A novel equivalence probability weighted power prior for using historical control data in an adaptive clinical trial design: A comparison to standard methods.

A standard two-arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down-weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.

Assessing efficacy in important subgroups in confirmatory trials: An example using Bayesian dynamic borrowing.

Assessment of efficacy in important subgroups - such as those defined by sex, age, race and region - in confirmatory trials is typically performed using separate analysis of the specific subgroup. This ignores relevant information from the complementary subgroup. Bayesian dynamic borrowing uses an informative prior based on analysis of the complementary subgroup and a weak prior distribution centred on a mean of zero to construct a robust mixture prior. This combination of priors allows for dynamic borrowing of prior information; the analysis learns how much of the complementary subgroup prior information to borrow based on the consistency between the subgroup of interest and the complementary subgroup. A tipping point analysis can be carried out to identify how much prior weight needs to be placed on the complementary subgroup component of the robust mixture prior to establish efficacy in the subgroup of interest. An attractive feature of the tipping point analysis is that it enables the evidence from the source subgroup, the evidence from the target subgroup, and the combined evidence to be displayed alongside each other. This method is illustrated with an example trial in severe asthma where efficacy in the adolescent subgroup was assessed using a mixture prior combining an informative prior from the adult data in the same trial with a non-informative prior.

Reducing Patient Burden in Clinical Trials Through the Use of Historical Controls: Appropriate Selection of Historical Data to Minimize Risk of Bias.

Historical data have been used to augment or replace control arms in some rare disease and pediatric clinical trials. With greater availability of historical data and new methodology such as dynamic borrowing, the inclusion of historical data in clinical trials is an increasingly appealing approach for larger disease areas as well, as this can result in increased power and precision and can minimize the burden on patients in clinical trials. However, sponsors must assess whether the potential biases incurred with this approach outweigh the benefits and discuss this trade-off with the regulatory agencies. This paper discusses important points for the appropriate selection of historical controls for inclusion in the analysis of primary and/or key secondary endpoint(s) in clinical trials. The general steps are as follows: (1) Assess whether a trial is a suitable candidate for this approach. (2) If it is, then carefully identify appropriate historical trials to minimize selection bias. (3) Refine the historical control set if appropriate, for example, by selecting subsets of studies or patients. Identification of trial settings that are amenable to historical borrowing and selection of appropriate historical data using the principles discussed in this paper has the potential to lead to more efficient estimation and decision making. Ultimately, this efficiency gain results in lower patient burden and gets effective drugs to patients more quickly.

A causal modelling framework for reference-based imputation and tipping point analysis in clinical trials with quantitative outcome.

We consider estimation in a randomised placebo-controlled or standard-of-care-controlled drug trial with quantitative outcome, where participants who discontinue an investigational treatment are not followed up thereafter, and the estimand follows a treatment policy strategy for handling treatment discontinuation. Our approach is also useful in situations where participants take rescue medication or a subsequent line of therapy and the estimand follows a hypothetical strategy to estimate the effect of initially randomised treatment in the absence of rescue or other active treatment. Carpenter et al proposed reference-based imputation methods which use a reference arm to inform the distribution of post-discontinuation outcomes and hence to inform an imputation model. However, the reference-based imputation methods were not formally justified. We present a causal model which makes an explicit assumption in a potential outcomes framework about the maintained causal effect of treatment after discontinuation. We use mathematical argument and a simulation study to show that the "jump to reference", "copy reference" and "copy increments in reference" reference-based imputation methods, with the control arm as the reference arm, are special cases of the causal model with specific assumptions about the causal treatment effect. We also show that the causal model provides a flexible and transparent framework for a tipping point sensitivity analysis in which we vary the assumptions made about the causal effect of discontinued treatment. We illustrate the approach with data from two longitudinal clinical trials.

Minimizing Patient Burden Through the Use of Historical Subject-Level Data in Innovative Confirmatory Clinical Trials: Review of Methods and Opportunities.

