Kirsty Rhodes

Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data

Objectives Estimation of between-study heterogeneity is problematic in small meta-analyses. Bayesian meta-analysis is beneficial because it allows incorporation of external evidence on heterogeneity. To facilitate this, we provide empirical evidence on the likely heterogeneity between studies in meta-analyses relating to specific research settings. Study Design and Setting Our analyses included 6,492 continuous-outcome meta-analyses within the Cochrane Database of Systematic Reviews. We investigated the influence of meta-analysis settings on heterogeneity by modeling study data from all meta-analyses on the standardized mean difference scale. Meta-analysis setting was described according to outcome type, intervention comparison type, and medical area. Predictive distributions for between-study variance expected in future meta-analyses were obtained, which can be used directly as informative priors. Results Among outcome types, heterogeneity was found to be lowest in meta-analyses of obstetric outcomes. Among intervention comparison types, heterogeneity was lowest in meta-analyses comparing two pharmacologic interventions. Predictive distributions are reported for different settings. In two example meta-analyses, incorporating external evidence led to a more precise heterogeneity estimate. Conclusion Heterogeneity was influenced by meta-analysis characteristics. Informative priors for between-study variance were derived for each specific setting. Our analyses thus assist the incorporation of realistic prior information into meta-analyses including few studies.

Methods for calculating confidence and credible intervals for the residual between-study variance in random effects meta-regression models

BackgroundMeta-regression is becoming increasingly used to model study level covariate effects. However this type of statistical analysis presents many difficulties and challenges. Here two methods for calculating confidence intervals for the magnitude of the residual between-study variance in random effects meta-regression models are developed. A further suggestion for calculating credible intervals using informative prior distributions for the residual between-study variance is presented.MethodsTwo recently proposed and, under the assumptions of the random effects model, exact methods for constructing confidence intervals for the between-study variance in random effects meta-analyses are extended to the meta-regression setting. The use of Generalised Cochran heterogeneity statistics is extended to the meta-regression setting and a Newton-Raphson procedure is developed to implement the Q profile method for meta-analysis and meta-regression. WinBUGS is used to implement informative priors for the residual between-study variance in the context of Bayesian meta-regressions.ResultsResults are obtained for two contrasting examples, where the first example involves a binary covariate and the second involves a continuous covariate. Intervals for the residual between-study variance are wide for both examples.ConclusionsStatistical methods, and R computer software, are available to compute exact confidence intervals for the residual between-study variance under the random effects model for meta-regression. These frequentist methods are almost as easily implemented as their established counterparts for meta-analysis. Bayesian meta-regressions are also easily performed by analysts who are comfortable using WinBUGS. Estimates of the residual between-study variance in random effects meta-regressions should be routinely reported and accompanied by some measure of their uncertainty. Confidence and/or credible intervals are well-suited to this purpose.

Association of comorbidity and health service usage among patients with dementia in the UK: a population-based study

Background The majority of people with dementia have other long-term diseases, the presence of which may affect the progression and management of dementia. This study aimed to identify subgroups with higher healthcare needs, by analysing how primary care consultations, number of prescriptions and hospital admissions by people with dementia varies with having additional long-term diseases (comorbidity). Methods A retrospective cohort study based on health data from the Clinical Practice Research Datalink (CPRD) was conducted. Incident cases of dementia diagnosed in the year starting 1/3/2008 were selected and followed for up to 5 years. The number of comorbidities was obtained from a set of 34 chronic health conditions. Service usage (primary care consultations, hospitalisations and prescriptions) and time-to-death were determined during follow-up. Multilevel negative binomial regression and Cox regression, adjusted for age and gender, were used to model differences in service usage and death between differing numbers of comorbidities. Results Data from 4999 people (14 866 person-years of follow-up) were analysed. Overall, 91.7% of people had 1 or more additional comorbidities. Compared with those with 2 or 3 comorbidities, people with ≥6 comorbidities had higher rates of primary care consultations (rate ratio (RR) 1.31, 95% CI 1.25 to 1.36), prescriptions (RR 1.68, 95% CI 1.57 to 1.81), and hospitalisation (RR 1.62, 95% CI 1.44 to 1.83), and higher risk of death (HR 1.56, 95% CI 1.37 to 1.78). Discussion In the UK, people with dementia with higher numbers of comorbidities die earlier and have considerably higher health service usage in terms of primary care consultations, hospital admissions and prescribing. This study provides strong evidence that comorbidity is a key factor that should be considered when allocating resources and planning care for people with dementia.

