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In the study of sentencing disparities, class related hypotheses have received considerably less attention than explanations based on offenders’ ethnicity. This is unfortunate since the two mechanisms are likely interrelated, at the very least as a result of their overlap in the population, with ethnic minorities being generally more deprived than the White majority. In this registered report we propose exploring the mediating and moderating effects between offenders’ area deprivation and their ethnic background using a novel administrative dataset capturing all offences processed through the England and Wales Crown Court. Specifically, we seek to test two key hypotheses: i) the reported ethnic disparities in sentencing are mediated and explained away by area deprivation; and ii) ethnic disparities are moderated by area deprivation, with ethnic disparities being narrower in the more deprived areas. Results from this empirical analysis will shed new light on the underlying causes of sentencing disparities, but crucially - if deprivation is shown to play a major role in the generation of ethnic disparities - they will also help inform the adequate policy responses to redress this problem.

Large research efforts have been directed at the exploration of ethnic disparities in the criminal justice system, documenting harsher treatment of minority ethnic defendants, across offence types, criminal justice decisions, and jurisdictions. However, most studies on the topic have relied on observational data, which can only approximate ‘like with like’ comparisons. As a result, researchers, practitioners and policy-makers have often been wary of interpreting such disparities as evidence of discrimination. We use causal diagrams to lay out explicitly the different ways estimates of ethnic discrimination derived from observational data could be biased. Beyond the commonly acknowledged problem of unobserved case characteristics, we also discuss other less well-known, yet likely more consequential problems: measurement error in the form of racially-determined case characteristics or as a result of high heterogeneity within the ‘Whites’ reference group, and selection bias from non-response and missing offender’s ethnicity data. We apply such causal framework to review findings from two recent studies showing ethnic disparities in custodial sentences imposed at the Crown Court (England and Wales), questioning whether the reported disparities should be interpreted as evidence of discrimination. We also use simulations to recreate the most comprehensive of those studies, and demonstrate how the reported ethnic disparities appear robust to a problem of unobserved case characteristics. We conclude that ethnic disparities observed in the Crown Court are likely reflecting evidence of direct discrimination in sentencing.

Summary Recent work (Seaman et al., 2013; Mealli & Rubin, 2015) attempts to clarify the not always well-understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., 2013; Pearl & Mohan, 2013) exploits always-observed covariates to give variable-based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable-based MAR to model dropout in certain contexts.

Sentence severity has increased in England and Wales in recent years. The causes of the increase remain unclear. One possible explanation relates to the introduction of sentencing guidelines, which seem to coincide in time with the increase in sentence severity. To date, investigations of this hypothesis have been limited to simple exploratory analyses or to specific offences. We use a new scale of sentence severity—developed using Thurstone scaling and the participation of 21 magistrates— and time-series modelling to explore whether a causal effect can be attributed to seven different guidelines. We corroborate the existence of an increase in sentence severity; however, we do not find conclusive evidence pointing at the guidelines having caused it.

Summary We explore the sensitivity of time varying confounding adjusted estimates to different dropout mechanisms. We extend the Heckman correction to two time points and explore selection models to investigate situations where the dropout process is driven by unobserved variables and the outcome respectively. The analysis is embedded in a Bayesian framework which provides several advantages. These include fitting a hierarchical structure to processes that repeat over time and avoiding exclusion restrictions in the case of the Heckman correction. We adopt the decision theoretic approach to causal inference which makes explicit the no-regime-dropout dependence assumption. We apply our methods to data from the ‘Counterweight programme’ pilot: a UK protocol to address obesity in primary care. A simulation study is also implemented.

Recent work (Seaman et al., 2013; Mealli & Rubin, 2015) attempts to clarify the not always well-understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., 2013; Pearl & Mohan, 2013) exploits always-observed covariates to give variable-based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable-based MAR to model dropout in certain contexts.

This is a correction to: The British Journal of Criminology, Volume 59, Issue 4, July 2019, Pages 979–1001, https://doi.org/10.1093/bjc/azz005

Case-control studies are particularly prone to selection bias, which can affect odds ratio estimation. Approaches to discovering and adjusting for selection bias have been proposed in the literature using graphical and heuristic tools as well as more complex statistical methods. The approach we propose is based on a survey-weighting method termed Bayesian post-stratification and follows from the conditional independences that characterise selection bias. We use our approach to perform a selection bias sensitivity analysis by using ancillary data sources that describe the target case-control population to re-weight the odds ratio estimates obtained from the study. The method is applied to two case-control studies, the first investigating the association between exposure to electromagnetic fields and acute lymphoblastic leukaemia in children and the second investigating the association between maternal occupational exposure to hairspray and a congenital anomaly in male babies called hypospadias. In both case-control studies, our method showed that the odds ratios were only moderately sensitive to selection bias.

The Regression Discontinuity (RD) design is a quasi-experimental design which emulates a randomised study by exploiting situations where treatment is assigned according to a continuous variable as is common in many drug treatment guidelines. The RD design literature focuses principally on continuous outcomes. In this paper we exploit the link between the RD design and instrumental variables to obtain a causal effect estimator, the risk ratio for the treated (RRT), for the RD design when the outcome is binary. Occasionally the RRT estimator can give negative lower confindence bounds. In the Bayesian framework we impose prior constraints that prevent this from happening. This is novel and cannot be easily reproduced in a frequentist framework. We compare our estimators to those based on estimating equation and generalized methods of moments methods. Based on extensive simulations our methods compare favourably with both methods. We apply our method on a real example to estimate the effect of statins on the probability of Low-density Lipoprotein (LDL) cholesterol levels reaching recommended levels., Comment: 29 pages, 4 figures

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.

SummaryIdentifying 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.

Regression discontinuity designs use observational data to examine treatment efficacy. This article uses the example of statin prescription in primary care to explain the concept of the method and how it can be used

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. NHS guidelines state that statins should be prescribed to patients with 10 year cardiovascular disease risk scores in excess of 20%. If we consider patients whose scores are close to this threshold we find that there is an element of random variation in both the risk score itself and its measurement. We can thus consider the threshold a randomising device assigning the prescription to units 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 it 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., Comment: 21 pages, 5 figures, 2 tables

Observational studies of human health and disease (basic, clinical and epidemiological) are vulnerable to methodological problems -such as selection bias and confounding- that make causal inferences problematic. Gene-disease associations are no exception, as they are commonly investigated using observational designs. A rich body of knowledge exists in medicine and epidemiology on the assessment of causal relationships involving personal and environmental causes of disease; it includes seminal causal criteria developed by Austin Bradford Hill and more recently applied directed acyclic graphs (DAGs). However, such knowledge has seldom been applied to assess causal relationships in clinical genetics and genomics, even in studies aimed at making inferences relevant for human health. Conversely, incorporating genetic causal knowledge into clinical and epidemiological causal reasoning is still a largely unexplored area. As the contribution of genetics to the understanding of disease aetiology becomes more important, causal assessment of genetic and genomic evidence becomes fundamental. The method we develop in this paper provides a simple and rigorous first step towards this goal. The present paper is an example of integrative research, i.e., research that integrates knowledge, data, methods, techniques, and reasoning from multiple disciplines, approaches and levels of analysis to generate knowledge that no discipline alone may achieve.

Background Hypospadias 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. Objective Our 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. Design We 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. Results In 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. Conclusions Excess 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.