Trading HIV for sheep: Risky sexual behavior and the response of female sex workers to Tabaski in Senegal.

We use a cohort of female sex workers (FSWs) in Senegal to show how large anticipated economic shocks lead to increased risky sexual behavior. Exploiting the exogenous timing of interviews, we study the effect of Tabaski, the most important Islamic festival celebrated in Senegal, in which most households purchase an expensive animal for sacrifice. Condom use, measured robustly via the list experiment, falls by between 27.3 percentage points (pp) (65.5%) and 43.1 pp (22.7%) in the 9 days before Tabaski, or a maximum of 49.5 pp (76%) in the 7 day period preceding Tabaski. The evidence suggests the economic pressures from Tabaski are key to driving the behavior change observed through the price premium for condomless sex. Those most exposed to the economic pressure from Tabaski were unlikely to be using condoms at all in the week before the festival. Our findings show that Tabaski leads to increased risky behaviors for FSWs, a key population at high risk of HIV infection, for at least 1 week every year and has implications for FSWs in all countries celebrating Tabaski or similar festivals. Because of the scale, frequency, and size of the behavioral response to shocks of this type, policy should be carefully designed to protect vulnerable women against anticipated shocks.

A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health.

We develop a flexible two-equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post-program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.

Did the ACA's "guaranteed issue" provision cause adverse selection into nongroup insurance? Analysis using a copula-based hurdle model.

Prior to the Affordable Care Act (ACA), insurance companies could charge higher premiums, or outright deny coverage, to people with preexisting health problems. But the ACA's "guaranteed issue" provision forbids such price discrimination and denials of coverage. This paper seeks to determine whether, after implementation of the ACA, nongroup private insurance plans have experienced adverse selection. Our empirical approach employs a copula-based hurdle regression model, with dependence modeled as a function of dimensions along which adverse selection might occur. Our main finding is that, after implementation of the ACA, nongroup insurance enrollees with preexisting health problems do not appear to exhibit adverse selection. This finding suggests that the ACA's mandate that everyone acquire coverage might have attracted enough healthy enrollees to offset any adverse selection.

Copula selection models for non-Gaussian outcomes that are missing not at random.

Missing not at random (MNAR) data pose key challenges for statistical inference because the substantive model of interest is typically not identifiable without imposing further (eg, distributional) assumptions. Selection models have been routinely used for handling MNAR by jointly modeling the outcome and selection variables and typically assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection approaches, for example, estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption compared with those assuming that nonresponse and outcome are jointly normally distributed. However, the proposed methods have been mostly restricted to a specific joint distribution (eg, bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterizes the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the effect of laparoscopic surgery on long-term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM.

Mixed binary-continuous copula regression models with application to adverse birth outcomes.

Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely, binary) whereas the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood-based approach for the resulting class of copula regression models and employ it in the context of modeling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested.

Penalized likelihood estimation of a trivariate additive probit model.

This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.

Evaluating treatment effectiveness under model misspecification: A comparison of targeted maximum likelihood estimation with bias-corrected matching.

Statistical approaches for estimating treatment effectiveness commonly model the endpoint, or the propensity score, using parametric regressions such as generalised linear models. Misspecification of these models can lead to biased parameter estimates. We compare two approaches that combine the propensity score and the endpoint regression, and can make weaker modelling assumptions, by using machine learning approaches to estimate the regression function and the propensity score. Targeted maximum likelihood estimation is a double-robust method designed to reduce bias in the estimate of the parameter of interest. Bias-corrected matching reduces bias due to covariate imbalance between matched pairs by using regression predictions. We illustrate the methods in an evaluation of different types of hip prosthesis on the health-related quality of life of patients with osteoarthritis. We undertake a simulation study, grounded in the case study, to compare the relative bias, efficiency and confidence interval coverage of the methods. We consider data generating processes with non-linear functional form relationships, normal and non-normal endpoints. We find that across the circumstances considered, bias-corrected matching generally reported less bias, but higher variance than targeted maximum likelihood estimation. When either targeted maximum likelihood estimation or bias-corrected matching incorporated machine learning, bias was much reduced, compared to using misspecified parametric models.

Adjusting HIV prevalence estimates for non-participation: an application to demographic surveillance.

