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Using the data from a naturalistic truck driving study, the paper examines how the effect of sleep duration upon driving risk would vary according to time. Specifically the interest is to explore how the time-varying effect of sleeping less than 7 hours would be different from that of sleeping greater than 7 hours.
The primary measure of driving risk is safety critical events, which is a recurrent event data. To analyze the data, the paper extends the Cox proportional hazards model by incorporating shared gamma frailties and time-varying coefficients. The frailty is to accommodate the heterogeneity of event risk across different driving trips. The time-varying coefficient is to capture the temporal change of sleep effect. Penalized B-splines will be applied for estimation of time-varying coefficients. The paper shows how the regression coefficients and smoothing parameters can be estimated simultaneously in mixed model setting.
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