The goal of clinical trial research is to deliver safe and efficacious new treatments to patients in need in a timely and cost-effective manner. There is precedent in using historical control data to reduce the number of concurrent control subjects required in developing medicines for rare diseases and other areas of unmet need. The purpose of this paper is to provide a review for a regulatory and industry audience of the current state of relevant statistical methods, and of the uptake of these approaches and the opportunities for broader use of historical data in confirmatory clinical trials. General principles to consider when incorporating historical control data in a new trial are presented. Bayesian and frequentist approaches are outlined including how the operating characteristics for such a trial can be obtained. Finally, examples of approved new treatments that incorporated historical controls in their confirmatory trials are presented.

Better decision making in drug development through adoption of formal prior elicitation.

With the continued increase in the use of Bayesian methods in drug development, there is a need for statisticians to have tools to develop robust and defensible informative prior distributions. Whilst relevant empirical data should, where possible, provide the basis for such priors, it is often the case that limitations in data and/or our understanding may preclude direct construction of a data-based prior. Formal expert elicitation methods are a key technique that can be used to determine priors in these situations. Within GlaxoSmithKline, we have adopted a structured approach to prior elicitation on the basis of the SHELF elicitation framework and routinely use this in conjunction with calculation of probability of success (assurance) of the next study(s) to inform internal decision making at key project milestones. The aim of this paper is to share our experiences of embedding the use of prior elicitation within a large pharmaceutical company, highlighting both the benefits and challenges of prior elicitation through a series of case studies. We have found that putting team beliefs into the shape of a quantitative probability distribution provides a firm anchor for all internal decision making, enabling teams to provide investment boards with formally appropriate estimates of the probability of trial success as well as robust plans for interim decision rules where appropriate. As an added benefit, the elicitation process provides transparency about the beliefs and risks of the potential medicine, ultimately enabling better portfolio and company-wide decision making.

Practical experiences of adopting assurance as a quantitative framework to support decision making in drug development.

All clinical trials are designed for success of their primary objectives. Hence, evaluating the probability of success (PoS) should be a key focus at the design stage both to support funding approval from sponsor governance boards and to inform trial design itself. Use of assurance-that is, expected success probability averaged over a prior probability distribution for the treatment effect-to quantify PoS of a planned study has grown across the industry in recent years, and has now become routine within the authors' company. In this paper, we illustrate some of the benefits of systematically adopting assurance as a quantitative framework to support decision making in drug development through several case-studies where evaluation of assurance has proved impactful in terms of trial design and in supporting governance-board reviews of project proposals. In addition, we describe specific features of how the assurance framework has been implemented within our company, highlighting the critical role that prior elicitation plays in this process, and illustrating how the overall assurance calculation may be decomposed into a sequence of conditional PoS estimates which can provide greater insight into how and when different development options are able to discharge risk.

Protective Effects of Smoke-free Legislation on Birth Outcomes in England: A Regression Discontinuity Design.

BACKGROUND: Environmental tobacco smoke has an adverse association with preterm birth and birth weight. England introduced a new law to make virtually all enclosed public places and workplaces smoke free on July 1, 2007. We investigated the effect of smoke-free legislation on birth outcomes in England using Hospital Episode Statistics (HES) maternity data. METHODS: We used regression discontinuity, a quasi-experimental study design, which can facilitate valid causal inference, to analyze short-term effects of smoke-free legislation on birth weight, low birth weight, gestational age, preterm birth, and small for gestational age. RESULTS: We analyzed 1,800,906 pregnancies resulting in singleton live-births in England between 1 January 2005 and 31 December 2009. In the 1 to 5 months following the introduction of the smoke-free legislation, for those entering their third trimester, the risk of low birth weight decreased by between 8% (95% confidence interval [CI]: 4%, 12%) and 14% (95% CI: 5%, 23%), very low birth weight between 28% (95% CI: 19%, 36%) and 32% (95% CI: 21%, 41%), preterm birth between 4% (95% CI: 1%, 8%) and 9% (95% CI: 2%, 16%), and small for gestational age between 5% (95% CI: 2%, 8%) and 9% (95% CI: 2%, 15%). The estimated impact of the smoke-free legislation varied by maternal age, deprivation, ethnicity, and region. CONCLUSIONS: The introduction of smoke-free legislation in England had an immediate estimated beneficial impact on birth outcomes overall, although we did not observe improvements across all age, ethnic, or deprivation groups.See video abstract at http://links.lww.com/EDE/B85.

