Meta-analysis of standardised mean differences from randomised trials with treatment-related clustering associated with care providers
In meta-analyses, where a continuous outcome is measured with different scales or standards, the summary statistic is the mean difference standardised to a common metric with a common variance. Where trial treatment is delivered by a person, nesting of patients within care providers leads to clustering that may interact with, or be limited to, one or more of the arms. Assuming a common standardising variance is less tenable and options for scaling the mean difference become numerous. Metrics suggested for cluster-randomised trials are within, between and total variances and for unequal variances, the control arm or pooled variances. We consider summary measures and individual-patient-data methods for meta-analysing standardised mean differences from trials with two-level nested clustering, relaxing independence and common variance assumptions, allowing sample sizes to differ across arms. A general metric is proposed with comparable interpretation across designs. The relationship between the method of standardisation and choice of model is explored, allowing for bias in the estimator and imprecision in the standardising metric. A meta-analysis of trials of counselling in primary care motivated this work. Assuming equal clustering effects across trials, the proposed random-effects meta-analysis model gave a pooled standardised mean difference of −0.27 (95% CI −0.45 to −0.08) using summary measures and −0.26 (95% CI −0.45 to −0.09) with the individual-patient-data. While treatment-related clustering has rarely been taken into account in trials, it is now recommended that it is considered in trials and meta-analyses. This paper contributes to the uptake of this guidance.
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