Competing risks data arise naturally in medical research, when subjects under study are at risk of more than one mutually exclusive event such as death from different causes. The competing risks framework also includes settings where different possible events are not mutually exclusive but the interest lies on the first occurring event. For example, in HIV studies where seropositive subjects are receiving highly active antiretroviral therapy (HAART), treatment interruption and switching to a new HAART regimen act as competing risks for the first major change in HAART. This article introduces competing risks data and critically reviews the widely used statistical methods for estimation and modelling of the basic (estimable) quantities of interest. We discuss the increasingly popular Fine and Gray model for subdistribution hazard of interest, which can be readily fitted using standard software under the assumption of administrative censoring. We present a simulation study, which explores the robustness of inference for the subdistribution hazard to the assumption of administrative censoring. This shows a range of scenarios within which the strictly incorrect assumption of administrative censoring has a relatively small effect on parameter estimates and confidence interval coverage. The methods are illustrated using data from HIV-1 seropositive patients from the collaborative multicentre study CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe).

When competing risks data arise, information on the actual cause of failure for some subjects might be missing. Therefore, a cause-specific proportional hazards model together with multiple imputation (MI) methods have been used to analyze such data. Modelling the cumulative incidence function is also of interest, and thus we investigate the proportional subdistribution hazards model (Fine and Gray model) together with MI methods as a modelling approach for competing risks data with missing cause of failure. Possible strategies for analyzing such data include the complete case analysis as well as an analysis where the missing causes are classified as an additional failure type. These approaches, however, may produce misleading results in clinical settings. In the present work we investigate the bias of the parameter estimates when fitting the Fine and Gray model in the above modelling approaches. We also apply the MI method and evaluate its comparative performance under various missing data scenarios. Results from simulation experiments showed that there is substantial bias in the estimates when fitting the Fine and Gray model with naive techniques for missing data, under missing at random cause of failure. Compared to those techniques the MI-based method gave estimates with much smaller biases and coverage probabilities of 95 per cent confidence intervals closer to the nominal level. All three methods were also applied on real data modelling time to AIDS or non-AIDS cause of death in HIV-1 infected individuals.

Losses to follow-up (LTFU) remain an important programmatic challenge. While numerous patient-level factors have been associated with LTFU, less is known about facility-level factors. Data from the East African International epidemiologic Databases to Evaluate AIDS (EA-IeDEA) Consortium was used to identify facility-level factors associated with LTFU in Kenya, Tanzania and Uganda. Patients were defined as LTFU if they had no visit within 12 months of the study endpoint for pre-ART patients or 6 months for patients on ART. Adjusting for patient factors, shared frailty proportional hazard models were used to identify the facility-level factors associated with LTFU for the pre- and post-ART periods. Data from 77,362 patients and 29 facilities were analyzed. Median age at enrolment was 36.0 years (Interquartile Range: 30.1, 43.1), 63.9% were women and 58.3% initiated ART. Rates (95% Confidence Interval) of LTFU were 25.1 (24.7–25.6) and 16.7 (16.3–17.2) per 100 person-years in the pre-ART and post-ART periods, respectively. Facility-level factors associated with increased LTFU included secondary-level care, HIV RNA PCR turnaround time >14 days, and no onsite availability of CD4 testing. Increased LTFU was also observed when no nutritional supplements were provided (pre-ART only), when TB patients were treated within the HIV program (pre-ART only), and when the facility was open ≤4 mornings per week (ART only). Our findings suggest that facility-based strategies such as point of care laboratory testing and separate clinic spaces for TB patients may improve retention.

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