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Summary: We develop a joint analysis approach for recurrent and nonrecurrent event processes subject to case I interval censorship, which are also known in literature as current count and current status data, respectively. We use a shared frailty to link the recurrent and nonrecurrent event processes, while leaving the distribution of the frailty fully unspecified. Conditional on the frailty, the recurrent event is assumed to follow a nonhomogeneous Poisson process, and the mean function of the recurrent event and the survival function of the nonrecurrent event are assumed to follow some general form of semiparametric transformation models. Estimation of the models is based on the pseudo‐likelihood and the conditional score techniques. The resulting estimators for the regression parameters and the unspecified baseline functions are shown to be consistent with rates of square and cubic roots of the sample size, respectively. Asymptotic normality with closed‐form asymptotic variance is derived for the estimator of the regression parameters. We apply the proposed method to a fracture‐osteoporosis survey data to identify risk factors jointly for fracture and osteoporosis in elders, while accounting for association between the two events within a subject. [ABSTRACT FROM AUTHOR]

This work, motivated by an osteoporosis survey study, considers regression analysis with incompletely observed current status data. Here the current status data, including an examination time and an indicator for whether or not the event of interest has occurred by the examination time, is not observed for all subjects. Instead, a surrogate outcome subject to misclassification of the current status is available for all subjects. We focus on semiparametric regression under transformation models, including the proportional hazards and proportional odds models as special cases. Under the missing at random mechanism where the missingness of the current status outcome can depend only on the observed surrogate outcome and covariates, we propose an approach of validation likelihood based on the likelihood from the validation subsample where the data are fully observed, with adjustments of the probability of observing the current status outcome, as well as the distribution of the surrogate outcome in the validation subsample. We propose an efficient computation algorithm for implementation, and derive consistency and asymptotic normality for inference with the proposed estimator. The application to the osteoporosis survey data and simulations reveal that the validation likelihood performs well; it removes the bias from the 'complete case' analysis discarding subjects with missing data, and achieves higher efficiency than the inverse probability weighting analysis. [ABSTRACT FROM AUTHOR]