Birth Weight, Ethnicity, and Exposure to Trihalomethanes and Haloacetic Acids in Drinking Water during Pregnancy in the Born in Bradford Cohort.

BACKGROUND: Evidence for a relationship between trihalomethane (THM) or haloacetic acid (HAA) exposure and adverse fetal growth is inconsistent. Disinfection by-products exist as complex mixtures in water supplies, but THMs and HAAs have typically been examined separately. OBJECTIVES: We investigated joint exposure at the individual level to THMs and HAAs in relation to birth weight in the multi-ethnic Born in Bradford birth cohort. METHODS: Pregnant women reported their water consumption and activities via questionnaire. These data were combined with area-level THM and HAA concentrations to estimate integrated uptake of THMs into blood and HAA ingestion, accounting for boiling/filtering. We examined the relationship between THM and HAA exposures and birth weight of up to 7,438 singleton term babies using multiple linear regression, stratified by ethnicity. RESULTS: Among Pakistani-origin infants, mean birth weight was significantly lower in association with the highest versus lowest tertiles of integrated THM uptake (e.g., -53.7 g; 95% CI: -89.9, -17.5 for ≥ 1.82 vs. < 1.05 µg/day of total THM) and there were significant trends (p < 0.01) across increasing tertiles, but there were no associations among white British infants. Neither ingestion of HAAs alone or jointly with THMs was associated with birth weight. Estimated THM uptake via showering, bathing, and swimming was significantly associated with lower birth weight in Pakistani-origin infants, when adjusting for THM and HAA ingestion via water consumption. CONCLUSIONS: To our knowledge, this is the largest DBP and fetal growth study to date with individual water use data, and the first to examine individual-level estimates of joint THM-HAA exposure. Our findings demonstrate associations between THM, but not HAA, exposure during pregnancy and reduced birth weight, but suggest this differs by ethnicity. This study suggests that THMs are not acting as a proxy for HAAs, or vice-versa. CITATION: Smith RB, Edwards SC, Best N, Wright J, Nieuwenhuijsen MJ, Toledano MB. 2016. Birth weight, ethnicity, and exposure to trihalomethanes and haloacetic acids in drinking water during pregnancy in the Born in Bradford cohort. Environ Health Perspect 124:681-689; http://dx.doi.org/10.1289/ehp.1409480.

The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting.

