Copula Models for Addressing Sample Selection in the Evaluation of Public Health Programmes: An Application to the Leeds Let's Get Active Study.

Sample selectivity is a recurrent problem in public health programmes and poses serious challenges to their evaluation. Traditional approaches to handle sample selection tend to rely on restrictive assumptions. The aim of this paper is to illustrate a copula-based selection model to handle sample selection in the evaluation of public health programmes. Motivated by a public health programme to promote physical activity in Leeds (England), we describe the assumptions underlying the copula selection, and its relative advantages compared with commonly used approaches to handle sample selection, such as inverse probability weighting and Heckman's selection model. We illustrate the methods in the Leeds Let's Get Active programme and show the implications of method choice for estimating the effect on individual's physical activity. The programme was associated with increased physical activity overall, but the magnitude of its effect differed according to adjustment method. The copula selection model led to a similar effect to the Heckman's approach but with relatively narrower 95% confidence intervals. These results remained relatively similar when different model specifications and alternative distributional assumptions were considered. The copula selection model can address important limitations of traditional approaches to address sample selection, such as the Heckman model, and should be considered in the evaluation of public health programmes, where sample selection is likely to be present.