Meta-analysis methods are used to integrate quantitative findings from a set of related research studies with the aim of providing more reliable and accurate estimates of a treatment effect [

1]. Traditionally a meta-analysis requires aggregate data (AD), extracted from publications or received directly from study authors. Summary statistics (e.g. log hazard ratios) are then synthesised using a fixed or random effects meta-analysis [

2], where random effects can account for between study heterogeneity in the treatment effect. Meta-regression models [

3] attempt to explain this excess heterogeneity with study-level covariates. However, the use of AD to conduct a meta-analysis has inherent problems, for example, hazard ratios are not always explicitly given in publications, leading to the development of alternative techniques to extract appropriate summary statistics [

4]. Despite this, even when using the methods of Parmar et al., it can still be difficult to extract hazard ratios, as shown by Riley et al. [

5].

An approach often considered the

*gold-standard *alternative to an AD meta-analysis is a meta-analysis of individual patient data (IPD), which utilises the raw data from each study. IPD meta-analyses have been shown to be most common when analyzing time-to-event data [

6]. The benefits of conducting an IPD meta-analysis with time-to-event data include: follow-up time can be longer and more up to date, analyses can be standardised across studies, model assumptions can be checked e.g. proportional hazards, and confounders can be adjusted for. However, IPD can be difficult to obtain, and a variety of methods have been developed to undertake meta-analyses from the published literature of time-to-event data. An early proposal by Dear [

7] showed how to jointly synthesise survival proportions reported at multiple times, by utilising their correlation and combining them in a multivariate meta-analysis using generalised least squares. Dear investigated only fixed effects, leading the extension of Arends et al. to incorporate random effects [

8]. Techniques to extract summary statistics from published studies have also been demonstated [

4] for the use in standard AD meta-analyses. Fiocco et al. recently used a Poisson correlated gamma-frailty approach to combine survival curves under heterogeniety, allowing the investigation of both between-study variance and within and between-arm correlations [

9]. A frailty approach has also been implemented by Feng et al. incorporating crossed random effects using penalized quasi-likelihood under a Poisson likelihood [

10]. Further extensions of AD meta-analyses include assessment of the proportional hazards assumption [

9,

11]

IPD meta-analyses of time-to-event data can use either a two-stage or one-stage approach. The most commonly used, the two-stage, is achieved by first fitting individual survival models to each trial. The chosen estimates of effect are then combined in a standard meta-analysis framework, now equivalent to an AD meta-analysis. In a one-stage IPD meta-analysis, patient data from all studies are analysed simultaneously within a hierarchical framework. This draws parallels with the analysis of IPD from multi-centre clinical trials, accommodating clustering within treatment centres; however, in a multi-centre trial the treatment effect is not often random, whereas in a meta-analysis it often is. This is because in a multi-centre trial we can achieve greater consistency in inclusion/exclusion criteria and other aspects of trial protocol, indicating that a fixed treatment effect is likely to be more appropriate. Senn discusses these issues in more detail [

12], but we emphasise that, although random-effects models are rarely used to analyse multi-centre trials, they could also adopt the methods we present here. Indeed, published trial analysis guidelines do state: "mixed models may be used to explore heterogeneity of the treatment effect. These models consider centre and treatment-by-centre effects to be random, and are especially relevant when the number of sites is large" [

13]. A range of hierarchical survival models within the Cox framework have been developed [

14-

17], which can effectively account for heterogeneity in treatment effect and baseline risk. However, these methods can have a high computational burden and/or rely on user-written programs, not currently available in standard statistical software [

16]. Furthermore, these models do not investigate the validity of the assumption of proportional hazards. These reasons serve as motivation to consider alternative approaches, such as the percentile ratio [

18] as a target of inference in this setting, developed predominantly for when the proportional hazards assumption appears violated.

The aim of this paper is to explore the use of Poisson regression, and the generalised mixed model extensions, to incorporate random effects to perform one- and two-stage IPD meta-analyses of time-to-event outcomes, as an alternative to hierarchical Cox models, and to extend the models to incorporate non-proportional hazards and treatment-effect modifiers.