Bayesian regression discontinuity designs: Incorporating clinical knowledge in the causal analysis of primary care data

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 table

The role of statistics in the era of big data: Electronic health records for healthcare research

The transferring of medical records into huge electronic databases has opened up opportunities for research but requires attention to data quality, study design and issues of bias and confounding

Survival extrapolation in the presence of cause specific hazards.

Health economic evaluations require estimates of expected survival from patients receiving different interventions, often over a lifetime. However, data on the patients of interest are typically only available for a much shorter follow-up time, from randomised trials or cohorts. Previous work showed how to use general population mortality to improve extrapolations of the short-term data, assuming a constant additive or multiplicative effect on the hazards for all-cause mortality for study patients relative to the general population. A more plausible assumption may be a constant effect on the hazard for the specific cause of death targeted by the treatments. To address this problem, we use independent parametric survival models for cause-specific mortality among the general population. Because causes of death are unobserved for the patients of interest, a polyhazard model is used to express their all-cause mortality as a sum of latent cause-specific hazards. Assuming proportional cause-specific hazards between the general and study populations then allows us to extrapolate mortality of the patients of interest to the long term. A Bayesian framework is used to jointly model all sources of data. By simulation, we show that ignoring cause-specific hazards leads to biased estimates of mean survival when the proportion of deaths due to the cause of interest changes through time. The methods are applied to an evaluation of implantable cardioverter defibrillators for the prevention of sudden cardiac death among patients with cardiac arrhythmia. After accounting for cause-specific mortality, substantial differences are seen in estimates of life years gained from implantable cardioverter defibrillators

Calibration of complex models through Bayesian evidence synthesis: a demonstration and tutorial.

Decision-analytic models must often be informed using data that are only indirectly related to the main model parameters. The authors outline how to implement a Bayesian synthesis of diverse sources of evidence to calibrate the parameters of a complex model. A graphical model is built to represent how observed data are generated from statistical models with unknown parameters and how those parameters are related to quantities of interest for decision making. This forms the basis of an algorithm to estimate a posterior probability distribution, which represents the updated state of evidence for all unknowns given all data and prior beliefs. This process calibrates the quantities of interest against data and, at the same time, propagates all parameter uncertainties to the results used for decision making. To illustrate these methods, the authors demonstrate how a previously developed Markov model for the progression of human papillomavirus (HPV-16) infection was rebuilt in a Bayesian framework. Transition probabilities between states of disease severity are inferred indirectly from cross-sectional observations of prevalence of HPV-16 and HPV-16-related disease by age, cervical cancer incidence, and other published information. Previously, a discrete collection of plausible scenarios was identified but with no further indication of which of these are more plausible. Instead, the authors derive a Bayesian posterior distribution, in which scenarios are implicitly weighted according to how well they are supported by the data. In particular, we emphasize the appropriate choice of prior distributions and checking and comparison of fitted models

Mapping of the EQ-5D index from clinical outcome measures and demographic variables in patients with coronary heart disease.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: The EuroQoL 5D (EQ-5D) is a questionnaire that provides a measure of utility for cost-effectiveness analysis. The EQ-5D has been widely used in many patient groups, including those with coronary heart disease. Studies often require patients to complete many questionnaires and the EQ-5D may not be gathered. This study aimed to assess whether demographic and clinical outcome variables, including scores from a disease specific measure, the Seattle Angina Questionnaire (SAQ), could be used to predict, or map, the EQ-5D index value where it is not available. METHODS: Patient-level data from 5 studies of cardiac interventions were used. The data were split into two groups - approximately 60% of the data were used as an estimation dataset for building models, and 40% were used as a validation dataset. Forward ordinary least squares linear regression methods and measures of prediction error were used to build a model to map to the EQ-5D index. Age, sex, a proxy measure of disease stage, Canadian Cardiovascular Society (CCS) angina severity class, treadmill exercise time (ETT) and scales of the SAQ were examined. RESULTS: The exertional capacity (ECS), disease perception (DPS) and anginal frequency scales (AFS) of the SAQ were the strongest predictors of the EQ-5D index and gave the smallest root mean square errors. A final model was chosen with age, gender, disease stage and the ECS, DPS and AFS scales of the SAQ. ETT and CCS did not improve prediction in the presence of the SAQ scales. Bland-Altman agreement between predicted and observed EQ-5D index values was reasonable for values greater than 0.4, but below this level predicted values were higher than observed. The 95% limits of agreement were wide (-0.34, 0.33). CONCLUSIONS: Mapping of the EQ-5D index in cardiac patients from demographics and commonly measured cardiac outcome variables is possible; however, prediction for values of the EQ-5D index below 0.4 was not accurate. The newly designed 5-level version of the EQ-5D with its increased ability to discriminate health states may improve prediction of EQ-5D index values

