Investigating trial and treatment heterogeneity in an individual patient data meta-analysis of survival data by means of the penalized maximum likelihood approach

Goodness-of-fit tests in proportional hazards models with random effects

This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on two real data sets one from biomedical research and one from veterinary medicine.

Sample size estimation for cancer randomized trials in the presence of heterogeneous populations

A key issue when designing clinical trials is the estimation of the number of subjects required. Assuming for multicenter trials or biomarker-stratified designs that the effect size between treatment arms is the same among the whole study population might be inappropriate. Limited work is available for properly determining the sample size for such trials. However, we need to account for both, the heterogeneity of the baseline hazards over clusters or strata but also the heterogeneity of the treatment effects, otherwise sample size estimates might be biased. Most existing methods account for either heterogeneous baseline hazards or treatment effects but they dot not allow to simultaneously account for both sources of variations. This article proposes an approach to calculate sample size formula for clustered or stratified survival data relying on frailty models. Both theoretical derivations and simulation results show the proposed approach can guarantee the desired power in worst case scenarios and is often much more efficient than existing approaches. Application to a real clinical trial designs is also illustrated.

Association of Pathologic Complete Response and Long-Term Survival Outcomes Among Patients Treated With Neoadjuvant Chemotherapy or Chemoradiotherapy for NSCLC: A Meta-Analysis

Introduction

Increased efforts to optimize outcomes for early stage NSCLC through the investigation of novel perioperative treatment strategies are ongoing. An emerging question is the role of pathologic response and its association with long-term clinical outcomes after neoadjuvant therapy.

Methods

To investigate the association of pathologic complete response (pCR) and event-free survival (EFS) and overall survival (OS), we performed a systematic review and meta-analysis identifying studies reporting on the prognostic impact of pCR after neoadjuvant chemotherapy or chemoradiotherapy. To evaluate this prognostic value, an aggregated data (AD) meta-analyses was conducted to estimate the pooled hazard ratios (HRs) of EFS and OS for pCR. Using reconstructed individual patient data (IPD), pooled Kaplan-Meier curves were obtained to estimate this association in a more granular fashion. Subgroup analyses were conducted to further explore the impacts of study-level characteristics.

Results

A total of 28 studies comprising 7011 patients were included in the AD meta-analysis, of which, IPD was available for 6274 patients from 24 studies. Results from our AD meta-analysis revealed a pooled pCR rate of 18% (95% confidence interval [CI]: 15%–21%), including significant improvements in OS (HR = 0.50, 95% CI: 0.45–0.56) and EFS (HR = 0.46, 95% CI: 0.37–0.57) on the basis of pCR status. Our IPD analysis revealed a 5-year OS rate of 63% (95% CI: 59.6–67.4) for patients with a pCR compared with 39% (95% CI: 34.5–44.5) for those without a pCR.

Conclusions

pCR after neoadjuvant chemotherapy plus or minus radiotherapy is associated with significant improvements in EFS and survival for patients with resectable NSCLC.

Individual participant data meta-analysis of intervention studies with time-to-event outcomes: A review of the methodology and an applied example

Many randomized trials evaluate an intervention effect on time-to-event outcomes. Individual participant data (IPD) from such trials can be obtained and combined in a so-called IPD meta-analysis (IPD-MA), to summarize the overall intervention effect. We performed a narrative literature review to provide an overview of methods for conducting an IPD-MA of randomized intervention studies with a time-to-event outcome. We focused on identifying good methodological practice for modeling frailty of trial participants across trials, modeling heterogeneity of intervention effects, choosing appropriate association measures, dealing with (trial differences in) censoring and follow-up times, and addressing time-varying intervention effects and effect modification (interactions).We discuss how to achieve this using parametric and semi-parametric methods, and describe how to implement these in a one-stage or two-stage IPD-MA framework. We recommend exploring heterogeneity of the effect(s) through interaction and non-linear effects. Random effects should be applied to account for residual heterogeneity of the intervention effect. We provide further recommendations, many of which specific to IPD-MA of time-to-event data from randomized trials examining an intervention effect.We illustrate several key methods in a real IPD-MA, where IPD of 1225 participants from 5 randomized clinical trials were combined to compare the effects of Carbamazepine and Valproate on the incidence of epileptic seizures.

