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Factors that are strongly associated with the outcome might retain their association even when adjusting for other variables. The methods are compared using an empirical example, to illustrate their advantages, differences and accessibility. Our methods all assume that between-study heterogeneity in baseline risk and factor-outcome associations exists, as it likely in practice, and so we only consider random-effects IPD-MA models.
We examine different assumptions concerning the random effects, and consider how the models can be extended to adjust for other factors. Hereto, we describe two two-stage and three one-stage models for estimating unadjusted and adjusted factors.