Empirical evidence about inconsistency among studies in a pair-wise meta-analysis

This paper investigates how inconsistency (as measured by the I2 statistic) among studies in a meta‐analysis may differ, according to the type of outcome data and effect measure. We used hierarchical models to analyse data from 3873 binary, 5132 continuous and 880 mixed outcome meta‐analyses within the Cochrane Database of Systematic Reviews. Predictive distributions for inconsistency expected in future meta‐analyses were obtained, which can inform priors for between‐study variance. Inconsistency estimates were highest on average for binary outcome meta‐analyses of risk differences and continuous outcome meta‐analyses. For a planned binary outcome meta‐analysis in a general research setting, the predictive distribution for inconsistency among log odds ratios had median 22% and 95% CI: 12% to 39%. For a continuous outcome meta‐analysis, the predictive distribution for inconsistency among standardized mean differences had median 40% and 95% CI: 15% to 73%. Levels of inconsistency were similar for binary data measured by log odds ratios and log relative risks. Fitted distributions for inconsistency expected in continuous outcome meta‐analyses using mean differences were almost identical to those using standardized mean differences. The empirical evidence on inconsistency gives guidance on which outcome measures are most likely to be consistent in particular circumstances and facilitates Bayesian meta‐analysis with an informative prior for heterogeneity.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data

Many meta‐analyses combine results from only a small number of studies, a situation in which the between‐study variance is imprecisely estimated when standard methods are applied. Bayesian meta‐analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta‐analysis using data augmentation, in which we represent an informative conjugate prior for between‐study variance by pseudo data and use meta‐regression for estimation. To assist in this, we derive predictive inverse‐gamma distributions for the between‐study variance expected in future meta‐analyses. These may serve as priors for heterogeneity in new meta‐analyses. In a simulation study, we compare approximate Bayesian methods using meta‐regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta‐regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta‐analysis is described. The proposed method facilitates Bayesian meta‐analysis in a way that is accessible to applied researchers.

The epidemiology of multimorbidity in primary care: a retrospective cohort study

Background Multimorbidity places a substantial burden on patients and the healthcare system, but few contemporary epidemiological data are available. Aim To describe the epidemiology of multimorbidity in adults in England, and quantify associations between multimorbidity and health service utilisation. Design and setting Retrospective cohort study, undertaken in England. Method The study used a random sample of 403 985 adult patients (aged ≥18 years), who were registered with a general practice on 1 January 2012 and included in the Clinical Practice Research Datalink. Multimorbidity was defined as having two or more of 36 long-term conditions recorded in patients’ medical records, and associations between multimorbidity and health service utilisation (GP consultations, prescriptions, and hospitalisations) over 4 years were quantified. Results In total, 27.2% of the patients involved in the study had multimorbidity. The most prevalent conditions were hypertension (18.2%), depression or anxiety (10.3%), and chronic pain (10.1%). The prevalence of multimorbidity was higher in females than males (30.0% versus 24.4% respectively) and among those with lower socioeconomic status (30.0% in the quintile with the greatest levels of deprivation versus 25.8% in that with the lowest). Physical–mental comorbidity constituted a much greater proportion of overall morbidity in both younger patients (18–44 years) and those patients with a lower socioeconomic status. Multimorbidity was strongly associated with health service utilisation. Patients with multimorbidity accounted for 52.9% of GP consultations, 78.7% of prescriptions, and 56.1% of hospital admissions. Conclusion Multimorbidity is common, socially patterned, and associated with increased health service utilisation. These findings support the need to improve the quality and efficiency of health services providing care to patients with multimorbidity at both practice and national level.

Between-trial heterogeneity in meta-analyses may be partially explained by reported design characteristics

Objective We investigated the associations between risk of bias judgments from Cochrane reviews for sequence generation, allocation concealment and blinding, and between-trial heterogeneity. Study Design and Setting Bayesian hierarchical models were fitted to binary data from 117 meta-analyses, to estimate the ratio λ by which heterogeneity changes for trials at high/unclear risk of bias compared with trials at low risk of bias. We estimated the proportion of between-trial heterogeneity in each meta-analysis that could be explained by the bias associated with specific design characteristics. Results Univariable analyses showed that heterogeneity variances were, on average, increased among trials at high/unclear risk of bias for sequence generation (λˆ 1.14, 95% interval: 0.57–2.30) and blinding (λˆ 1.74, 95% interval: 0.85–3.47). Trials at high/unclear risk of bias for allocation concealment were on average less heterogeneous (λˆ 0.75, 95% interval: 0.35–1.61). Multivariable analyses showed that a median of 37% (95% interval: 0–71%) heterogeneity variance could be explained by trials at high/unclear risk of bias for sequence generation, allocation concealment, and/or blinding. All 95% intervals for changes in heterogeneity were wide and included the null of no difference. Conclusion Our interpretation of the results is limited by imprecise estimates. There is some indication that between-trial heterogeneity could be partially explained by reported design characteristics, and hence adjustment for bias could potentially improve accuracy of meta-analysis results.

