On combining dose—response data from epidemiological studies by meta‐analysis

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Abstract
Using data from a meta‐analysis of the effects of oestrogen replacement therapy on the development of breast cancer, we compared alternative methods for combining dose—response slopes from epidemiological studies. We evaluated issues related both to summarizing data from single studies and to combining results from multiple studies. Findings related to the analysis of individual dose—response studies include: (1) a method of weighing studies that gives greater influence to dose—response slopes that conform to the linear relation of relative risk to duration can lead to large differences in calculated weights as a function of non‐linearity; (2) a regression model using a variable‐intercept resulted in a mean dose—response slope that increased as much as threefold when compared with the values obtained with a zero‐intercept model. When combining results from multiple studies, we found: (1) calculating standard errors of mean dose—response slopes by methods that allow for both among‐study and within‐study variability (a random‐effects type model) gave values different from a method that assumes homogeneity and equal within‐study precision (a fixed‐effects model); (2) the random‐effects model gives mean and standard error results most similar to a bootstrap resampling method as increasing heterogeneity is observed (however, this model could give biased mean estimates compared with the bootstrap method); (3) a components‐of‐variance model compares favourably with the bootstrap and is easier to apply than the random‐effects model. Based on these findings, we recommend the use of methods which incorporate heterogeneity to guard against underestimating the standard error. However, caution is urged because bias in point estimates can occur if extreme heterogeneity is present. Two other observations affect the interpretation of data combined from multiple studies. First, inclusion into a model of quality scores assigned by blinded reviewers had little effect on the mean dose—response slope and its standard error. Second, the number of studies required to achieve desired statistical power, varies with effect size.