INTRODUCTION: HIV testing is a cornerstone of efforts to combat the HIV epidemic, and testing conducted as part of surveillance provides invaluable data on the spread of infection and the effectiveness of campaigns to reduce the transmission of HIV. However, participation in HIV testing can be low, and if respondents systematically select not to be tested because they know or suspect they are HIV positive (and fear disclosure), standard approaches to deal with missing data will fail to remove selection bias. We implemented Heckman-type selection models, which can be used to adjust for missing data that are not missing at random, and established the extent of selection bias in a population-based HIV survey in an HIV hyperendemic community in rural South Africa. METHODS: We used data from a population-based HIV survey carried out in 2009 in rural KwaZulu-Natal, South Africa. In this survey, 5565 women (35%) and 2567 men (27%) provided blood for an HIV test. We accounted for missing data using interviewer identity as a selection variable which predicted consent to HIV testing but was unlikely to be independently associated with HIV status. Our approach involved using this selection variable to examine the HIV status of residents who would ordinarily refuse to test, except that they were allocated a persuasive interviewer. Our copula model allows for flexibility when modelling the dependence structure between HIV survey participation and HIV status. RESULTS: For women, our selection model generated an HIV prevalence estimate of 33% (95% CI 27-40) for all people eligible to consent to HIV testing in the survey. This estimate is higher than the estimate of 24% generated when only information from respondents who participated in testing is used in the analysis, and the estimate of 27% when imputation analysis is used to predict missing data on HIV status. For men, we found an HIV prevalence of 25% (95% CI 15-35) using the selection model, compared to 16% among those who participated in testing, and 18% estimated with imputation. We provide new confidence intervals that correct for the fact that the relationship between testing and HIV status is unknown and requires estimation. CONCLUSIONS: We confirm the feasibility and value of adopting selection models to account for missing data in population-based HIV surveys and surveillance systems. Elements of survey design, such as interviewer identity, present the opportunity to adopt this approach in routine applications. Where non-participation is high, true confidence intervals are much wider than those generated by standard approaches to dealing with missing data suggest.

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.

A semiparametric bivariate probit model for joint modeling of outcomes in STEMI patients.

In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient's condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.

Evaluating treatment effectiveness in patient subgroups: a comparison of propensity score methods with an automated matching approach.

Propensity score (Pscore) matching and inverse probability of treatment weighting (IPTW) can remove bias due to observed confounders, if the Pscore is correctly specified. Genetic Matching (GenMatch) matches on the Pscore and individual covariates using an automated search algorithm to balance covariates. This paper compares common ways of implementing Pscore matching and IPTW, with Genmatch for balancing time-constant baseline covariates}. The methods are considered when estimates of treatment effectiveness are required for patient subgroups, and the treatment allocation process differs by subgroup. We apply these methods in a prospective cohort study that estimates the effectiveness of Drotrecogin alfa activated, for subgroups of patients with severe sepsis. In a simulation study we compare the methods when the Pscore is correctly specified, and then misspecified by ignoring the subgroup-specific treatment allocation. The simulations also consider poor overlap in baseline covariates, and different sample sizes. In the case study, GenMatch reports better covariate balance than IPTW or Pscore matching. In the simulations with correctly specified Pscores, good overlap and reasonable sample sizes, all methods report minimal bias. When the Pscore is misspecified, GenMatch reports the least imbalance and bias. With small sample sizes, IPTW is the most efficient approach, but all methods report relatively high bias of treatment effects. This study shows that overall GenMatch achieves the best covariate balance for each subgroup, and is more robust to Pscore misspecification than common alternative Pscore approaches.

Methods for estimating subgroup effects in cost-effectiveness analyses that use observational data.

Decision makers require cost-effectiveness estimates for patient subgroups. In nonrandomized studies, propensity score (PS) matching and inverse probability of treatment weighting (IPTW) can address overt selection bias, but only if they balance observed covariates between treatment groups. Genetic matching (GM) matches on the PS and individual covariates using an automated search algorithm to directly balance baseline covariates. This article compares these methods for estimating subgroup effects in cost-effectiveness analyses (CEA). The motivating case study is a CEA of a pharmaceutical intervention, drotrecogin alfa (DrotAA), for patient subgroups with severe sepsis (n = 2726). Here, GM reported better covariate balance than PS matching and IPTW. For the subgroup at a high level of baseline risk, the probability that DrotAA was cost-effective ranged from 30% (IPTW) to 90% (PS matching and GM), at a threshold of £20 000 per quality-adjusted life-year. We then compared the methods in a simulation study, in which initially the PS was correctly specified and then misspecified, for example, by ignoring the subgroup-specific treatment assignment. Relative performance was assessed as bias and root mean squared error (RMSE) in the estimated incremental net benefits. When the PS was correctly specified and inverse probability weights were stable, each method performed well; IPTW reported the lowest RMSE. When the subgroup-specific treatment assignment was ignored, PS matching and IPTW reported covariate imbalance and bias; GM reported better balance, less bias, and more precise estimates. We conclude that if the PS is correctly specified and the weights for IPTW are stable, each method can provide unbiased cost-effectiveness estimates. However, unlike IPTW and PS matching, GM is relatively robust to PS misspecification.

Penalised regression splines: theory and application to medical research.

Generalised additive models (GAMs) allow for flexible functional dependence of a response variable on covariates. The aim of this article is to provide an accessible overview of GAMs based on the penalised likelihood approach with regression splines. In contrast to the classical backfitting, the penalised likelihood framework taken here provides researchers with an efficient computational method for automatic multiple smoothing parameter selection, which can determine the functional form of any relationship from the data. We illustrate through an example how the use of this methodology can help to gain insights into medical research.