Label-invariant models for the analysis of meta-epidemiological data

Rich meta‐epidemiological data sets have been collected to explore associations between intervention effect estimates and study‐level characteristics. Welton et al proposed models for the analysis of meta‐epidemiological data, but these models are restrictive because they force heterogeneity among studies with a particular characteristic to be at least as large as that among studies without the characteristic. In this paper we present alternative models that are invariant to the labels defining the 2 categories of studies. To exemplify the methods, we use a collection of meta‐analyses in which the Cochrane Risk of Bias tool has been implemented. We first investigate the influence of small trial sample sizes (less than 100 participants), before investigating the influence of multiple methodological flaws (inadequate or unclear sequence generation, allocation concealment, and blinding). We fit both the Welton et al model and our proposed label‐invariant model and compare the results. Estimates of mean bias associated with the trial characteristics and of between‐trial variances are not very sensitive to the choice of model. Results from fitting a univariable model show that heterogeneity variance is, on average, 88% greater among trials with less than 100 participants. On the basis of a multivariable model, heterogeneity variance is, on average, 25% greater among trials with inadequate/unclear sequence generation, 51% greater among trials with inadequate/unclear blinding, and 23% lower among trials with inadequate/unclear allocation concealment, although the 95% intervals for these ratios are very wide. Our proposed label‐invariant models for meta‐epidemiological data analysis facilitate investigations of between‐study heterogeneity attributable to certain study characteristics.

Financial incentives improve recognition but not treatment of cardiovascular risk factors in severe mental illness

Objectives Severe mental illness (SMI) is associated with premature cardiovascular disease, prompting the UK primary care payment-for-performance system (Quality and Outcomes Framework, QOF) to incentivise annual physical health reviews. This study aimed to assess the QOF’s impact on detection and treatment of cardiovascular risk factors in people with SMI. Methods A retrospective open cohort study of UK general practice was conducted between 1996 and 2014, using segmented logistic regression with 2004 and 2011 as break points, reflecting the introduction of relevant QOF incentives in these years. 67239 SMI cases and 359951 randomly-selected unmatched controls were extracted from the Clinical Practice Research Datalink (CPRD). Results There was strong evidence (p≤0.015) the 2004 QOF indicator (general health) resulted in an immediate increase in recording of elevated cholesterol (odds ratio 1.37 (95% confidence interval 1.24 to 1.51)); obesity (OR 1.21 (1.06 to 1.38)); and hypertension (OR 1.19 (1.04 to 1.38)) in the SMI group compared with the control group, which was sustained in subsequent years. Similar findings were found for diabetes, although the evidence was weaker (p = 0.059; OR 1.21 (0.99 to 1.49)). There was evidence (p<0.001) of a further, but unsustained, increase in recording of elevated cholesterol and obesity in the SMI group following the 2011 QOF indicator (cardiovascular specific). There was no clear evidence that the QOF indicators affected the prescribing of lipid modifying medications or anti-diabetic medications. Conclusion Incentivising general physical health review for SMI improves identification of cardiovascular risk factors, although the additional value of specifically incentivising cardiovascular risk factor assessment is unclear. However, incentives do not affect pharmacological management of these risks.

Computationally efficient methods for fitting mixed models to electronic health records data

Motivated by two case studies using primary care records from the Clinical Practice Research Datalink, we describe statistical methods that facilitate the analysis of tall data, with very large numbers of observations. Our focus is on investigating the association between patient characteristics and an outcome of interest, while allowing for variation among general practices. We explore ways to fit mixed-effects models to tall data, including predictors of interest and confounding factors as covariates, and including random intercepts to allow for heterogeneity in outcome among practices. We introduce (1) weighted regression and (2) meta-analysis of estimated regression coefficients from each practice. Both methods reduce the size of the dataset, thus decreasing the time required for statistical analysis. We compare the methods to an existing subsampling approach. All methods give similar point estimates, and weighted regression and meta-analysis give similar standard errors for point estimates to analysis of the entire dataset, but the subsampling method gives larger standard errors. Where all data are discrete, weighted regression is equivalent to fitting the mixed model to the entire dataset. In the presence of a continuous covariate, meta-analysis is useful. Both methods are easy to implement in standard statistical software.