Application of gap time analysis with flexible hazards to pulmonary exacerbations in the EPIC observational study.

Cystic fibrosis and other chronic lung disease clinical trials often use time to first pulmonary exacerbation (PEx) or total PEx count as endpoints. The use of these outcomes may fail to capture patterns or timing of multiple exacerbations and how covariates influence the risk of future exacerbations. Analysis of gap times between PEx provides a useful framework to understand risks of subsequent events, particularly to assess if there is a temporary increase in a hazard of a subsequent PEx following the occurrence of a PEx. This may be useful for estimating the amount of time needed to follow patients after a PEx and predicting which patients are more likely to have multiple PEx. We propose a smoothed hazard for gap times to account for elevated hazards after exacerbations. A simulation study was conducted to explore model performance and was able to appropriately estimate parameters in all situations with an underlying change point with independent or correlated recurrent events. Models with different change-point structures and trends are compared using Early Pseudomonas Infection Control (EPIC) observational study data, using a quasi-likelihood modification of the Akaike information criterion; a model with a change-point provided a better fit than a model without one. The analysis suggests that the change point may be 1.8 years (SE 0.09) after the end of a PEx. Models including covariates in the hazard function revealed that having one or two copies of the Δ$\Delta$ F508 mutation, female sex, and higher numbers of previous PEx were significantly associated with increased risk of another PEx.