A flexible parametric accelerated failure time model and the extension to time-dependent acceleration factors.

Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, that is, shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this article, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommodate time-dependent acceleration factors. Delayed entry is also allowed, and hence, time-dependent covariates. We evaluate the proposed model through simulation, showing substantial improvements compared to standard parametric AFT models. We also show analytically and through simulations that the AFT models are collapsible, suggesting that this model class will be well suited to causal inference. We illustrate the methods with a data set of patients with breast cancer. Finally, we provide highly efficient, user-friendly Stata, and R software packages.

Early transfusion patterns improve the Molecular International Prognostic Scoring System (IPSS-M) prediction in myelodysplastic syndromes.

BACKGROUND: The Molecular International Prognostic Scoring System (IPSS-M) is the new gold standard for diagnostic outcome prediction in patients with myelodysplastic syndromes (MDS). This study was designed to assess the additive prognostic impact of dynamic transfusion parameters during early follow-up. METHODS: We retrieved complete transfusion data from 677 adult Swedish MDS patients included in the IPSS-M cohort. Time-dependent erythrocyte transfusion dependency (E-TD) was added to IPSS-M features and analyzed regarding overall survival and leukemic transformation (acute myeloid leukemia). A multistate Markov model was applied to assess the prognostic value of early changes in transfusion patterns. RESULTS: Specific clinical and genetic features were predicted for diagnostic and time-dependent transfusion patterns. Importantly, transfusion state both at diagnosis and within the first year strongly predicts outcomes in both lower (LR) and higher-risk (HR) MDSs. In multivariable analysis, 8-month landmark E-TD predicted shorter survival independently of IPSS-M (p < 0.001). A predictive model based on IPSS-M and 8-month landmark E-TD performed significantly better than a model including only IPSS-M. Similar trends were observed in an independent validation cohort (n = 218). Early transfusion patterns impacted both future transfusion requirements and outcomes in a multistate Markov model. CONCLUSION: The transfusion requirement is a robust and available clinical parameter incorporating the effects of first-line management. In MDS, it provides dynamic risk information independently of diagnostic IPSS-M and, in particular, clinical guidance to LR MDS patients eligible for potentially curative therapeutic intervention.

Multiple imputation strategies for missing event times in a multi-state model analysis.

In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times may not be known. Motivated by a real dataset of patients who received stem cell transplants, we considered the setting in which some event times were exactly observed and some were missing. In our setting, there was little information about the time intervals in which the missing event times occurred and missingness depended on the event type, given the analysis model covariates. These additional challenges limited the usefulness of some missing data methods (maximum likelihood, complete case analysis, and inverse probability weighting). We show that multiple imputation (MI) of event times can perform well in this setting. MI is a flexible method that can be used with any complete data analysis model. Through an extensive simulation study, we show that MI by predictive mean matching (PMM), in which sampling is from a set of observed times without reliance on a specific parametric distribution, has little bias when event times are missing at random, conditional on the observed data. Applying PMM separately for each sub-group of patients with a different pathway through the MSM tends to further reduce bias and improve precision. We recommend MI using PMM methods when performing MSM analysis with Markov models and partially observed event times.

Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study.

Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one-stage and two-stage approaches to meta-analyzing individual patient data (IPD) in a multi-state survival setting when the number and size of studies being meta-analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi-state IPD were simulated from study- and transition-specific hazard functions. One-stage frailty and two-stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population-level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real-world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out-performed by two-stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta-analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay.

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group.

BACKGROUND: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. METHODS: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. RESULTS: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. CONCLUSIONS: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models.

In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions ( C I F $CIF$ s) derived using flexible parametric survival models. An initial analysis on the colon cancer data from the population-based Swedish Cancer Register indicates such an influence. A simulation study is conducted in order to assess the impact of the choice of timescale for other cause mortality on the bias of the estimated C I F s $CIFs$ and how different factors may influence the bias. We also use regression standardization methods in order to obtain marginal C I F $CIF$ estimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias in C I F $CIF$ for cancer mortality ( C I F 1 $CIF_{1}$ ) under all approaches. It also leads to a low degree of bias in C I F $CIF$ for other cause mortality ( C I F 2 $CIF_{2}$ ), provided that the effect of age at diagnosis is included in the model with sufficient flexibility, with higher bias under scenarios where a covariate has a time-varying effect on the hazard rate for other cause mortality on the attained age scale.

Multiple imputation strategies for a bounded outcome variable in a competing risks analysis.

In patient follow-up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as "bounded" or "interval-censored." Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood-based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log-normal regression with postimputation back-transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.

A multistate model incorporating estimation of excess hazards and multiple time scales.