Impact of model misspecification in shared frailty survival models

Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modeled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (eg, gamma or lognormal). Despite that, in the context of parametric frailty models, little is known about the impact of misspecifying the baseline hazard or the frailty distribution or both. Therefore, our aim is to quantify the impact of such misspecification in a wide variety of clinically plausible scenarios via Monte Carlo simulation, using open-source software readily available to applied researchers. We generate clustered survival data assuming various baseline hazard functions, including mixture distributions with turning points, and assess the impact of sample size, variance of the frailty, baseline hazard function, and frailty distribution. Models compared include standard parametric distributions and more flexible spline-based approaches; we also included semiparametric Cox models. The resulting bias can be clinically relevant. In conclusion, we highlight the importance of fitting models that are flexible enough and the importance of assessing model fit. We illustrate our conclusions with two applications using data on diabetic retinopathy and bladder cancer. Our results show the importance of assessing model fit with respect to the baseline hazard function and the distribution of the frailty: misspecifying the former leads to biased relative and absolute risk estimates, whereas misspecifying the latter affects absolute risk estimates and measures of heterogeneity.

Percutaneous Coronary Intervention vs Coronary Artery Bypass Grafting in Patients With Left Main Coronary Artery Stenosis: A Systematic Review and Meta-analysis

Importance

In patients with left main coronary artery (LMCA) stenosis, coronary artery bypass grafting (CABG) has been the standard therapy for several decades. However, some studies suggest that percutaneous coronary intervention (PCI) with drug-eluting stents may be an acceptable alternative.

Objective

To compare the long-term safety of PCI with drug-eluting stent vs CABG in patients with LMCA stenosis.

Data Sources

PubMed, Scopus, EMBASE, Web of Knowledge, and ScienceDirect databases were searched from December 18, 2001, to February 1, 2017. Inclusion criteria were randomized clinical trial, patients with LMCA stenosis, PCI vs CABG, exclusive use of drug-eluting stents, and clinical follow-up of 3 or more years.

Data Extraction and Synthesis

Trial-level hazard ratios (HRs) and 95% CIs were pooled by fixed-effect and random-effects models with inverse variance weighting. Time-to-event individual patient data for the primary end point were reconstructed. Sensitivity analyses according to drug-eluting stent generation and coronary artery disease complexity were performed.

Main Outcomes and Measures

The primary end point was a composite of all-cause death, myocardial infarction, or stroke at long-term follow-up. Secondary end points included repeat revascularization and a composite of all-cause death, myocardial infarction, stroke, or repeat revascularization at long-term follow-up.

Results

A total of 4 randomized clinical trials were pooled; 4394 patients were included in the analysis. Of these, 3371 (76.7%) were men; pooled mean age was 65.4 years. According to Grading of Recommendations, Assessment, Development and Evaluation, evidence quality with respect to the primary composite end point was high. Percutaneous coronary intervention and CABG were associated with a comparable risk of all-cause death, myocardial infarction, or stroke both by fixed-effect (HR, 1.06; 95% CI, 0.90-1.24; P = .48) and random-effects (HR, 1.06; 95% CI, 0.85-1.32; P = .60) analysis. Sensitivity analyses according to low to intermediate Synergy Between PCI With Taxus and Cardiac Surgery (SYNTAX) score (random-effects: HR, 1.02; 95% CI, 0.74-1.41; P = .89) and drug-eluting stent generation (first generation: HR, 0.90; 95% CI, 0.68-1.20; P = .49; second generation: HR, 1.19; 95% CI, 0.82-1.73; P = .36) were consistent. Kaplan-Meier curve reconstruction did not show significant variations over time between the techniques, with a 5-year incidence of all-cause death, myocardial infarction, or stroke of 18.3% (319 events) in patients treated with PCI and 16.9% (292 events) in patients treated with CABG. However, repeat revascularization after PCI was increased (HR, 1.70; 95% CI, 1.42-2.05; P < .001). Other individual secondary end points did not differ significantly between groups. Finally, pooled estimates of trials with LMCA stenosis tended overall to differ significantly from those of trials with multivessel coronary artery disease without left main LMCA stenosis.

