Long term survival after a first transient ischaemic attack in England: A retrospective matched cohort study.

OBJECTIVE: Transient ischaemic attacks (TIA) serve as warning signs for future stroke, and the impact of TIA on long term survival is uncertain. We assessed the long-term hazards of all-cause mortality following a first episode of a transient ischaemic attack (TIA). DESIGN: Retrospective matched cohort study. METHODS: Cohort study using electronic primary health care records from The Health Improvement Network (THIN) database in the United Kingdom. Cases born in or before 1960, resident in England, with a first diagnosis of TIA between January 1986 and January 2017 were matched to three controls on age, sex and general practice. The primary outcome was all-cause mortality. The hazards of all-cause mortality were estimated using a time-varying Double-Cox Weibull survival model with a random frailty effect of general practice, while adjusting for different socio-demographic factors, medical therapies, and comorbidities. RESULTS: 20,633 cases and 58,634 controls were included. During the study period, 24,176 participants died comprising of 7,745 (37.5%) cases and 16,431(28.0%) controls. In terms of hazards of mortality, cases aged 39 to 60 years at the first TIA event had the highest hazard ratio (HR) of mortality compared to their 39-60 years matched controls (HR = 3.04 (2.91 - 3.18)). The HR for cases aged 61-70 years, 71-76 years and 77+ years were 1.98 (1.55 - 2.30), 1.79 (1.20 - 2.07) and 1.52 (1.15 - 1.97) compared to their same-aged matched controls. Cases aged 39-60 at TIA onset who were prescribed aspirin were associated with reduced HR of 0.93 (0.84 - 1.01), 0.90 (0.82 - 0.98) and 0.88 (0.80 - 0.96) at 5, 10 and 15 years respectively, compared to the same aged cases who were not prescribed any antiplatelet. Statistically significant reductions in hazard ratios were observed with aspirin at 10 and 15 years in all age groups. Hazard ratio point estimates for other antiplatelets (dipyridamole or clopidogrel) and dual antiplatelet therapy were very similar to aspirin at 5, 10 and 15 years but with wider confidence intervals that included 1. There was no survival benefit associated with antiplatelet prescription in controls. CONCLUSIONS: The overall risk of death was considerably elevated in all age groups after a first-ever TIA event. Aspirin prescription was associated with a reduced risk. These findings support the use of aspirin in secondary prevention for people with a TIA. The results do not support the use of antiplatelet medication in people without TIA.

Estimation in meta-analyses of mean difference and standardized mean difference.

Methods for random-effects meta-analysis require an estimate of the between-study variance, τ2 . The performance of estimators of τ2 (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study-level effects and also the performance of related estimators of the overall effect. However, as we show, the performance of the methods varies widely among effect measures. For the effect measures mean difference (MD) and standardized MD (SMD), we use improved effect-measure-specific approximations to the expected value of Q for both MD and SMD to introduce two new methods of point estimation of τ2 for MD (Welch-type and corrected DerSimonian-Laird) and one WT interval method. We also introduce one point estimator and one interval estimator for τ2 in SMD. Extensive simulations compare our methods with four point estimators of τ2 (the popular methods of DerSimonian-Laird, restricted maximum likelihood, and Mandel and Paule, and the less-familiar method of Jackson) and four interval estimators for τ2 (profile likelihood, Q-profile, Biggerstaff and Jackson, and Jackson). We also study related point and interval estimators of the overall effect, including an estimator whose weights use only study-level sample sizes. We provide measure-specific recommendations from our comprehensive simulation study and discuss an example.

Estimation in meta-analyses of response ratios.

BACKGROUND: For outcomes that studies report as the means in the treatment and control groups, some medical applications and nearly half of meta-analyses in ecology express the effect as the ratio of means (RoM), also called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR. METHODS: In random-effects meta-analysis of LRR, with normal and lognormal data, we studied the performance of estimators of the between-study variance, τ2, (measured by bias and coverage) in assessing heterogeneity of study-level effects, and also the performance of related estimators of the overall effect in the log scale, λ. We obtained additional empirical evidence from two examples. RESULTS: The results of our extensive simulations showed several challenges in using LRR as an effect measure. Point estimators of τ2 had considerable bias or were unreliable, and interval estimators of τ2 seldom had the intended 95% coverage for small to moderate-sized samples (n<40). Results for estimating λ differed between lognormal and normal data. CONCLUSIONS: For lognormal data, we can recommend only SSW, a weighted average in which a study's weight is proportional to its effective sample size, (when n≥40) and its companion interval (when n≥10). Normal data posed greater challenges. When the means were far enough from 0 (more than one standard deviation, 4 in our simulations), SSW was practically unbiased, and its companion interval was the only option.

Meta-analysis of binary outcomes via generalized linear mixed models: a simulation study.

