A semiparametric recurrent events model with time-varying coefficients

Abstract

We consider a recurrent events model with time-varying coefficients motivated by two clinical applications. We use a random effects (Gaussian frailty) model to describe the intensity of recurrent events. The model can accommodate both time-varying and time-constant coefficients. We use the penalized spline method to estimate the time-varying coefficients. We use Laplace approximation to evaluate the penalized likelihood without a closed form. We estimate the smoothing parameters in a similar way to variance components. We conduct simulations to evaluate the performance of the estimates for both time-varying and time-independent coefficients. We apply this method to analyze two data sets: a stroke study and a child wheeze study.

Figure 1

Setting I: simulation results for the varying-coefficient function β(t). (a) Penalized spline estimate of β̂(t): estimate, dotted; true β(t), solid. (b) Point-wise empirical coverage probability of β(t), the average coverage probability is 96.4%.

Figure 2

Setting II: simulation results for the varying-coefficient function function β(t). (a) Penalized spline estimate of β̂(t): dotted; true β(t), solid. (b) Point-wise Empirical coverage probability of β(t), the average coverage probability is 96.5%.

Figure 3

Application I: Time-varying effect of log PC₃₀ on recurrent wheezing: β̂(age), solid; 95% point-wise confidence interval, dotted; log PC₃₀ in constant coefficient model, dashed. A horizontal line at 0 is present for better comparison.

Figure 4

Application II: Time-varying effect of the performance score on stroke readmission: β̂(time), solid; 95% point-wise confidence interval, dotted; performance score effect in constant coefficient model, dashed.