The importance of having IPD available has been established, allowing a full exploration of between-study heterogeneity [34] and the verification of model assumptions. By obtaining IPD, computational issues may become apparent with the sheer size of patient data being analysed when incorporating random effects. This issue is clearly highlighted when using other large datasets within the hierarchical Cox framework [14]. However, it should be noted that a variety of techniques have been developed to investigate heterogeneity and non-proportional hazards, for example, when combining aggregate level data from published studies [4, 7–9, 11].

In this paper, our aim was to illustrate an effective alternative to hierarchical Cox models, minimising computational issues and providing further interpretational benefits. Through minimal splitting of follow-up time, reliable estimates of effect can be obtained. Choice of interval lengths will depend on the underlying shape of the hazard function; however, the hazard ratio may be insensitive to the baseline, as illustrated by consistent estimates of the treatment effect across the 3 choices of interval length used in this paper. By combining the Poisson approach with the collapsing technique described above, we can dramatically reduce computation time. When analysing data with rare events, such models may be further advantageous through the need of less intervals. Differential follow-up times between trials can also be accounted for through this approach. Our approach provides direct estimates of the baseline hazard rate which is clinically important. These estimates allow the calculation of risk differences, or number needed to treat [40]. However, a limitation of our approach is that the collapsing technique described cannot be used with truly continuous covariates, such as age measured in days.

Investigation of random treatment effect models showed a marked underestimation of heterogeneity under the classical approach. This may in fact be explained by the tendency of maximum likelihood to underestimate variance parameters [28]. Under the Bayesian approach we observed improved performance, with comparatively lower absolute biases; however, it must be noted that, given the nature of the MCMC algorithm, the Bayesian approach will always provide a positive estimate of between study heterogeneity. A recent simulation study emphasised the need for care when choosing non-informative priors on variance parameters [41], which has specific relevance when investigating heterogeneity in the treatment effect, as in Models C and D. An alternative estimation procedure, such as h-likelihood [42], could be investigated.

It must be noted that if purely interested in a pooled treatment effect, then there is no advantage in pursuing a one-stage over a two-stage approach; however, investigation of treatment effect modifiers and modelling assumptions should be conducted simultaneously, which can only be done effectively through a one-stage approach. Although previous work has provided effective methods to investigate heterogeneity in the meta-analysis setting [14–17], we feel our approach provides a highly simplistic alternative which can incorporate the investigation of non-proportional hazards in covariate effects, and that of treatment-effect modifiers, both of which should be considered in any IPD meta-analysis.

In our analysis of the hypertension dataset, we observed a 27.4% (95% CI: 16.55, 37.0%) reduction in the mortality rate when a patient is overweight compared to a non-overweight patient, with treatment group held constant. Although this is a surprising result, it is one that has been identified previously [43]. Previous work by one of the authors of this article has also observed this relationship between BMI and mortality; however, further identified that the true factor lowering risk is height, i.e. lower risk is seen for overweight patients because they tend to be taller [44].

The approach detailed in this paper has the further benefit of allowing adjustment for confounders to be implemented simply. This becomes important when analysing IPD from observational studies, where the need to adjust for confounders is often paramount [45].

The flexibility of the Poisson approach described may be extended through the use of splines to model not only the baseline hazard, but also any time-dependent effects [21]. This would result in more plausible predictions, allowing a continuous function estimate of both.

Finally, we recognise that the IPD approach does not necessarily solve all the problems for meta-analysis [46]; in particular, IPD may not be available from all the studies requested. In this situation a sensitivity analysis may be needed to examine whether IPD meta-analysis conclusions remain robust when aggregate data from non-IPD studies are additionally included as far as possible [35].