A review of health utilities using the EQ-5D in studies of cardiovascular disease

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.Abstract Background The EQ-5D has been extensively used to assess patient utility in trials of new treatments within the cardiovascular field. The aims of this study were to review evidence of the validity and reliability of the EQ-5D, and to summarise utility scores based on the use of the EQ-5D in clinical trials and in studies of patients with cardiovascular disease. Methods A structured literature search was conducted using keywords related to cardiovascular disease and EQ-5D. Original research studies of patients with cardiovascular disease that reported EQ-5D results and its measurement properties were included. Results Of 147 identified papers, 66 met the selection criteria, with 10 studies reporting evidence on validity or reliability and 60 reporting EQ-5D responses (VAS or self-classification). Mean EQ-5D index-based scores ranged from 0.24 (SD 0.39) to 0.90 (SD 0.16), while VAS scores ranged from 37 (SD 21) to 89 (no SD reported). Stratification of EQ-5D index scores by disease severity revealed that scores decreased from a mean of 0.78 (SD 0.18) to 0.51 (SD 0.21) for mild to severe disease in heart failure patients and from 0.80 (SD 0.05) to 0.45 (SD 0.22) for mild to severe disease in angina patients. Conclusions The published evidence generally supports the validity and reliability of the EQ-5D as an outcome measure within the cardiovascular area. This review provides utility estimates across a range of cardiovascular subgroups and treatments that may be useful for future modelling of utilities and QALYs in economic evaluations within the cardiovascular area.Published versio

Survival extrapolation using the poly-Weibull model.

Recent studies of (cost-) effectiveness in cardiothoracic transplantation have required estimation of mean survival over the lifetime of the recipients. In order to calculate mean survival, the complete survivor curve is required but is often not fully observed, so that survival extrapolation is necessary. After transplantation, the hazard function is bathtub-shaped, reflecting latent competing risks which operate additively in overlapping time periods. The poly-Weibull distribution is a flexible parametric model that may be used to extrapolate survival and has a natural competing risks interpretation. In addition, treatment effects and subgroups can be modelled separately for each component of risk. We describe the model and develop inference procedures using freely available software. The methods are applied to two problems from cardiothoracic transplantation

Cost-effectiveness of initial stress cardiovascular MR, stress SPECT or stress echocardiography as a gate-keeper test, compared with upfront invasive coronary angiography in the investigation and management of patients with stable chest pain: Mid-term outcomes from the CECaT randomised controlled trial

Objectives: To compare outcomes and cost-effectiveness of various initial imaging strategies in the management of stable chest pain in a long-term prospective randomised trial. Setting: Regional cardiothoracic referral centre in the east of England. Participants: 898 patients (69% man) entered the study with 869 alive at 2 years of follow-up. Patients were included if they presented for assessment of stable chest pain with a positive exercise test and no prior history of ischaemic heart disease. Exclusion criteria were recent infarction, unstable symptoms or any contraindication to stress MRI. Primary outcome measures: The primary outcomes of this follow-up study were survival up to a minimum of 2 years post-treatment, quality-adjusted survival and cost-utility of each strategy. Results: 898 patients were randomised. Compared with angiography, mortality was marginally higher in the groups randomised to cardiac MR (HR 2.6, 95% CI 1.1 to 6.2), but similar in the single photon emission CT-methoxyisobutylisonitrile (SPECT-MIBI; HR 1.0, 95% CI 0.4 to 2.9) and ECHO groups (HR 1.6, 95% CI 0.6 to 4.0). Although SPECT-MIBI was marginally superior to other non-invasive tests there were no other significant differences between the groups in mortality, quality-adjusted survival or costs. Conclusions: Non-invasive cardiac imaging can be used safely as the initial diagnostic test to diagnose coronary artery disease without adverse effects on patient outcomes or increased costs, relative to angiography. These results should be interpreted in the context of recent advances in imaging technology. Trial registration: ISRCTN 47108462, UKCRN 3696