Conclusions and Relevance

Percutaneous coronary intervention and CABG show comparable safety in patients with LMCA stenosis and low to intermediate-complexity coronary artery disease. However, repeat revascularization is more common after PCI.

Multilevel model with random effects for clustered survival data with multiple failure outcomes

We present a multilevel frailty model for handling serial dependence and simultaneous heterogeneity in survival data with a multilevel structure attributed to clustering of subjects and the presence of multiple failure outcomes. One commonly observes such data, for example, in multi-institutional, randomized placebo-controlled trials in which patients suffer repeated episodes (eg, recurrent migraines) of the disease outcome being measured. The model extends the proportional hazards model by incorporating a random covariate and unobservable random institution effect to respectively account for treatment-by-institution interaction and institutional variation in the baseline risk. Moreover, a random effect term with correlation structure driven by a first-order autoregressive process is attached to the model to facilitate estimation of between patient heterogeneity and serial dependence. By means of the generalized linear mixed model methodology, the random effects distribution is assumed normal and the residual maximum likelihood and the maximum likelihood methods are extended for estimation of model parameters. Simulation studies are carried out to evaluate the performance of the residual maximum likelihood and the maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. We demonstrate the practical feasibility of the modeling methodology by analyzing real data from a double-blind randomized multi-institutional clinical trial, designed to examine the effect of rhDNase on the occurrence of respiratory exacerbations among patients with cystic fibrosis.

A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes

Background

Individual patient data meta-analyses (IPD-MA) are often performed using a one-stage approach-- a form of generalized linear mixed model (GLMM) for binary outcomes. We compare (i) one-stage to two-stage approaches (ii) the performance of two estimation procedures (Penalized Quasi-likelihood-PQL and Adaptive Gaussian Hermite Quadrature-AGHQ) for GLMMs with binary outcomes within the one-stage approach and (iii) using stratified study-effect or random study-effects.

Methods

We compare the different approaches via a simulation study, in terms of bias, mean-squared error (MSE), coverage and numerical convergence, of the pooled treatment effect (β₁) and between-study heterogeneity of the treatment effect (τ₁²). We varied the prevalence of the outcome, sample size, number of studies and variances and correlation of the random effects.

Results

The two-stage and one-stage methods produced approximately unbiased β₁ estimates. PQL performed better than AGHQ for estimating τ₁² with respect to MSE, but performed comparably with AGHQ in estimating the bias of β₁ and of τ₁². The random study-effects model outperformed the stratified study-effects model in small size MA.

Conclusion

The one-stage approach is recommended over the two-stage method for small size MA. There was no meaningful difference between the PQL and AGHQ procedures. Though the random-intercept and stratified-intercept approaches can suffer from their underlining assumptions, fitting GLMM with a random-intercept are less prone to misfit and has good convergence rate.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0307-7) contains supplementary material, which is available to authorized users.

Analysis of clustered competing risks data using subdistribution hazard models with multivariate frailties

Competing risks data often exist within a center in multi-center randomized clinical trials where the treatment effects or baseline risks may vary among centers. In this paper, we propose a subdistribution hazard regression model with multivariate frailty to investigate heterogeneity in treatment effects among centers from multi-center clinical trials. For inference, we develop a hierarchical likelihood (or h-likelihood) method, which obviates the need for an intractable integration over the frailty terms. We show that the profile likelihood function derived from the h-likelihood is identical to the partial likelihood, and hence it can be extended to the weighted partial likelihood for the subdistribution hazard frailty models. The proposed method is illustrated with a dataset from a multi-center clinical trial on breast cancer as well as with a simulation study. We also demonstrate how to present heterogeneity in treatment effects among centers by using a confidence interval for the frailty for each individual center and how to perform a statistical test for such heterogeneity using a restricted h-likelihood.

