Recurrent
event time data and more general multiple event time data are commonly analyzed
using extensions of Cox regression, or proportional hazards regression, as used
with single event time data. These methods treat covariates, either
time-invariant or time-varying, as having multiplicative effects while general
dependence on time is left un-estimated. An adaptive approach is formulated for
analyzing multiple event time data. Conditional hazard rates are modeled in
terms of dependence on both time and covariates using fractional polynomials
restricted so that the conditional hazard rates are positive-valued and so that
excess time probability functions (generalizing survival functions for single
event times) are decreasing. Maximum likelihood is used to estimate parameters
adjusting for right censored event times. Likelihood cross-validation (LCV)
scores are used to compare models. Adaptive searches through alternate
conditional hazard rate models are controlled by LCV scores combined with
tolerance parameters. These searches identify effective models for the
underlying multiple event time data. Conditional hazard regression is
demonstrated using data on times between tumor recurrence for bladder cancer
patients. Analyses of theory-based models for these data using extensions of
Cox regression provide conflicting results on effects to treatment group and
the initial number of tumors. On the other hand, fractional polynomial analyses
of these theory-based models provide consistent results identifying significant
effects to treatment group and initial number of tumors using both model-based
and robust empirical tests. Adaptive analyses further identify distinct
moderation by group of the effect of tumor order and an additive effect to
group after controlling for nonlinear effects to initial number of tumors and
tumor order. Results of example analyses indicate that adaptive conditional
hazard rate modeling can generate useful insights into multiple event time
data.
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