BACKGROUND: To plan for pensions and health and social services, future mortality and life expectancy need to be forecast. Consistent forecasts for all subnational units within a country are very rare. Our aim was to forecast mortality and life expectancy for England and Wales' districts. METHODS: We developed Bayesian spatiotemporal models for forecasting of age-specific mortality and life expectancy at a local, small-area level. The models included components that accounted for mortality in relation to age, birth cohort, time, and space. We used geocoded mortality and population data between 1981 and 2012 from the Office for National Statistics together with the model with the smallest error to forecast age-specific death rates and life expectancy to 2030 for 375 of England and Wales' 376 districts. We measured model performance by withholding recent data and comparing forecasts with this withheld data. FINDINGS: Life expectancy at birth in England and Wales was 79·5 years (95% credible interval 79·5-79·6) for men and 83·3 years (83·3-83·4) for women in 2012. District life expectancies ranged between 75·2 years (74·9-75·6) and 83·4 years (82·1-84·8) for men and between 80·2 years (79·8-80·5) and 87·3 years (86·0-88·8) for women. Between 1981 and 2012, life expectancy increased by 8·2 years for men and 6·0 years for women, closing the female-male gap from 6·0 to 3·8 years. National life expectancy in 2030 is expected to reach 85·7 (84·2-87·4) years for men and 87·6 (86·7-88·9) years for women, further reducing the female advantage to 1·9 years. Life expectancy will reach or surpass 81·4 years for men and reach or surpass 84·5 years for women in every district by 2030. Longevity inequality across districts, measured as the difference between the 1st and 99th percentiles of district life expectancies, has risen since 1981, and is forecast to rise steadily to 8·3 years (6·8-9·7) for men and 8·3 years (7·1-9·4) for women by 2030. INTERPRETATION: Present forecasts underestimate the expected rise in life expectancy, especially for men, and hence the need to provide improved health and social services and pensions for elderly people in England and Wales. Health and social policies are needed to curb widening life expectancy inequalities, help deprived districts catch up in longevity gains, and avoid a so-called grand divergence in health and longevity. FUNDING: UK Medical Research Council and Public Health England.

Analysing the health effects of simultaneous exposure to physical and chemical properties of airborne particles.

BACKGROUND: Airborne particles are a complex mix of organic and inorganic compounds, with a range of physical and chemical properties. Estimation of how simultaneous exposure to air particles affects the risk of adverse health response represents a challenge for scientific research and air quality management. In this paper, we present a Bayesian approach that can tackle this problem within the framework of time series analysis. METHODS: We used Dirichlet process mixture models to cluster time points with similar multipollutant and response profiles, while adjusting for seasonal cycles, trends and temporal components. Inference was carried out via Markov Chain Monte Carlo methods. We illustrated our approach using daily data of a range of particle metrics and respiratory mortality for London (UK) 2002-2005. To better quantify the average health impact of these particles, we measured the same set of metrics in 2012, and we computed and compared the posterior predictive distributions of mortality under the exposure scenario in 2012 vs 2005. RESULTS: The model resulted in a partition of the days into three clusters. We found a relative risk of 1.02 (95% credible intervals (CI): 1.00, 1.04) for respiratory mortality associated with days characterised by high posterior estimates of non-primary particles, especially nitrate and sulphate. We found a consistent reduction in the airborne particles in 2012 vs 2005 and the analysis of the posterior predictive distributions of respiratory mortality suggested an average annual decrease of -3.5% (95% CI: -0.12%, -5.74%). CONCLUSIONS: We proposed an effective approach that enabled the better understanding of hidden structures in multipollutant health effects within time series analysis. It allowed the identification of exposure metrics associated with respiratory mortality and provided a tool to assess the changes in health effects from various policies to control the ambient particle matter mixtures.

Robust bayesian sensitivity analysis for case-control studies with uncertain exposure misclassification probabilities.

Exposure misclassification in case-control studies leads to bias in odds ratio estimates. There has been considerable interest recently to account for misclassification in estimation so as to adjust for bias as well as more accurately quantify uncertainty. These methods require users to elicit suitable values or prior distributions for the misclassification probabilities. In the event where exposure misclassification is highly uncertain, these methods are of limited use, because the resulting posterior uncertainty intervals tend to be too wide to be informative. Posterior inference also becomes very dependent on the subjectively elicited prior distribution. In this paper, we propose an alternative "robust Bayesian" approach, where instead of eliciting prior distributions for the misclassification probabilities, a feasible region is given. The extrema of posterior inference within the region are sought using an inequality constrained optimization algorithm. This method enables sensitivity analyses to be conducted in a useful way as we do not need to restrict all of our unknown parameters to fixed values, but can instead consider ranges of values at a time.

Diagram-based Analysis of Causal Systems (DACS): elucidating inter-relationships between determinants of acute lower respiratory infections among children in sub-Saharan Africa.

