Evaluation of Methods for the Statistical Analysis of Exacerbations in Cystic Fibrosis

Abstract

Reducing pulmonary exacerbations (PEx) is an important goal in the treatment of Cystic Fibrosis (CF). Endpoints based on PEx are relatively commonly used in the evaluation of new therapies. There are two different ways that one might consider modeling exacerbations: We can model an overall rate (count of PEx in a patient), or model a frequency (time-to-recurrent PEx events). These two endpoints necessitate the use of different types of models. In this study, we evaluate 7 methodologies for modeling the relationship between treatment and PEx in CF: 4 in the Poisson-modeling family for count outcome, and 3 in the Proportional hazard modeling family for time-to-event outcome. In Chapter 1, we review the theoretical framing of all 7 models, including the assumptions of each model. In Chapter 2 we conduct simulated experiments, where I evaluate and compare the power and type 1 error rates of all 7 models. We consider scenarios with different amounts of over-dispersion, sample sizes, and censoring schemes. Finally, in Chapter 3, we apply all 7 models to two previous CF trials, and summarize findings on the performance of these methods. Our results show that for count outcome, Poisson regression is not reliable when the outcome is over-dispersed. Other models from the Poisson-modeling family that deal with over-dispersion all worked well in every scenario considered. We additionally note that the negative binomial model is more computationally efficient than the similar Poisson GLMM (with Gaussian random effects). Furthermore, the negative binomial model explicitly accounts for between-person variability: In contrast the quasi-Poisson only implicitly accounts for that variability. Thus we recommend use of the negative binomial model for modeling PEx as a count-based outcome. For modeling PEx as a time-to-event outcome, we found that results from the Cox-PH model and from the two recurrent event model (AG model and PWP methods) may differ if treatment effect is heterogeneous over first vs recurrent events. In particular, in the two CF trials, it appears that effects on the first event were vastly different than effects on later events. Choice of model, in this case, should be based on two things. First, the scientific question should be considered: Is the investigator interested in the effect of treatment on the first event (in which case we recommend the standard Cox PH model); or the effect averaged over recurrent events as well? (In which case we suggest use of PWP methodology). Second, one must consider the effect of confounding and post-randomization intervention: Patients receive treatment after their first exacerbation, if this is given differently between arms (based on an effect of treatment on first exacerbation), then the standard estimate of effect on later events may be biased. If one expects this bias to be severe, then likely only time-to- first event should be analyzed. Future work related to this thesis could study effects from administrative decisions on method performance. For example, there are multiple candidate definitions of PEx, and it would be useful to study if choice of PEx definition might affect relative performance of our 7 models. This thesis offers an overview of some common methods that are appropriate for CF endpoints, and hopefully can help researchers in model selection for statistical analysis in CF trials in the future.