One-stage individual participant data meta-analysis models: estimation of treatment-covariate interactions must avoid ecological bias by separating out within-trial and across-trial information

Stratified medicine utilizes individual‐level covariates that are associated with a differential treatment effect, also known as treatment‐covariate interactions. When multiple trials are available, meta‐analysis is used to help detect true treatment‐covariate interactions by combining their data. Meta‐regression of trial‐level information is prone to low power and ecological bias, and therefore, individual participant data (IPD) meta‐analyses are preferable to examine interactions utilizing individual‐level information. However, one‐stage IPD models are often wrongly specified, such that interactions are based on amalgamating within‐ and across‐trial information. We compare, through simulations and an applied example, fixed‐effect and random‐effects models for a one‐stage IPD meta‐analysis of time‐to‐event data where the goal is to estimate a treatment‐covariate interaction. We show that it is crucial to centre patient‐level covariates by their mean value in each trial, in order to separate out within‐trial and across‐trial information. Otherwise, bias and coverage of interaction estimates may be adversely affected, leading to potentially erroneous conclusions driven by ecological bias. We revisit an IPD meta‐analysis of five epilepsy trials and examine age as a treatment effect modifier. The interaction is −0.011 (95% CI: −0.019 to −0.003; p = 0.004), and thus highly significant, when amalgamating within‐trial and across‐trial information. However, when separating within‐trial from across‐trial information, the interaction is −0.007 (95% CI: −0.019 to 0.005; p = 0.22), and thus its magnitude and statistical significance are greatly reduced. We recommend that meta‐analysts should only use within‐trial information to examine individual predictors of treatment effect and that one‐stage IPD models should separate within‐trial from across‐trial information to avoid ecological bias. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Short term versus long term dual antiplatelet therapy after implantation of drug eluting stent in patients with or without diabetes: systematic review and meta-analysis of individual participant data from randomised trials

OBJECTIVE

 To compare clinical outcomes between short term (up to 6 months) and long term (12 months) dual antiplatelet therapy (DAPT) after placement of a drug eluting stent in patients with and without diabetes.

DESIGN

 Individual participant data meta-analysis. Cox proportional regression models stratified by trial were used to assess the impact of diabetes on outcomes.

DATA SOURCE

 Medline, Embase, and Cochrane databases and proceedings of international meetings searched for randomised controlled trials comparing durations of DAPT after placement of a drug eluting stent. Individual patient data pooled from six DAPT trials.

PRIMARY OUTCOME

 Primary study outcome was one year risk of major adverse cardiac events (MACE), defined as cardiac death, myocardial infarction, or definite/probable stent thrombosis. All analyses were conducted by intention to treat.

RESULTS

 Six trials including 11 473 randomised patients were pooled. Of these patients, 3681 (32.1%) had diabetes and 7708 (67.2%) did not (mean age 63.7 (SD 9.9) and 62.8 (SD 10.1), respectively), and in 84 (0.7%) the information was missing. Diabetes was an independent predictor of MACE (hazard ratio 2.30, 95% confidence interval 1.01 to 5.27; P=0.048 At one year follow-up, long term DAPT was not associated with a decreased risk of MACE compared with short term DAPT in patients with (1.05, 0.62 to 1.76; P=0.86) or without (0.97, 0.67 to 1.39; P=0.85) diabetes (P=0.33 for interaction). The risk of myocardial infarction did not differ between the two DAPT regimens (0.95, 0.58 to 1.54; P=0.82; for those with diabetes and 1.15, 0.68 to 1.94; P=0.60; for those without diabetes (P=0.84 for interaction). There was a lower risk of definite/probable stent thrombosis with long term DAPT among patients with (0.26, 0.09 to 0.80; P=0.02) than without (1.42, 0.68 to 2.98; P=0.35) diabetes, with positive interaction testing (P=0.04 for interaction), although the landmark analysis showed a trend towards benefit in both groups. Long term DAPT was associated with higher rates of major or minor bleeding, irrespective of diabetes (P=0.37 for interaction).