As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies and cardiovascular disease. To provide clinically relevant population-level measures of late effects, it is of importance to (1) simultaneously estimate the risks of both morbidity and mortality, (2) partition these risks into the component expected in the absence of cancer and the component due to the cancer and its treatment, and (3) incorporate the multiple time scales of attained age, calendar time, and time since diagnosis. Multistate models provide a framework for simultaneously studying morbidity and mortality, but do not solve the problem of partitioning the risks. However, this partitioning can be achieved by applying a relative survival framework, allowing us to directly quantify the excess risk. This article proposes a combination of these two frameworks, providing one approach to address (1) to (3). Using recently developed methods in multistate modeling, we incorporate estimation of excess hazards into a multistate model. Both intermediate and absorbing state risks can be partitioned and different transitions are allowed to have different and/or multiple time scales. We illustrate our approach using data on Hodgkin lymphoma patients and excess risk of diseases of the circulatory system, and provide user-friendly Stata software with accompanying example code.

Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology.

BACKGROUND: Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model. METHODS: Predictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry). RESULTS: Despite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model. CONCLUSION: We conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The multistate package in Stata facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.

Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus.

BACKGROUND: Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various measures to be estimated that are of great epidemiological importance. However, increased complexity of the multi-state setting and predictions over time for individuals with different covariate patterns may lead to increased difficulty in communicating the estimated measures. The need for easy and meaningful communication of the analysis results motivated the development of a web tool to address these issues. RESULTS: MSMplus is a publicly available web tool, developed via the Shiny R package, with the aim of enhancing the understanding of multi-state model analyses results. The results from any multi-state model analysis are uploaded to the application in a pre-specified format. Through a variety of user-tailored interactive graphs, the application contributes to an improvement in communication, reporting and interpretation of multi-state analysis results as well as comparison between different approaches. The predicted measures that can be supported by MSMplus include, among others, the transition probabilities, the transition intensity rates, the length of stay in each state, the probability of ever visiting a state and user defined measures. Representation of differences, ratios and confidence intervals of the aforementioned measures are also supported. MSMplus is a useful tool that enhances communication and understanding of multi-state model analyses results. CONCLUSIONS: Further use and development of web tools should be encouraged in the future as a means to communicate scientific research.

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study.

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.

Changes in Body Mass Index and Rates of Death and Transplant in Hemodialysis Patients: A Latent Class Joint Modeling Approach.

BACKGROUND: The relationship between body mass index (BMI) and patient survival in end-stage kidney disease is not well understood and has been the subject of much debate over recent years. METHODS: This study used a latent class joint modeling approach to identify latent groups that underpinned associations between patterns of change in BMI during hemodialysis and two competing events: transplant and death without transplant. We included all adult patients who initiated chronic hemodialysis treatment in Australia or New Zealand between 2005 and 2014. RESULTS: There were 16,414 patients included in the analyses; 2,365 (14%) received a transplant, 5,639 (34%) died before transplant, and 8,410 (51%) were administratively censored. Our final model characterized patients based on five broad patterns of weight change (BMI trajectories): "late BMI decline" (about 2 years after commencing hemodialysis); "rapid BMI decline" (immediately after commencing hemodialysis); "stable and normal/overweight BMI"; "stable and morbidly obese BMI"; or "increasing BMI." Mortality rates were highest among classes with declining BMI, and the timing of weight loss coincided with the timing of increases in mortality. Within the two stable BMI classes, death rates were slightly lower among the morbidly obese. CONCLUSIONS: The findings from this descriptive analysis suggest a paradoxical association between obesity and better survival. However, they also suggest that the shape of the BMI trajectory is important, with stable BMI trajectories being beneficial. Future research should be aimed at understanding the causes of weight changes during dialysis, to determine whether there could be strategies to improve patient survival.

Measuring and Analyzing Length of Stay in Critical Care Trials.

BACKGROUND: In randomized clinical trials among critically ill patients, it is uncertain how choices regarding the measurement and analysis of nonmortal outcomes measured in terms of duration, such as intensive care unit (ICU) length of stay (LOS), affect studies' conclusions. OBJECTIVES: Assess the definitions and analytic methods used for ICU LOS analyses in published randomized clinical trials. RESEARCH DESIGN: This is a systematic review and statistical simulation study. RESULTS: Among the 80 of 150 trials providing sufficient information regarding the chosen definition of ICU LOS, 3 different start times (ICU admission, trial enrollment/randomization, receipt of intervention) and 2 end times (discharge readiness, actual discharge) were used. In roughly three quarters of these studies, ICU LOS was compared using approaches that did not explicitly account for death, either by ignoring it entirely or stratifying the analyses by survival status. The remaining studies used time-to-event (discharge) models censoring at death or applied a fixed LOS value to patients who died. In statistical simulations, we showed that each analytic approach tested a different question regarding ICU LOS, and that approaches that do not explicitly account for death often produce misleading or ambiguous conclusions when treatments produce small effects on mortality, even if those are not detected as significant in the trial. CONCLUSIONS: There is considerable variability in how ICU LOS is measured and analyzed which impairs the ability to compare results across trials and can produce spurious conclusions. Analyses of duration-based outcomes such as LOS should jointly assess the impact of the intervention on mortality to yield correct interpretations.