BACKGROUND: Systematic reviews and meta-analyses of binary outcomes are widespread in all areas of application. The odds ratio, in particular, is by far the most popular effect measure. However, the standard meta-analysis of odds ratios using a random-effects model has a number of potential problems. An attractive alternative approach for the meta-analysis of binary outcomes uses a class of generalized linear mixed models (GLMMs). GLMMs are believed to overcome the problems of the standard random-effects model because they use a correct binomial-normal likelihood. However, this belief is based on theoretical considerations, and no sufficient simulations have assessed the performance of GLMMs in meta-analysis. This gap may be due to the computational complexity of these models and the resulting considerable time requirements. METHODS: The present study is the first to provide extensive simulations on the performance of four GLMM methods (models with fixed and random study effects and two conditional methods) for meta-analysis of odds ratios in comparison to the standard random effects model. RESULTS: In our simulations, the hypergeometric-normal model provided less biased estimation of the heterogeneity variance than the standard random-effects meta-analysis using the restricted maximum likelihood (REML) estimation when the data were sparse, but the REML method performed similarly for the point estimation of the odds ratio, and better for the interval estimation. CONCLUSIONS: It is difficult to recommend the use of GLMMs in the practice of meta-analysis. The problem of finding uniformly good methods of the meta-analysis for binary outcomes is still open.

Beta-binomial model for meta-analysis of odds ratios.

In meta-analysis of odds ratios (ORs), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative REM for ORs uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra-class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta-distributed, resulting in beta-binomial distributions. We propose two new estimators of the ICC for meta-analysis in this setting. One is based on the inverted Breslow-Day test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's Q. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the Mantel-Haenszel approach to estimation of ORs is extended to the beta-binomial model, and we study performance of various ICC estimators when used in the Mantel-Haenszel or the inverse-variance method to combine ORs in meta-analysis. The results of the simulations show that the improved gamma-based estimator of ICC is superior for small sample sizes, and the Breslow-Day-based estimator is the best for n⩾100. The Mantel-Haenszel-based estimator of OR is very biased and is not recommended. The inverse-variance approach is also somewhat biased for ORs≠1, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the beta-binomial model a feasible alternative to the standard REM for meta-analysis of ORs. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies.

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability p̂, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence.

On the Q statistic with constant weights for standardized mean difference.

Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value is also used in several popular estimators of the between-study variance, τ 2 . Those applications generally have not considered the implications of its use of estimated variances in the inverse-variance weights. Importantly, those weights make approximating the distribution of Q (more explicitly, Q IV ) rather complicated. As an alternative, we investigate a new Q statistic, Q F , whose constant weights use only the studies' effective sample sizes. For the standardized mean difference as the measure of effect, we study, by simulation, approximations to distributions of Q IV and Q F , as the basis for tests of heterogeneity and for new point and interval estimators of τ 2 . These include new DerSimonian-Kacker-type moment estimators based on the first moment of Q F , and novel median-unbiased estimators. The results show that: an approximation based on an algorithm of Farebrother follows both the null and the alternative distributions of Q F reasonably well, whereas the usual chi-squared approximation for the null distribution of Q IV and the Biggerstaff-Jackson approximation to its alternative distribution are poor; in estimating τ 2 , our moment estimator based on Q F is almost unbiased, the Mandel - Paule estimator has some negative bias in some situations, and the DerSimonian-Laird and restricted maximum likelihood estimators have considerable negative bias; and all 95% interval estimators have coverage that is too high when τ 2 = 0 , but otherwise the Q-profile interval performs very well.

Exploring consequences of simulation design for apparent performance of methods of meta-analysis.

Contemporary statistical publications rely on simulation to evaluate performance of new methods and compare them with established methods. In the context of random-effects meta-analysis of log-odds-ratios, we investigate how choices in generating data affect such conclusions. The choices we study include the overall log-odds-ratio, the distribution of probabilities in the control arm, and the distribution of study-level sample sizes. We retain the customary normal distribution of study-level effects. To examine the impact of the components of simulations, we assess the performance of the best available inverse-variance-weighted two-stage method, a two-stage method with constant sample-size-based weights, and two generalized linear mixed models. The results show no important differences between fixed and random sample sizes. In contrast, we found differences among data-generation models in estimation of heterogeneity variance and overall log-odds-ratio. This sensitivity to design poses challenges for use of simulation in choosing methods of meta-analysis.

A Q statistic with constant weights for assessing heterogeneity in meta-analysis.

The conventional Q statistic, using estimated inverse-variance (IV) weights, underlies a variety of problems in random-effects meta-analysis. In previous work on standardized mean difference and log-odds-ratio, we found superior performance with an estimator of the overall effect whose weights use only group-level sample sizes. The Q statistic with those weights has the form proposed by DerSimonian and Kacker. The distribution of this Q and the Q with IV weights must generally be approximated. We investigate approximations for those distributions, as a basis for testing and estimating the between-study variance (τ2 ). A simulation study, with mean difference as the effect measure, provides a framework for assessing accuracy of the approximations, level and power of the tests, and bias in estimating τ2 . Two examples illustrate estimation of τ2 and the overall mean difference. Use of Q with sample-size-based weights and its exact distribution (available for mean difference and evaluated by Farebrother's algorithm) provides precise levels even for very small and unbalanced sample sizes. The corresponding estimator of τ2 is almost unbiased for 10 or more small studies. This performance compares favorably with the extremely liberal behavior of the standard tests of heterogeneity and the largely biased estimators based on inverse-variance weights.

