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Objectives: Estimation of the cascade of HIV care is essential for evaluating care and treatment programs, informing policy makers and assessing targets such as 90-90-90. A challenge to estimating the cascade based on electronic health record concerns patients "churning" in and out of care. Correctly estimating this dynamic phenomenon in resource-limited settings, such as those found in sub-Saharan Africa, is challenging because of the significant death under-reporting. An approach to partially recover information on the unobserved deaths is a double-sampling design, where a small subset of individuals with a missed clinic visit is intensively outreached in the community to actively ascertain their vital status. This approach has been adopted in several programs within the East Africa regional IeDEA consortium, the context of our motivating study. The objective of this paper is to propose a semiparametric method for the analysis of competing risks data with incomplete outcome ascertainment. Methods: Based on data from double-sampling designs, we propose a semiparametric inverse probability weighted estimator of key outcomes during a gap in care, which are crucial pieces of the care cascade puzzle. Results: Simulation studies suggest that the proposed estimators provide valid estimates in settings with incomplete outcome ascertainment under a set of realistic assumptions. These studies also illustrate that a naïve complete-case analysis can provide seriously biased estimates. The methodology is applied to electronic health record data from the East Africa IeDEA Consortium to estimate death and return to care during a gap in care. Conclusions: The proposed methodology provides a robust approach for valid inferences about return to care and death during a gap in care, in settings with death under-reporting. Ultimately, the resulting estimates will have significant consequences on program construction, resource allocation, policy and decision making at the highest levels. [ABSTRACT FROM AUTHOR]

Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size (ICS), a situation where the outcomes under study are associated with the size of the cluster. In addition, the cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with an ICS and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional cause-specific hazards model and propose a maximum partial pseudolikelihood estimator under a missing at random assumption. To make the latter assumption more plausible in practice, we allow for auxiliary variables that may be related to the probability of missingness. The proposed method does not impose assumptions regarding the within-cluster dependence and allows for ICS. The asymptotic properties of the proposed estimators for both regression coefficients and infinite-dimensional parameters, such as the marginal cumulative incidence functions, are rigorously established. Simulation studies show that the proposed method performs well and that methods that ignore the within-cluster dependence and the ICS lead to invalid inferences. The proposed method is applied to competing risks data from a large multicenter HIV study in sub-Saharan Africa where a significant portion of causes of failure is missing. [ABSTRACT FROM AUTHOR]

We consider a class of partially linear transformation models with interval-censored competing risks data. Under a semiparametric generalized odds rate specification for the cause-specific cumulative incidence function, we obtain optimal estimators of the large number of parametric and nonparametric model components via maximizing the likelihood function over a joint B-spline and Bernstein polynomial spanned sieve space. Our specification considers a relatively simpler finite-dimensional parameter space, approximating the infinite-dimensional parameter space as n → ∞, thereby allowing us to study the almost sure consistency, and rate of convergence for all parameters, and the asymptotic distributions and efficiency of the finite-dimensional components. We study the finite sample performance of our method through simulation studies under a variety of scenarios. Furthermore, we illustrate our methodology via application to a dataset on HIV-infected individuals from sub-Saharan Africa. [ABSTRACT FROM AUTHOR]

Misclassification of outcomes or event types is common in health sciences research and can lead to serious bias when estimating the cumulative incidence functions in settings with competing risks. Recent work has shown how to estimate nonparametric cumulative incidence functions in the presence of nondifferential outcome misclassification when the misclassification probabilities are known. Here, we extend this approach to account for misclassification that is differential with respect to important predictors of the outcome using misclassification probabilities estimated from external validation data. Moreover, we propose a bootstrap approach in which the observations from both the main study data and the external validation study are resampled to allow the uncertainty in the misclassification probabilities to propagate through the analysis into the final confidence intervals, ensuring appropriate confidence interval coverage probabilities. The proposed estimator is shown to be uniformly consistent and simulation studies indicate that both the estimator and the standard error estimation approach perform well in finite samples. The methodology is applied to estimate the cumulative incidence of death and disengagement from HIV care in a large cohort of HIV infected individuals in sub-Saharan Africa, where a significant death underreporting issue leads to outcome misclassification. This analysis uses external validation data from a separate study conducted in the same country. [ABSTRACT FROM AUTHOR]

This study examines nonparametric estimations of a transition probability matrix of a nonhomogeneous Markov process with a finite state space and a partially observed absorbing state. We impose a missing-at-random assumption and propose a computationally efficient nonparametric maximum pseudolikelihood estimator (NPMPLE). The estimator depends on a parametric model that is used to estimate the probability of each absorbing state for the missing observations based, potentially, on auxiliary data. For the latter model, we propose a formal goodness-of-fit test based on a residual process. Using modern empirical process theory, we show that the estimator is uniformly consistent and converges weakly to a tight mean-zero Gaussian random field. We also provide a methodology for constructing simultaneous confidence bands. Simulation studies show that the NPMPLE works well with small sample sizes and that it is robust against some degree of misspecification of the parametric model for the missing absorbing states. The method is illustrated using HIV data from sub-Saharan Africa to estimate the transition probabilities of death and disengagement from HIV care. [ABSTRACT FROM AUTHOR]

Many biomedical and clinical studies with time-to-event outcomes involve competing risks data. These data are frequently subject to interval censoring. This means that the failure time is not precisely observed but is only known to lie between two observation times such as clinical visits in a cohort study. Not taking into account the interval censoring may result in biased estimation of the cause-specific cumulative incidence function, an important quantity in the competing risks framework, used for evaluating interventions in populations, for studying the prognosis of various diseases, and for prediction and implementation science purposes. In this work, we consider the class of semiparametric generalized odds rate transformation models in the context of sieve maximum likelihood estimation based on B-splines. This large class of models includes both the proportional odds and the proportional subdistribution hazard models (i.e., the Fine-Gray model) as special cases. The estimator for the regression parameter is shown to be consistent, asymptotically normal and semiparametrically efficient. Simulation studies suggest that the method performs well even with small sample sizes. As an illustration, we use the proposed method to analyze data from HIV-infected individuals obtained from a large cohort study in sub-Saharan Africa. We also provide the R function ciregic that implements the proposed method and present an illustrative example. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]