BACKGROUND: Effective interventions require evidence on how individual causal pathways jointly determine disease. Based on the concept of systems epidemiology, this paper develops Diagram-based Analysis of Causal Systems (DACS) as an approach to analyze complex systems, and applies it by examining the contributions of proximal and distal determinants of childhood acute lower respiratory infections (ALRI) in sub-Saharan Africa. RESULTS: Diagram-based Analysis of Causal Systems combines the use of causal diagrams with multiple routinely available data sources, using a variety of statistical techniques. In a step-by-step process, the causal diagram evolves from conceptual based on a priori knowledge and assumptions, through operational informed by data availability which then undergoes empirical testing, to integrated which synthesizes information from multiple datasets. In our application, we apply different regression techniques to Demographic and Health Survey (DHS) datasets for Benin, Ethiopia, Kenya and Namibia and a pooled World Health Survey (WHS) dataset for sixteen African countries. Explicit strategies are employed to make decisions transparent about the inclusion/omission of arrows, the sign and strength of the relationships and homogeneity/heterogeneity across settings.Findings about the current state of evidence on the complex web of socio-economic, environmental, behavioral and healthcare factors influencing childhood ALRI, based on DHS and WHS data, are summarized in an integrated causal diagram. Notably, solid fuel use is structured by socio-economic factors and increases the risk of childhood ALRI mortality. CONCLUSIONS: Diagram-based Analysis of Causal Systems is a means of organizing the current state of knowledge about a specific area of research, and a framework for integrating statistical analyses across a whole system. This partly a priori approach is explicit about causal assumptions guiding the analysis and about researcher judgment, and wrong assumptions can be reversed following empirical testing. This approach is well-suited to dealing with complex systems, in particular where data are scarce.

Aircraft noise and cardiovascular disease near Heathrow airport in London: small area study.

OBJECTIVE: To investigate the association of aircraft noise with risk of stroke, coronary heart disease, and cardiovascular disease in the general population. DESIGN: Small area study. SETTING: 12 London boroughs and nine districts west of London exposed to aircraft noise related to Heathrow airport in London. POPULATION: About 3.6 million residents living near Heathrow airport. Risks for hospital admissions were assessed in 12 110 census output areas (average population about 300 inhabitants) and risks for mortality in 2378 super output areas (about 1500 inhabitants). MAIN OUTCOME MEASURES: Risk of hospital admissions for, and mortality from, stroke, coronary heart disease, and cardiovascular disease, 2001-05. RESULTS: Hospital admissions showed statistically significant linear trends (P<0.001 to P<0.05) of increasing risk with higher levels of both daytime (average A weighted equivalent noise 7 am to 11 pm, L(Aeq),16 h) and night time (11 pm to 7 am, Lnight) aircraft noise. When areas experiencing the highest levels of daytime aircraft noise were compared with those experiencing the lowest levels (>63 dB v ≤ 51 dB), the relative risk of hospital admissions for stroke was 1.24 (95% confidence interval 1.08 to 1.43), for coronary heart disease was 1.21 (1.12 to 1.31), and for cardiovascular disease was 1.14 (1.08 to 1.20) adjusted for age, sex, ethnicity, deprivation, and a smoking proxy (lung cancer mortality) using a Poisson regression model including a random effect term to account for residual heterogeneity. Corresponding relative risks for mortality were of similar magnitude, although with wider confidence limits. Admissions for coronary heart disease and cardiovascular disease were particularly affected by adjustment for South Asian ethnicity, which needs to be considered in interpretation. All results were robust to adjustment for particulate matter (PM10) air pollution, and road traffic noise, possible for London boroughs (population about 2.6 million). We could not distinguish between the effects of daytime or night time noise as these measures were highly correlated. CONCLUSION: High levels of aircraft noise were associated with increased risks of stroke, coronary heart disease, and cardiovascular disease for both hospital admissions and mortality in areas near Heathrow airport in London. As well as the possibility of causal associations, alternative explanations such as residual confounding and potential for ecological bias should be considered.

