7.4 Weiss (2005, p. 353) describes a patient controlled analgesia study presented by Henderson and Shimakura (2003). The number of selfadministered doses in a 4-hour period was recorded for each patient for each of 12 consecutive periods. Two groups of patients were considered: a 1-milligram (mg) per dose group and a 2 milligram. The variables in the data set are id (subject id), grouplmg = 1 for subjects in the 1-mg group, 0 in the 2-mg group, count (# of self-administered dosages), and time (dose period). The data is found in selfdose.xls.

(a) Plot count and (count) versus time and comment on which transformation of count appears to be most appropriate. Does there appear to be a linear relationship of ln(count) with time!

(b) When considering a model with both categorical and continuous regressors, the interpretation of model coefficients is often aided by centering the continuous regressors (here time could be considered continuous). After centering time, determine the most appropriate Poisson mixed effects model.

(c) Overlay plots of the estimated marginal mean number of selfadministered doses for the 1-mg group and 2-mg groups over time and interpret the plot.