Transformation bias in mixed effects models of meta-analysis

When binary data exhibit the greater variation than expected, the statistical methods have to account for extra-binomial variation. Possible explanations for extra-binomial variation include intra-cluster dependence or the variability of binomial probabilities. Both of these reasons lead to overdispersion of binomial counts and the resulting heterogeneity in their meta-analysis. Variance stabilizing or normalizing transformations are often applied to binomial counts to enable the use of standard methods based on normality. In meta-analysis, this is routinely done for the inference on overall effect measure. However, these transformations might result in biases in the presence of overdispersion. We study biases arising in the result of transformations of binary variables in the random or mixed effects models. We demonstrate considerable biases arising from standard log-odds and arcsine transformations both for single studies and in meta-analysis. We also explore possibilities of bias correction. In meta-analysis, the heterogeneity of the log odds ratios across the studies is usually incorporated by standard (additive) random effects model (REM). An alternative, multiplicative random effects model is based on the concept of an overdispersion. The multiplicative factor in this overdispersed random effects model can be interpreted as an intra-class correlation parameter. This model arises when one or both binomial distributions in the 2 by 2 tables are changed to betabinomial distributions. The Mantel-Haenzsel and inverse-variance approaches are extended to this setting. The estimation of the random effect parameter is based on profiling the modified Breslow-Day test and improving the approximation for distribution of Q statistic in Mandel-Paule method. The biases and coverages from new methods are compared to standard methods through simulation studies. The misspecification of the REM in respect to the mechanism of its generation is an important issue which is also discussed in this thesis

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, τ 2. The performance of estimators of τ 2 (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 τ 2 for MD (Welch-type and corrected DerSimonian-Laird) and one WT interval method. We also introduce one point estimator and one interval estimator for τ 2 in SMD. Extensive simulations compare our methods with four point estimators of τ 2 (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 τ 2 (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

Survival benefits of statin therapy in primary care: landmark analyses

Statins have been widely prescribed for primary and secondary prevention of cardiovascular disease since clinical trials have demonstrated the survival benefits. However, the threshold of cardiac risk at which to prescribe statins is still controversial, especially at older ages when everyone would be eligible solely due to their age. Our study aim was to dynamically predict the survival benefits associated with statin therapy over the course of 25 years in patients aged 60 residential in England or Wales

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

Outcomes of blood pressure targets in clinical trial versus primary care setting

Objective: The primary objective was to compare outcomes of different systolic blood pressure (SBP) targets in the US clinical setting and the UK primary care setting. / Methods: Data from the SPRINT randomised control trial and The Health Improvement Network (THIN) primary care database were used to develop survival models for longevity and adverse renal outcome (ARO, main adverse effect) at different SBP targets given treatment in people without diabetes and chronic kidney disease. The hazard of all-cause mortality or ARO associated with SBP targets was calculated by a multilevel Cox’s proportional hazards regression, adjusted for sex, age, race, smoking, BMI, SBP, cardiovascular disease, number of antihypertensive agents at baseline, additional medication after trial entry, their interaction, and clinical site. / Results: Compared to SBP target of ≤120 mmHg, SBP target of ≤140 mmHg was associated with increased hazard of mortality of 1.42 (1.06-1.90) in SPRINT, but with decreased hazard of 0.70 (0.65-0.76) in THIN. Both in SPRINT and THIN, SBP target of ≤140 mmHg was associated with decreased hazard of ARO of 0.32 (0.22-0.46) and 0.87 (0.80-0.95), respectively. Additional antihypertensive agents (3+) were associated with increased hazards of both outcomes, with HRs of 1.71-1.74 in SPRINT and 1.43-2.23 in THIN, yet being on 2 agents had survival benefits in SPRINT (HRs 0.70-0.79). / Conclusions: Lower SBP target was associated with survival benefits in the clinical setting, but with increased hazard of mortality in the primary care setting. In both settings, polypharmacy patients tended to be worse off. An intensive control of SBP may benefit a selected subgroup of patients, but it appears harmful for the broader population

Dynamic hazards modelling for predictive longevity risk assessment

Predictive risk assessment and risk stratification models based on geodemographic postcode-based consumer classification are widely used in the pension and life insurance industry. However, these are static socio-economic models not directly related to health information. Health information is increasingly used for annuity underwriting in the UK, using health status when the annuity is purchased. In real life, people develop new health conditions and lifestyle habits and can start and stop a certain treatment regime at any time. This requires the ability to dynamically classify clients into time-varying risk profiles based on the presence of evolving health-related conditions, treatments and outcomes. We incorporate landmark analysis of electronic health records (EHR), in combination with the baseline hazards described by Gompertz survival distributions, for dynamic prediction of survival probabilities and life expectancy. We discuss a case-study based on landmark analysis of the survival experience of a cohort of 110,243 healthy participants who reached age 60 between 1990–2000

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, (Formula presented.). 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, (Formula presented.)) rather complicated. As an alternative, we investigate a new Q statistic, (Formula presented.), 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 (Formula presented.) and (Formula presented.), as the basis for tests of heterogeneity and for new point and interval estimators of (Formula presented.). These include new DerSimonian–Kacker-type moment estimators based on the first moment of (Formula presented.), 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 (Formula presented.) reasonably well, whereas the usual chi-squared approximation for the null distribution of (Formula presented.) and the Biggerstaff–Jackson approximation to its alternative distribution are poor; in estimating (Formula presented.), our moment estimator based on (Formula presented.) 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 (Formula presented.), 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

The effect of hormone replacement therapy on the survival of UK women: a retrospective cohort study 1984−2017

Objective: To estimate the effect of estrogen-only and combined hormone replacement therapy (HRT) on the hazards of overall and age-specific all-cause mortality in healthy women aged 46–65 at first prescription. Design: Matched cohort study. Setting: Electronic primary care records from The Health Improvement Network (THIN) database, UK (1984−2017). Population: 105 199 HRT users (cases) and 224 643 non-users (controls) matched on age and general practice. Methods: Weibull-Double-Cox regression models adjusted for age at first treatment, birth cohort, type 2 diabetes, hypertension and hypertension treatment, coronary heart disease, oophorectomy, hysterectomy, body mass index, smoking and deprivation status. Main outcome measures: All-cause mortality. Results: A total of 21 751 women died over an average of 13.5 years follow-up per participant, of whom 6329 were users and 15 422 non-users. The adjusted hazard ratio (HR) of overall all-cause mortality in combined HRT users was 0.91 (95% CI 0.88−0.94), and in estrogen-only users was 0.99 (0.93−1.07), compared with non-users. Age-specific adjusted HRs for participants aged 46–50, 51–55, 56–60 and 61–65 years at first treatment were 0.98 (0.92−1.04), 0.87 (0.82−0.92), 0.88 (0.82−0.93) and 0.92 (0.85−0.98) for combined HRT users compared with non-users, and 1.01 (0.84−1.21), 1.03 (0.89−1.18), 0.98 (0.86−1.12) and 0.93 (0.81−1.07) for estrogen-only users, respectively. Conclusions: Combined HRT was associated with a 9% lower risk of all-cause mortality and estrogen-only formulation was not associated with any significant changes