Time trends in biological fertility in Western Europe.

We investigated trends in biological fertility in a comprehensive analysis of 5 major European data sets with data on time to pregnancy (TTP) and proportion of contraceptive failures. In particular, we distinguished a period effect from a birth cohort effect (lifelong tendency) in both sexes. Attempts at conception not resulting in birth were excluded. We analyzed data on pregnancies occurring in 9,247 couples between 1953 and 1993 and performed sensitivity analyses to check the robustness of findings. Separate analyses of each time effect showed an increasing fertility trend. Mutually adjusted analyses demonstrated that this rise was visible as a male cohort effect for both TTP and contraceptive failure. On the other hand, the female birth cohort effect showed a slight fall in the first half of the study period for both TTP and contraceptive failure. As a period effect, fertility remained generally stable, the slight trends in TTP and contraceptive failure being in opposite directions, likely indicating an artifact. The rising trend accords with most previous evidence. The increasing trend in male fertility does not contradict the previously reported semen quality deterioration, the effects of which are calculated to be small. The declining female fertility accords with a falling dizygotic twinning rate during the same period.

The contributions of risk factor trends to cardiometabolic mortality decline in 26 industrialized countries.

BACKGROUND: Cardiovascular disease mortality has declined and diabetes mortality has increased in high-income countries. We estimated the potential role of trends in population body mass index, systolic blood pressure, serum total cholesterol and smoking in cardiometabolic mortality decline in 26 industrialized countries. METHODS: Mortality data were from national vital statistics. Body mass index, systolic blood pressure and serum total cholesterol were from a systematic analysis of population-based data. We estimated the associations between change in cardiometabolic mortality and changes in risk factors, adjusted for change in per-capita gross domestic product. We calculated the potential contribution of risk factor trends to mortality decline. RESULTS: Between 1980 and 2009, age-standardized cardiometabolic mortality declined in all 26 countries, with the annual decline between <1% in Mexico to ≈ 5% in Australia. Across the 26 countries together, risk factor trends may have accounted for ≈ 48% (men) and ≈ 40% (women) of cardiometabolic mortality decline. Risk factor trends may have accounted for >60% of decline among men and women in Finland and Switzerland, men in New Zealand and France, and women in Italy; their benefits were smallest in Mexican, Portuguese, and Japanese men and Mexican women. Risk factor trends may have slowed down mortality decline in Chilean men and women and had virtually no effect in Argentinean women. The contributions of risk factors to mortality decline seemed substantially larger among men than among women in the USA, Canada and The Netherlands. CONCLUSIONS: Industrialized countries have varied widely in the extent of risk factor prevention, and its likely benefits for cardiometabolic mortality.

Chlorination by-products in tap water and semen quality in England and Wales.

OBJECTIVES: Disinfection by-products (DBPs) have been associated with adverse semen outcomes in laboratory animals, although the evidence for trihalomethanes (THMs) is limited. Three small epidemiological studies found little evidence for an association between DBPs and adverse semen outcomes in humans. Using data from a large case-referent study (Chemicals and Pregnancy Study, Chaps-UK), we investigated the association between total THM (TTHM), chloroform and total brominated THMs and sperm concentration, percent motile sperm and motile sperm concentration (MSC). METHODS: Chaps-UK recruited men from 13 fertility clinics in nine urban centres across England and Wales between 1999 and 2002. We linked modelled THM concentrations in water zones to semen quality data for 642 cases (men with low MSC) and 926 referents (other men investigated for infertility), based on the men's residence during semen sampling. We assessed risk of low MSC in relation to DBP exposure using continuous THM concentrations. A secondary analysis investigated continuous outcomes (MSC, sperm concentration and percent motile sperm). RESULTS: In the case-referent analysis there was little evidence of elevated risk associated with chloroform, total brominated THM or TTHM concentration after adjustment (OR per 10 µg/L TTHM 1.01; 95% CI 0.91 to 1.12). Similarly, there was no significant effect of THMs on the continuous outcomes. CONCLUSIONS: In the largest study to date on DBPs in public water supplies, and semen quality we found that concentrations of THMs were not associated with poor semen quality. Large-scale investigation of other DBPs (eg, haloacetic acids) and other semen quality parameters (eg, sperm morphology and/or sperm DNA integrity) is recommended.

