Dynamic modelling of a challenge-escalation cross-over study of treatment of capsaicin-induced coughing

In a complex seven-period cross-over trial to study the effects of a drug in attenuating capsaicin-induced coughing, counts of numbers of coughs were recorded 32 times in each period. Subjects were subjected to four escalating levels of capsaicin at each of one and five hours after treatment, with counts of coughs being recorded in four one-minute intervals at each level. Such longitudinal count studies often show considerable individual variability about any regression curve that might be fitted. We develop a non-linear autoregressive model for such count data that also allows for overdispersion.