CONCLUSIONS

 Although the presence of diabetes emerged as an independent predictor of MACE after implantation of a drug eluting stent, compared with short term DAPT, long term DAPT did not reduce the risk of MACE but increased the risk of bleeding among patients with stents with and without diabetes.

Investigating covariate-by-centre interaction in survival data

In survival analysis, assessing the existence of potential centre effects on the baseline hazard or on the effect of fixed covariates on the baseline hazard, such as treatment-by-centre interaction, is a frequent clinical concern in multicentre studies. Survival models with random effects on the baseline hazard and/or on the effect of the covariates of interest have been largely applied, for instance, to investigate potential centre effects. We aimed to develop a procedure to routinely test for multiple random effects in survival analyses. We propose a statistic and a permutation approach to test whether all or a subset of components of the variance-covariance matrix of random effects are non-zero in a mixed-effects Cox model framework. Performances of the proposed permutation tests are examined under different null hypotheses corresponding to the different components of the variance-covariance matrix, i.e ., to the different random effects considered on the baseline hazard and/or on the covariates effects. Several alternative hypotheses are evaluated using simulations. The results indicate that the permutation tests have valid type I error rates under the null and achieve satisfactory power under all alternatives. The procedure is applied to two European cohorts of haematological stem cell transplants in acute leukaemia to investigate the heterogeneity across centres in leukaemia-free survival and the potential heterogeneity in prognostic factors effects across centres.

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification

A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available information. User-friendly Stata software is provided.

Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis

Background

The difference in restricted mean survival time (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗), the area between two survival curves up to time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials. A challenge in individual patient data (IPD) meta-analyses is to account for the trial effect. We aimed at comparing different methods to estimate the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗ from an IPD meta-analysis.

Methods

We compared four methods: the area between Kaplan-Meier curves (experimental vs. control arm) ignoring the trial effect (Naïve Kaplan-Meier); the area between Peto curves computed at quintiles of event times (Peto-quintile); the weighted average of the areas between either trial-specific Kaplan-Meier curves (Pooled Kaplan-Meier) or trial-specific exponential curves (Pooled Exponential). In a simulation study, we varied the between-trial heterogeneity for the baseline hazard and for the treatment effect (possibly correlated), the overall treatment effect, the time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, the number of trials and of patients, the use of fixed or DerSimonian-Laird random effects model, and the proportionality of hazards. We compared the methods in terms of bias, empirical and average standard errors. We used IPD from the Meta-Analysis of Chemotherapy in Nasopharynx Carcinoma (MAC-NPC) and its updated version MAC-NPC2 for illustration that included respectively 1,975 and 5,028 patients in 11 and 23 comparisons.

Results

The Naïve Kaplan-Meier method was unbiased, whereas the Pooled Exponential and, to a much lesser extent, the Pooled Kaplan-Meier methods showed a bias with non-proportional hazards. The Peto-quintile method underestimated the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗, except with non-proportional hazards at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗= 5 years. In the presence of treatment effect heterogeneity, all methods except the Pooled Kaplan-Meier and the Pooled Exponential with DerSimonian-Laird random effects underestimated the standard error of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗. Overall, the Pooled Kaplan-Meier method with DerSimonian-Laird random effects formed the best compromise in terms of bias and variance. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast },=,10,\kern0.5em ,\mathrm{years}\right) $$\end{document}rmstDt∗=10years estimated with the Pooled Kaplan-Meier method was 0.49 years (95 % CI: [−0.06;1.03], p = 0.08) when comparing radiotherapy plus chemotherapy vs. radiotherapy alone in the MAC-NPC and 0.59 years (95 % CI: [0.34;0.84], p < 0.0001) in the MAC-NPC2.

Conclusions

We recommend the Pooled Kaplan-Meier method with DerSimonian-Laird random effects to estimate the difference in restricted mean survival time from an individual-patient data meta-analysis.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0137-z) contains supplementary material, which is available to authorized users.

