber, Alan; Goodwin, Victoria A.; Pickering, Ruth M.
Abstract: A common design for a falls prevention trial is to assess falling at baseline, randomize participants into an intervention or control group, and ask them to record the number of falls they experience during a follow‐up period of time. This paper addresses how best to include the baseline count in the analysis of the follow‐up count of falls in negative binomial (NB) regression. We examine the performance of various approaches in simulated datasets where both counts are generated from a mixed Poisson distribution with shared random subject effect. Including the baseline count after log‐transformation as a regressor in NB regression ( NB‐logged ) or as an offset ( NB‐offset ) resulted in greater power than including the untransformed baseline count ( NB‐unlogged ). Cook and Wei's conditional negative binomial (CNB) model replicates the underlying process generating the data. In our motivating dataset, a statistically significant intervention effect resulted from the NB‐logged, NB‐offset, and CNB models, but not from NB‐unlogged, and large, outlying baseline counts were overly influential in NB‐unlogged but not in NB‐logged . We conclude that there is little to lose by including the log‐transformed baseline count in standard NB regression compared to CNB for moderate to larger sized datasets.