We consider a class of semiparametric marginal rate models for analyzing recurrent event data. In these models, both time-varying and time-free effects are present, and the estimation of time-varying effects may result in non-smooth regression functions. A typical approach for avoiding this problem and producing smooth functions is based on kernel methods. The traditional kernel-based approach, however, assumes a common degree of smoothness for all time-varying regression functions, which may result in suboptimal estimators if the functions have different levels of smoothness. In this paper, we extend the traditional approach by introducing different bandwidths for different regression functions. First, we establish the asymptotic properties of the suggested estimators. Next, we demonstrate the superiority of our proposed method using two finite-sample simulation studies. Finally, we illustrate our methodology by analyzing a real-world heart disease dataset.

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