Get real in individual participant data (IPD) meta-analysis: a review of the methodology

Individual participant data (IPD) meta-analysis is an increasingly used approach for synthesizing and investigating treatment effect estimates. Over the past few years, numerous methods for conducting an IPD meta-analysis (IPD-MA) have been proposed, often making different assumptions and modeling choices while addressing a similar research question. We conducted a literature review to provide an overview of methods for performing an IPD-MA using evidence from clinical trials or non-randomized studies when investigating treatment efficacy. With this review, we aim to assist researchers in choosing the appropriate methods and provide recommendations on their implementation when planning and conducting an IPD-MA.

Measures of single arm outcome in meta-analyses of rare events in the presence of competing risks

When performing single arm meta-analyses of rare events in small populations, if the outcome of interest is incidence, it is not uncommon to have at least one study with zero events, especially in the presence of competing risks. In this paper, we address the problem of how to include studies with zero events in inverse variance meta-analyses when individual patient data are not available, going beyond the naïve approach of not including the study or the use of a continuity correction. The proposed solution is the arcsine transformation of the crude cumulative incidence as its approximate variance, which is inversely proportional to the sample size, can be calculated also for studies with a zero estimate. As an alternative, generalized linear mixed models (GLMM) can be used. Simulations were performed to compare the results from inverse variance method meta-analyses of the arcsine transformed cumulative incidence to those obtained from meta-analyses of the cumulative incidence itself and of the logit transformation of the cumulative incidence. The comparisons have been carried out for different scenarios of heterogeneity, incidence, and censoring and for competing and not competing risks. The arcsine transformation showed the smallest bias and the highest coverage among models assuming within study normality. At the same time, the GLMM model had the best performance at very low incidences. The proposed method was applied to the clinical context that motivated this work, i.e. a meta-analysis of 5-year crude cumulative incidence of central nervous system recurrences in children treated for acute lymphoblastic leukemia.

Risk estimation of multiple recurrence and progression of non muscle invasive bladder carcinoma using new mathematical models

OBJECTIVE

To apply new mathematical models according to Non Muscle Invasive Bladder Carcinoma (NMIBC) biological characteristics and enabling an accurate risk estimation of multiple recurrences and tumor progression. The classical Cox model is not valid for the assessment of this kind of events becausethe time betweenrecurrencesin the same patientmay be stronglycorrelated. These new models for risk estimation of recurrence/progression lead to individualized monitoring and treatment plan.

MATERIALS AND METHODS

960 patients with primary NMIBC were enrolled. The median follow-up was 48.1 (3-160) months. Results obtained were validated in 240 patients from other center. Transurethral resection of the bladder (TURB) and random bladder biopsy were performed. Subsequently, adjuvant localized chemotherapy was performed. The variables analyzed were: number and tumor size, age, chemotherapy and histopathology. The endpoints were time to recurrence and time to progression. Cox model and its extensions were used as joint frailty model for multiple recurrence and progression. Model accuracy was calculated using Harrell's concordance index (c-index).

RESULTS

468 (48.8%) patients developed at least one tumor recurrence and tumor progression was reported in 52 (5.4%) patients. Variables for multiple-recurrence risk are: age, grade, number, size, treatment and the number of prior recurrences. All these together with age, stage and grade are the variables for progression risk. Concordance index was 0.64 and 0.85 for multiple recurrence and progression respectively.

CONCLUSION

the high concordance reported besides to the validation process in external source, allow accurate multi-recurrence/progression risk estimation. As consequence, it is possible to schedule a follow-up and treatment individualized plan in new and recurrent NMCB cases.

Variable selection in subdistribution hazard frailty models with competing risks data

The proportional subdistribution hazards model (i.e. Fine-Gray model) has been widely used for analyzing univariate competing risks data. Recently, this model has been extended to clustered competing risks data via frailty. To the best of our knowledge, however, there has been no literature on variable selection method for such competing risks frailty models. In this paper, we propose a simple but unified procedure via a penalized h-likelihood (HL) for variable selection of fixed effects in a general class of subdistribution hazard frailty models, in which random effects may be shared or correlated. We consider three penalty functions, least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD) and HL, in our variable selection procedure. We show that the proposed method can be easily implemented using a slight modification to existing h-likelihood estimation approaches. Numerical studies demonstrate that the proposed procedure using the HL penalty performs well, providing a higher probability of choosing the true model than LASSO and SCAD methods without losing prediction accuracy. The usefulness of the new method is illustrated using two actual datasets from multi-center clinical trials.

