<p>In the analysis of recurrent event data, some covariates are time independent and have a nonlinear effect, such as the efficacy of some drugs; while other covariates are internally time dependent, such as blood pressure. By combining these two cases, we formulate a partially linear model for the rate function of the recurrent event data with intermittently observed covariates. For the first case, the I-spline function approximation is utilized. For the second case, kernel smoothing is applied to impute the time-dependent covariates from the observation process. A pseudo-partial likelihood profile method is mainly used to estimate the model. Bootstrap is used to estimate the variance of the estimator. Various simulations are conducted to evaluate the estimation method compared to other models and methods, and real data is taken as an example to illustrate.</p>