On the Assumption of Bivariate Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence

Background: Heckman-type selection models have been used to control HIV prevalence estimates for selection bias when participation in HIV testing and HIV status are associated after controlling for observed variables. These models typically rely on the strong assumption that the error terms in the participation and the outcome equations that comprise the model are distributed as bivariate normal.
Methods: We introduce a novel approach for relaxing the bivariate normality assumption in selection models using copula functions. We apply this method to estimating HIV prevalence and new confidence intervals (CI) in the 2007 Zambia Demographic and Health Survey (DHS) by using interviewer identity as the selection variable that predicts participation (consent to test) but not the outcome (HIV status).
Results: We show in a simulation study that selection models can generate biased results when the bivariate normality assumption is violated. In the 2007 Zambia DHS, HIV prevalence estimates are similar irrespective of the structure of the association assumed between participation and outcome. For men, we estimate a population HIV prevalence of 21% (95% CI = 16%–25%) compared with 12% (11%–13%) among those who consented to be tested; for women, the corresponding figures are 19% (13%–24%) and 16% (15%–17%).
Conclusions: Copula approaches to Heckman-type selection models are a useful addition to the methodological toolkit of HIV epidemiology and of epidemiology in general. We develop the use of this approach to systematically evaluate the robustness of HIV prevalence estimates based on selection models, both empirically and in a simulation study.

Statin use after diagnosis of breast cancer and survival: a population-based cohort study

BACKGROUND: Preclinical studies have shown that statins, particularly simvastatin, can prevent growth in breast cancer cell lines and animal models. We investigated whether statins used after breast cancer diagnosis reduced the risk of breast cancer-specific, or all-cause, mortality in a large cohort of breast cancer patients.

METHODS: A cohort of 17,880 breast cancer patients, newly diagnosed between 1998 and 2009, was identified from English cancer registries (from the National Cancer Data Repository). This cohort was linked to the UK Clinical Practice Research Datalink, providing prescription records, and to the Office of National Statistics mortality data (up to 2013), identifying 3694 deaths, including 1469 deaths attributable to breast cancer. Unadjusted and adjusted hazard ratios (HRs) for breast cancer-specific, and all-cause, mortality in statin users after breast cancer diagnosis were calculated using time-dependent Cox regression models. Sensitivity analyses were conducted using multiple imputation methods, propensity score methods and a case-control approach.

RESULTS: There was some evidence that statin use after a diagnosis of breast cancer had reduced mortality due to breast cancer and all causes (fully adjusted HR = 0.84 [95% confidence interval = 0.68-1.04] and 0.84 [0.72-0.97], respectively). These associations were more marked for simvastatin 0.79 (0.63-1.00) and 0.81 (0.70-0.95), respectively.

CONCLUSIONS: In this large population-based breast cancer cohort, there was some evidence of reduced mortality in statin users after breast cancer diagnosis. However, these associations were weak in magnitude and were attenuated in some sensitivity analyses.