Using simulation studies to evaluate statistical methods.

Simulation studies are computer experiments that involve creating data by pseudo-random sampling. A key strength of simulation studies is the ability to understand the behavior of statistical methods because some "truth" (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analyzed, and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting, and presentation. In particular, this tutorial provides a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods, and performance measures ("ADEMP"); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine, which included at least one simulation study and identify areas for improvement.

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.

Adjusting Expected Mortality Rates Using Information From a Control Population: An Example Using Socioeconomic Status.

Expected or reference mortality rates are commonly used in the calculation of measures such as relative survival in population-based cancer survival studies and standardized mortality ratios. These expected rates are usually presented according to age, sex, and calendar year. In certain situations, stratification of expected rates by other factors is required to avoid potential bias if interest lies in quantifying measures according to such factors as, for example, socioeconomic status. If data are not available on a population level, information from a control population could be used to adjust expected rates. We have presented two approaches for adjusting expected mortality rates using information from a control population: a Poisson generalized linear model and a flexible parametric survival model. We used a control group from BCBaSe-a register-based, matched breast cancer cohort in Sweden with diagnoses between 1992 and 2012-to illustrate the two methods using socioeconomic status as a risk factor of interest. Results showed that Poisson and flexible parametric survival approaches estimate similar adjusted mortality rates according to socioeconomic status. Additional uncertainty involved in the methods to estimate stratified, expected mortality rates described in this study can be accounted for using a parametric bootstrap, but this might make little difference if using a large control population.

Mammographic Density Reduction as a Prognostic Marker for Postmenopausal Breast Cancer: Results Using a Joint Longitudinal-Survival Modeling Approach.

Previous studies have linked reductions in mammographic density after a breast cancer diagnosis to an improved prognosis. These studies focused on short-term change, using a 2-stage process, treating estimated change as a fixed covariate in a survival model. We propose the use of a joint longitudinal-survival model. This enables us to model long-term trends in density while accounting for dropout as well as for measurement error. We studied the change in mammographic density after a breast cancer diagnosis and its association with prognosis (measured by cause-specific mortality), overall and with respect to hormone replacement therapy and tamoxifen treatment. We included 1,740 women aged 50-74 years, diagnosed with breast cancer in Sweden during 1993-1995, with follow-up until 2008. They had a total of 6,317 mammographic density measures available from the first 5 years of follow-up, including baseline measures. We found that the impact of the withdrawal of hormone replacement therapy on density reduction was larger than that of tamoxifen treatment. Unlike previous studies, we found that there was an association between density reduction and survival, both for tamoxifen-treated women and women who were not treated with tamoxifen.

Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences.

Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.

Flexible parametric modelling of the cause-specific cumulative incidence function.

Competing risks arise with time-to-event data when individuals are at risk of more than one type of event and the occurrence of one event precludes the occurrence of all other events. A useful measure with competing risks is the cause-specific cumulative incidence function (CIF), which gives the probability of experiencing a particular event as a function of follow-up time, accounting for the fact that some individuals may have a competing event. When modelling the cause-specific CIF, the most common model is a semi-parametric proportional subhazards model. In this paper, we propose the use of flexible parametric survival models to directly model the cause-specific CIF where the effect of follow-up time is modelled using restricted cubic splines. The models provide smooth estimates of the cause-specific CIF with the important advantage that the approach is easily extended to model time-dependent effects. The models can be fitted using standard survival analysis tools by a combination of data expansion and introducing time-dependent weights. Various link functions are available that allow modelling on different scales and have proportional subhazards, proportional odds and relative absolute risks as particular cases. We conduct a simulation study to evaluate how well the spline functions approximate subhazard functions with complex shapes. The methods are illustrated using data from the European Blood and Marrow Transplantation Registry showing excellent agreement between parametric estimates of the cause-specific CIF and those obtained from a semi-parametric model. We also fit models relaxing the proportional subhazards assumption using alternative link functions and/or including time-dependent effects. Copyright © 2016 John Wiley & Sons, Ltd.

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.