Forum de statistique : conférence « Meta-analysis in practice: back to basics »

- Forum de statistiques
Prof. Elena Kulinskaya

School of Computing Sciences
University of East Anglia UEA
Norwich, UK

Abstract: Meta-analyses (MAs) generally follow a standard approach, established many years ago and codified in many guidelines and numerous software packages. The approach for random-effects MA involves the following steps: (a) Estimated variances of the study-level effects are substituted for the unknown true variances; (b) the between-study (heterogeneity) variance, τ-squared, is estimated by a generic method; (c) the estimate of the overall effect is obtained as a weighted average of the study-level effects, using inverse-variance weights; (d) the variance of the estimated overall effect is estimated by the reciprocal of the sum of the weights; and (e) a normal-theory confidence interval for the overall effect is centered at its estimate.

Most of these steps involve assumptions that are usually not valid. Because of below-nominal coverage at step (e), the latest methodology publications recommend a confidence interval based on the t-distribution and a different estimate of the variance, developed by Hartung & Knapp (2001) and Sidik & Jonkman (2002).

In this talk, I aim to move beyond two fallacies: (a) all effect measures can be analysed generically, and (b) estimated inverse-variance weights are the best way to combine study effects. I show that estimation of τ-squared should use methods specific to the effect measure. For estimating the overall effect, we advocate weights that do not involve estimated variances. We use fixed weights; i.e., the weights depend on nothing more than the studies’ sample sizes, as suggested by Hedges and Olkin (1985), Hunter and Schmidt (1990), and many others. Specifically, we use the weights proportional to the effective sample size. This approach yields unbiased estimates of the overall effect with little loss of efficiency.

To estimate τ-squared, we use improved approximations to the distribution of Cochran’s Q for the particular effect measure. Such approximations were developed for the standardised mean difference (SMD) in Kulinskaya, Dollinger and Bjørkestøl (2011) and for the log-odds-ratio in Kulinskaya and Dollinger (2015).

To achieve coverage close to the nominal 95%, we center the confidence interval for the overall effect at the fixed-weight estimate and use critical values from the t-distribution, in the spirit of Hartung & Knapp, and Sidik & Jonkman.

In this talk, I present results of the extensive simulations comparing our approach with various methods that follow the standard MA approach focusing on the standardised mean difference and on the log-odds-ratio.

(Joint work with Ilyas Bakbergenuly and David Hoaglin)

Date et heure
Jeudi, 8 Novembre, 2018 - 11:00
Salle Murray, Aquatis Hotel, route de Berne 148, 1010 Lausanne

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