Primary squamous cell carcinomas in the thyroid gland: an individual participant data meta-analysis

Primary squamous cell carcinomas arising from the thyroid gland (SCCTh) is extremely rare diseases, which have never been fully studied. Thus, we performed a systematic review and individual participant data meta-analysis of published SCCTh cases, to understand the clinical characteristics and to identify the prognostic factors of primary SCCTh. A literature search was conducted within Medline, EMBASE, Cochrane library databases and KoreaMed using the following Medical Subject Headings (MeSH) keywords: “primary,” “squamous,” “carcinoma,” “cancer,” and “thyroid.” Eighty-four patients' individual data from 39 articles and five patients' data in our institute were selected for analysis (N = 89). The mean age at diagnosis was 63.0 years (range, 24–90) and female preponderance (M:F = 1:2) was noted. The commonest complaint was the anterior neck mass, followed by dyspnea or dysphagia, and extension to the adjacent structure was found in 72%. The median survival was 9.0 months (95% CI, 6.0–23.0) and 3-year survival rate (3YSR) was 37.6% by Kaplan–Meier method, but only 20.1% by a shared frailty model for adjusting heterogeneity. Complete resection (R0) of tumors was the only significant prognostic factor in multivariable analysis, and the benefit of adjuvant treatment was not proved. The prognosis of patients with SCCTh is very poor (20% in 3YSR), but complete resection of disease is correlated with improved survival. To achieve complete surgical eradication of tumors, early detection and accurate diagnosis should be emphasized.

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

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.

Permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study

When analysing multicentre data, it may be of interest to test whether the distribution of the endpoint varies among centres. In a mixed-effect model, testing for such a centre effect consists in testing to zero a random centre effect variance component. It has been shown that the usual asymptotic χ(2) distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In the case of censored data, mixed-effects Cox models have been used to account for random effects, but few works have concentrated on testing to zero the variance component of the random effects. We propose a permutation test, using random permutation of the cluster indices, to test for a centre effect in multilevel censored data. Results from a simulation study indicate that the permutation tests have correct type I error rates, contrary to standard likelihood ratio tests, and are more powerful. The proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients.

Concordance measures in shared frailty models: application to clustered data in cancer prognosis

Frailty models are gaining interest in prognostic studies, especially because of the spread of multicenter studies. However, little research has been performed to extend prognostic tools to frailty models, including discrimination measures. As previously performed for the Harrell's c-index, we extended two different discrimination measures (the model-based concordance probability estimation of Gönen and Heller and the nonparametric Uno's c-index) to take into account cluster membership. We calculate measures at three levels: between-group, where only patients with different frailties are compared, within-group, where only patients sharing the same frailty are compared, and overall. We performed simulations to study the impact of group size and the number of groups on these measures. Results showed that the two measures can be extended to frailty models while remaining independent from censoring distribution, provided that the group size is sufficient. We apply the extended measures to two real datasets, a meta-analysis and a large multicenter trial.

Interval estimation of random effects in proportional hazards models with frailties

Semi-parametric frailty models are widely used to analyze clustered survival data. In this article, we propose the use of the hierarchical likelihood interval for individual frailties. We study the relationship between hierarchical likelihood, empirical Bayesian, and fully Bayesian intervals for frailties. We show that our proposed interval can be interpreted as a frequentist confidence interval and Bayesian credible interval under a uniform prior. We also propose an adjustment of the proposed interval to avoid null intervals. Simulation studies show that the proposed interval preserves the nominal confidence level. The procedure is illustrated using data from a multicenter lung cancer clinical trial.

Individual patient data meta-analysis of survival data using Poisson regression models

Background

An Individual Patient Data (IPD) meta-analysis is often considered the gold-standard for synthesising survival data from clinical trials. An IPD meta-analysis can be achieved by either a two-stage or a one-stage approach, depending on whether the trials are analysed separately or simultaneously. A range of one-stage hierarchical Cox models have been previously proposed, but these are known to be computationally intensive and are not currently available in all standard statistical software. We describe an alternative approach using Poisson based Generalised Linear Models (GLMs).

