Identifying direct and indirect effects is a common problem in the social science and medical literature and can be described as follows. A treatment is administered and a response is recorded. However, another variable mediates the effect of the treatment on the response, in some way "channelling" a part of the treatment effect. The question is how to extricate the direct and channelled (indirect) effects from one another when it is not possible to intervene on the mediating variable. The aim of the paper is to tackle this problem by using a model for direct and indirect effects based on the decision theoretic framework for causal inference. Copyright 2007 Royal Statistical Society.

Retrospective case-control studies are more susceptible to selection bias than other epidemiologic studies as by design they require that both cases and controls are representative of the same population. However, as cases and control recruitment processes are often different, it is not always obvious that the necessary exchangeability conditions hold. Selection bias typically arises when the selection criteria are associated with the risk factor under investigation. We develop a method which produces bias-adjusted estimates for the odds ratio. Our method hinges on 2 conditions. The first is that a variable that separates the risk factor from the selection criteria can be identified. This is termed the "bias breaking" variable. The second condition is that data can be found such that a bias-corrected estimate of the distribution of the bias breaking variable can be obtained. We show by means of a set of examples that such bias breaking variables are not uncommon in epidemiologic settings. We demonstrate using simulations that the estimates of the odds ratios produced by our method are consistently closer to the true odds ratio than standard odds ratio estimates using logistic regression. Further, by applying it to a case-control study, we show that our method can help to determine whether selection bias is present and thus confirm the validity of study conclusions when no evidence of selection bias can be found.

BackgroundHypospadias is one of the most common urogenital congenital anomalies affecting baby boys. Prevalence estimates in Europe range from 4 to 24 per 10,000 births, depending on definition, with higher rates reported from the United States. Relatively little is known about potential risk factors, but a role for endocrine-disrupting chemicals (EDCs) has been proposed.ObjectiveOur goal was to elucidate the risk of hypospadias associated with occupational exposure of the mother to endocrine-disruptor chemicals, use of folate supplementation during pregnancy, and vegetarianism.DesignWe designed a case–control study of 471 hypospadias cases referred to surgeons and 490 randomly selected birth controls, born 1 January 1997–30 September 1998 in southeast England. Telephone interviews of mothers elicited information on folate supplementation during pregnancy and vegetarianism. We used a job exposure matrix to classify occupational exposure.ResultsIn multiple logistic regression analysis, there were increased risks for self-reported occupational exposure to hair spray [exposed vs. nonexposed, odds ratio (OR) = 2.39; 95% confidence interval (CI), 1.40–4.17] and phthalate exposure obtained by a job exposure matrix (OR = 3.12; 95% CI, 1.04–11.46). There was a significantly reduced risk of hypospadias associated with of folate use during the first 3 months of pregnancy (OR = 0.64; 95% CI, 0.44–0.93). Vegetarianism was not associated with hypospadias risk.ConclusionsExcess risks of hypospadias associated with occupational exposures to phthalates and hair spray suggest that antiandrogenic EDCs may play a role in hypospadias. Folate supplementation in early pregnancy may be protective.

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The regression discontinuity (RD) design is a quasi‐experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. It can be applied in any context where a particular treatment or intervention is administered according to a pre‐specified rule linked to a continuous variable. Such thresholds are common in primary care drug prescription where the RD design can be used to estimate the causal effect of medication in the general population. Such results can then be contrasted to those obtained from randomised controlled trials (RCTs) and inform prescription policy and guidelines based on a more realistic and less expensive context. In this paper, we focus on statins, a class of cholesterol‐lowering drugs, however, the methodology can be applied to many other drugs provided these are prescribed in accordance to pre‐determined guidelines. Current guidelines in the UK state that statins should be prescribed to patients with 10‐year cardiovascular disease risk scores in excess of 20%. If we consider patients whose risk scores are close to the 20% risk score threshold, we find that there is an element of random variation in both the risk score itself and its measurement. We can therefore consider the threshold as a randomising device that assigns statin prescription to individuals just above the threshold and withholds it from those just below. Thus, we are effectively replicating the conditions of an RCT in the area around the threshold, removing or at least mitigating confounding. We frame the RD design in the language of conditional independence, which clarifies the assumptions necessary to apply an RD design to data, and which makes the links with instrumental variables clear. We also have context‐specific knowledge about the expected sizes of the effects of statin prescription and are thus able to incorporate this into Bayesian models by formulating informative priors on our causal parameters. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.