Cardiothoracic ratio from postero-anterior chest radiographs: a simple, reproducible and independent marker of disease severity and outcome in adults with congenital heart disease.

OBJECTIVE: The wide spectrum of intracardiac anatomy and reparative surgery available for adults with congenital heart disease (ACHD) makes uniform measurement of cardiac size and disease severity challenging. The aim of this study was to assess the prognostic potential of cardiothoracic ratio, a simple marker of cardiomegaly, in a large cohort of ACHD. PATIENTS AND SETTING: Chest radiographs from 3033 ACHD patients attending our institution between 1998 and 2007 and 113 normal controls of similar age were analyzed blindly. DESIGN: Cardiothoracic ratio derived from plain postero-anterior chest radiographs, was compared between ACHD patients and controls, different diagnostic subgroups and different functional classes. Relationship between cardiothoracic ratio and survival was assessed using Cox regression. RESULTS: Average cardiothoracic ratio in ACHD was 52.0±7.6% (over 50% in 56.4%), significantly higher in all ACHD diagnostic subgroups compared to controls (42.3±4.0%, p<0.0001) and highest in the "complex" cardiac anatomy, Ebstein's anomaly and Eisenmenger subgroups. Cardiothoracic ratio related to functional class, but was high even in asymptomatic patients. During a median follow-up of 4.2years, 164 patients died. Patients with a cardiothoracic ratio >55% had an 8-fold increased risk of death compared to those in the lowest tertile (<48%). Even patients with mildly increased cardiothoracic ratio (48-55%) had an adjusted 3.6-fold increased mortality compared to the lowest tertile. CONCLUSIONS: Cardiothoracic ratio derived from postero-anterior chest radiographs is a simple, and reproducible marker, which relates to functional class and predicts independently mortality risk in ACHD patients.

BaySTDetect: detecting unusual temporal patterns in small area data via Bayesian model choice.

Space-time modeling of small area data is often used in epidemiology for mapping chronic disease rates and by government statistical agencies for producing local estimates of, for example, unemployment or crime rates. Although there is typically a general temporal trend, which affects all areas similarly, abrupt changes may occur in a particular area, e.g. due to emergence of localized predictors/risk factor(s) or impact of a new policy. Detection of areas with "unusual" temporal patterns is therefore important as a screening tool for further investigations. In this paper, we propose BaySTDetect, a novel detection method for short-time series of small area data using Bayesian model choice between two competing space-time models. The first model is a multiplicative decomposition of the area effect and the temporal effect, assuming one common temporal pattern across the whole study region. The second model estimates the time trends independently for each area. For each area, the posterior probability of belonging to the common trend model is calculated, which is then used to classify the local time trend as unusual or not. Crucial to any detection method, we provide a Bayesian estimate of the false discovery rate (FDR). A comprehensive simulation study has demonstrated the consistent good performance of BaySTDetect in detecting various realistic departure patterns in addition to estimating well the FDR. The proposed method is applied retrospectively to mortality data on chronic obstructive pulmonary disease (COPD) in England and Wales between 1990 and 1997 (a) to test a hypothesis that a government policy increased the diagnosis of COPD and (b) to perform surveillance. While results showed no evidence supporting the hypothesis regarding the policy, an identified unusual district (Tower Hamlets in inner London) was later recognized to have higher than national rates of hospital readmission and mortality due to COPD by the National Health Service, which initiated various local enhanced services to tackle the problem. Our method would have led to an early detection of this local health issue.