Methods

We illustrate, through application and simulation, the Poisson approach both classically and in a Bayesian framework, in two-stage and one-stage approaches. We outline the benefits of our one-stage approach through extension to modelling treatment-covariate interactions and non-proportional hazards. Ten trials of hypertension treatment, with all-cause death the outcome of interest, are used to apply and assess the approach.

Results

We show that the Poisson approach obtains almost identical estimates to the Cox model, is additionally computationally efficient and directly estimates the baseline hazard. Some downward bias is observed in classical estimates of the heterogeneity in the treatment effect, with improved performance from the Bayesian approach.

Conclusion

Our approach provides a highly flexible and computationally efficient framework, available in all standard statistical software, to the investigation of not only heterogeneity, but the presence of non-proportional hazards and treatment effect modifiers.

A joint model for the dependence between clustered times to tumour progression and deaths: A meta-analysis of chemotherapy in head and neck cancer

The observation of time to tumour progression (TTP) or progression-free survival (PFS) may be terminated by a terminal event. In this context, deaths may be due to tumour progression, and the time to the major failure event (death) may be correlated with the TTP. The usual assumption of independence between the TTP process and death, required by many commonly used statistical methods, can be violated. Furthermore, although the relationship between TTP and time to death is most relevant to the anti-cancer drug development or to evaluation of TTP as a surrogate endpoint, statistical models that try to describe the dependence structure between these two characteristics are not frequently used. We propose a joint frailty model for the analysis of two survival endpoints, TTP and time to death, or PFS and time to death, in the context of data clustering (e.g. at the centre or trial level). This approach allows us to simultaneously evaluate the prognostic effects of covariates on the two survival endpoints, while accounting both for the relationship between the outcomes and for data clustering. We show how a maximum penalized likelihood estimation can be applied to a nonparametric estimation of the continuous hazard functions in a general joint frailty model with right censoring and delayed entry. The model was motivated by a large meta-analysis of randomized trials for head and neck cancers (Meta-Analysis of Chemotherapy in Head and Neck Cancers), in which the efficacy of chemotherapy on TTP or PFS and overall survival was investigated, as adjunct to surgery or radiotherapy or both.

Frailty modelling for survival data from multi-centre clinical trials

Despite the use of standardized protocols in, multi-centre, randomized clinical trials, outcome may vary between centres. Such heterogeneity may alter the interpretation and reporting of the treatment effect. Below, we propose a general frailty modelling approach for investigating, inter alia, putative treatment-by-centre interactions in time-to-event data in multi-centre clinical trials. A correlated random effects model is used to model the baseline risk and the treatment effect across centres. It may be based on shared, individual or correlated random effects. For inference we develop the hierarchical-likelihood (or h-likelihood) approach which facilitates computation of prediction intervals for the random effects with proper precision. We illustrate our methods using disease-free time-to-event data on bladder cancer patients participating in an European Organization for Research and Treatment of Cancer trial, and a simulation study. We also demonstrate model selection using h-likelihood criteria.

Meta-analysis of summary survival curve data

The use of standard univariate fixed- and random-effects models in meta-analysis has become well known in the last 20 years. However, these models are unsuitable for meta-analysis of clinical trials that present multiple survival estimates (usually illustrated by a survival curve) during a follow-up period. Therefore, special methods are needed to combine the survival curve data from different trials in a meta-analysis. For this purpose, only fixed-effects models have been suggested in the literature. In this paper, we propose a multivariate random-effects model for joint analysis of survival proportions reported at multiple time points and in different studies, to be combined in a meta-analysis. The model could be seen as a generalization of the fixed-effects model of Dear (Biometrics 1994; 50:989-1002). We illustrate the method by using a simulated data example as well as using a clinical data example of meta-analysis with aggregated survival curve data. All analyses can be carried out with standard general linear MIXED model software.