Relationship between the EQ-5D index and measures of clinical outcomes in selected studies of cardiovascular interventions.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: The EuroQoL 5D (EQ-5D) has been widely used in studies of cardiac disease, but its measurement properties in this group are not well established. The study aimed to quantify the relationship between measures commonly used in studies of cardiac disease and the EQ-5D index across different levels of disease severity. METHODS: Patient-level data from 7 studies of cardiac interventions were used, which included randomised trials and observational studies. Relationships between the EQ-5D index and commonly used cardiac measures, Canadian Cardiovascular Society (CCS) angina severity class, treadmill exercise time (ETT) and scales of the Seattle Angina Questionnaire (SAQ) were examined. Mixed effects linear regression was used to assess these relationships, with the EQ-5D index as the response. RESULTS: Study sample sizes ranged from 68 to 2419. Mean baseline EQ-5D index ranged from 0.77 in patients at diagnosis (95% CI 0.75, 0.78) to 0.43 in patients with advanced disease (95% CI 0.39, 0.48) and differed significantly across studies (p < 0.001). There was evidence of a ceiling effect in patients at diagnosis. The minimum clinically important difference of a one minute increase in ETT was associated with a 0.019 (95% CI 0.014, 0.025) increase in EQ-5D index. One class increase in CCS was associated with a 0.11 (95% CI 0.09, 0.13) decrease in EQ-5D index. A 10 unit increase in SAQ scales was associated with increases between 0.04 and 0.07 in EQ-5D index (95% CIs 0.03, 0.05 and 0.05, 0.08). Tests of heterogeneity indicated the EQ-5D-covariate relationships were consistent across levels of disease severity for ETT and the treatment satisfaction scale of the SAQ, but heterogeneous for age, gender, CCS angina class and other scales of the SAQ. CONCLUSION: The EQ-5D index varies with coronary disease severity. The relationship between the EQ-5D index and an outcome measure used in cardiac intervention studies, ETT, was consistent across disease severity levels, but the relationship between demographic variables, CCS angina class and most of the SAQ scales and the EQ-5D index was heterogeneous for patients with different levels of coronary disease. Differences in the EQ-5D index associated with clinically important differences in cardiac measures can be quantified and vary between three important examples - angina class, ETT and SAQ

Use of a Structured Mirrors Intervention Does Not Reduce Delirium Incidence But May Improve Factual Memory Encoding in Cardiac Surgical ICU Patients Aged Over 70 Years: A Pilot Time-Cluster Randomized Controlled Trial.

Introduction: Post-operative delirium remains a significant problem, particularly in the older surgical patient. Previous evidence suggests that the provision of supplementary visual feedback about ones environment via the use of a mirror may positively impact on mental status and attention (core delirium diagnostic domains). We aimed to explore whether use of an evidence-based mirrors intervention could be effective in reducing delirium and improving post-operative outcomes such as factual memory encoding of the Intensive Care Unit (ICU) environment in older cardiac surgical patients. Methods: This was a pilot time-cluster randomized controlled trial at a 32-bed ICU, enrolling 223 patients aged 70 years and over, admitted to ICU after elective or urgent cardiac surgery from October 29, 2012 to June 23, 2013. The Mirrors Group received a structured mirrors intervention at set times (e.g., following change in mental status). The Usual Care Group received the standard care without mirrors. Primary outcome was ICU delirium incidence; secondary outcomes were ICU delirium days, ICU days with altered mental status or inattention, total length of ICU stay, physical mobilization (balance confidence) at ICU discharge, recall of factual and delusional ICU memories at 12 weeks, Health-Related Quality of Life at 12 weeks, and acceptability of the intervention. Results: The intervention was not associated with a significant reduction in ICU delirium incidence [Mirrors: 20/115 (17%); Usual Care: 17/108 (16%)] or duration [Mirrors: 1 (1-3); Usual Care: 2 (1-8)]. Use of the intervention on ICU was predictive of significantly higher recall of factual (but not delusional) items at 12 weeks after surgery (p = 0.003) and acceptability was high, with clinicians using mirrors at 86% of all recorded hourly observations. The intervention did not significantly impact on other secondary outcomes. Conclusion: Use of a structured mirrors intervention on the post-operative ICU does not reduce delirium, but may result in improved factual memory encoding in older cardiac surgical patients. This effect may occur via mechanisms unrelated to delirium, altered mental status, or inattention. The intervention may provide a new means of improving outcomes in patients at risk of post-ICU anxiety and/or Post-Traumatic Stress Disorder. Trial Registration: Clinicaltrials.gov identifier NCT01599689