Do statins reduce mortality in older people? Findings from a longitudinal study using primary care records.

OBJECTIVE: Assess whether statins reduce mortality in the general population aged 60 years and above. DESIGN: Retrospective cohort study. SETTING: Primary care practices contributing to The Health Improvement Network database, England and Wales, 1990-2017. PARTICIPANTS: Cohort who turned age 60 between 1990 and 2000 with no previous cardiovascular disease or statin prescription and followed up until 2017. RESULTS: Current statin prescription was associated with a significant reduction in all-cause mortality from age 65 years onward, with greater reductions seen at older ages. The adjusted HRs of mortality associated with statin prescription at ages 65, 70, 75, 80 and 85 years were 0.76 (95% CI 0.71 to 0.81), 0.71 (95% CI 0.68 to 0.75), 0.68 (95% CI 0.65 to 0.72), 0.63 (95% CI 0.53 to 0.73) and 0.54 (95% CI 0.33 to 0.92), respectively. The adjusted HRs did not vary by sex or cardiac risk. CONCLUSIONS: Using regularly updated clinical information on sequential treatment decisions in older people, mortality predictions were updated every 6 months until age 85 years in a combined primary and secondary prevention population. The consistent mortality reduction of statins from age 65 years onward supports their use where clinically indicated at age 75 and older, where there has been particular uncertainty of the benefits.

Methods for estimating between-study variance and overall effect in meta-analysis of odds ratios.

In random-effects meta-analysis the between-study variance ( τ2 ) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating τ2 and the overall effect and produce confidence intervals with below-nominal coverage. An improved approximation to the moments of Cochran's Q statistic, suggested by Kulinskaya and Dollinger (KD), yields new point and interval estimators of τ2 and of the overall log-odds-ratio. Another, simpler approach (SSW) uses weights based only on study-level sample sizes to estimate the overall effect. In extensive simulations we compare our proposed estimators with established point and interval estimators for τ2 and point and interval estimators for the overall log-odds-ratio (including the Hartung-Knapp-Sidik-Jonkman interval). Additional simulations included three estimators based on generalized linear mixed models and the Mantel-Haenszel fixed-effect estimator. Results of our simulations show that no single point estimator of τ2 can be recommended exclusively, but Mandel-Paule and KD provide better choices for small and large numbers of studies, respectively. The KD estimator provides reliable coverage of τ2 . Inverse-variance-weighted estimators of the overall effect are substantially biased, as are the Mantel-Haenszel odds ratio and the estimators from the generalized linear mixed models. The SSW estimator of the overall effect and a related confidence interval provide reliable point and interval estimation of the overall log-odds-ratio.

Pitfalls of using the risk ratio in meta-analysis.

For meta-analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta-analyses use the risk ratio (RR) and its logarithm because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study-level event rates in the interval (0, 1). These complications pose a particular challenge for random-effects models, both in applications and in generating data for simulations. As background, we review the conventional random-effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log-binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta-binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta-analyses that used RR suggest bias in the results from the conventional inverse-variance-weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research.

Optimal SBP targets in routine clinical care.

OBJECTIVE: Compare outcomes of intensive treatment of SBP to less than 120 mmHg versus standard treatment to less than 140 mmHg in the US clinical Systolic Blood Pressure Intervention Trial (SPRINT) with similar hypertensive patients managed in routine primary care in the United Kingdom. METHODS: Hypertensive patients aged 50-90 without diabetes or chronic kidney disease (CKD) were selected in SPRINT and The Health Improvement Network (THIN) database. Patients were enrolled in 2010-2013 and followed-up to 2015 (SPRINT N = 4112; THIN N = 8631). Cox's proportional hazards regressions were fitted to estimate the hazard of all-cause mortality or CKD (main adverse effect) associated with intensive treatment, adjusted for sex, age, ethnicity, smoking, blood pressure, cardiovascular disease, aspirin, statin, number of antihypertensive drugs at baseline, change in number of antihypertensive drugs at trial entry, and clinical site. RESULTS: Almost half of the patients had intensive treatment (43-45%). In SPRINT, intensive treatment was associated with a decreased hazard of mortality of 0.63 (0.43-0.92), while in THIN with an increased hazard of 1.66 (1.28-2.15). In THIN, this effect was time-dependent. Intensive treatment was associated with an increased hazard of CKD of 2.67 (1.74-4.11) in SPRINT and 1.35 (1.08-1.70) in THIN. In THIN, this effect differed by the number of antihypertensive drugs prescribed at baseline. CONCLUSION: It appears that intensive treatment of SBP may be harmful in the general population where all have access to routine healthcare as with the UK National Health Services, but could be beneficial in high-risk patients who are closely monitored.