Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis.

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Abstract

Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta-analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log-cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non-PH (time-dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss-Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta-analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta-analysis of prognostic factor studies in patients with breast cancer. User-friendly Stata software is provided to implement the methods.

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Meta-regression detected associations between heterogeneous treatment effects and study-level, but not patient-level, factors.

Paul Landais, Jesse Berlin, Christopher H Schmid … (2004)

Two investigations evaluate Bayesian meta-regression for detecting treatment interactions. The first compares analyses of aggregate and individual patient data on 1,860 subjects from 11 trials testing angiotensin converting enzyme (ACE) inhibitors for nondiabetic kidney disease. The second explores meta-regression for detecting treatment interaction on 671 covariates, including the baseline risk, from 232 meta-analyses of binary outcomes compiled from the Cochrane Collaboration and the medical literature. In the ACE inhibitor study, treatment effects were homogeneous so meta-regression identified no interactions. Analysis of individual patient data using a multilevel model, however, discovered that treatment reduced glomerular filtration rate (GFR) more among patients with higher baseline proteinuria. The second investigation found meta-regression most effective for detecting treatment interactions with study-level factors in meta-analyses with >10 studies, heterogeneous treatment effects, or significant overall treatment effects. Under all three conditions, 46% of meta-regressions produced strong interactions (posterior probability >0.995) compared with 6% otherwise. Baseline risk was associated with the odds ratio in 6% of meta-analyses, half the rate found using maximum likelihood. Meta-regression can detect interactions of treatment with study-level factors when treatment effects are heterogeneous. Individual patient data are needed for patient-level factors and homogeneous effects.

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Bivariate random-effects meta-analysis and the estimation of between-study correlation

Richard Riley, Keith R. Abrams, Alexander J Sutton … (2007)

Background When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (ρ B ). Methods In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. Results The normal BRMA model estimates ρ B as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on ρ ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFbpGCgaqcaaaa@2E83@ B . Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating ρ B . Conclusion A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners.

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Investigating heterogeneity in an individual patient data meta-analysis of time to event outcomes.

Catrin Smith, Paula Williamson, Anthony Marson (2005)

Differences across studies in terms of design features and methodology, clinical procedures, and patient characteristics, are factors that can contribute to variability in the treatment effect between studies in a meta-analysis (statistical heterogeneity). Regression modelling can be used to examine relationships between treatment effect and covariates with the aim of explaining the variability in terms of clinical, methodological, or other factors. Such an investigation can be undertaken using aggregate data or individual patient data. An aggregate data approach can be problematic as sufficient data are rarely available and translating aggregate effects to individual patients can often be misleading. An individual patient data approach, although usually more resource demanding, allows a more thorough investigation of potential sources of heterogeneity and enables a fuller analysis of time to event outcomes in meta-analysis. Hierarchical Cox regression models are used to identify and explore the evidence for heterogeneity in meta-analysis and examine the relationship between covariates and censored failure time data in this context. Alternative formulations of the model are possible and illustrated using individual patient data from a meta-analysis of five randomized controlled trials which compare two drugs for the treatment of epilepsy. The models are further applied to simulated data examples in which the degree of heterogeneity and magnitude of treatment effect are varied. The behaviour of each model in each situation is explored and compared. Copyright 2005 John Wiley & Sons, Ltd.

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DOI:: 10.1002/sim.6191

PubMed ID:: 24789760

Keywords: mixed effects,flexible parametric models,adaptive Gauss-Hermite quadrature,survival analysis

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Keywords: mixed effects, flexible parametric models, adaptive Gauss-Hermite quadrature, survival analysis

Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis.

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Most cited references 19

Meta-regression detected associations between heterogeneous treatment effects and study-level, but not patient-level, factors.

Bivariate random-effects meta-analysis and the estimation of between-study correlation

Investigating heterogeneity in an individual patient data meta-analysis of time to event outcomes.

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