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For risk factors that are binary, if zero cell counts occur in some of the included studies (e. when all patients with the risk factor presence also have the outcome), the likelihood function may not converge or converges in an unstable factor-outcome association. For all case studies, in the two-stage models we used MLE in the first stage and MLE, REML or MOM in the second stage.

For the one-stage models we used adaptive Gauss-Hermite Quadrature with 1 (Laplacian approximation) and 5 quadrature points. Assuming the random effects are normally distributed with between-study standard deviation, then an approximate prediction interval for the factor-outcome association in an unspecified study can be obtained as.