Statistica Sinica 13(2003), 1135-1145

APPLYING THE LAW OF ITERATED LOGARITHM

TO CUMULATIVE META-ANALYSIS OF

A CONTINUOUS ENDPOINT

K. K. Gordon Lan, Mingxiu Hu and Joseph C. Cappelleri

Pfizer Inc.

Abstract: Cumulative meta-analysis typically involves performing an updated meta-analysis every time a new trial is added to a series of similar trials, which by definition involves multiple inspections. Since the studies are often conducted at different times with different protocols, the heterogeneity among studies is generally not ignorable and the estimation of the between-study variation poses the biggest challenge in cumulative meta-analyses because the testing process generally starts with a small number of studies. This is one of the major reasons why the conventional group sequential methods do not perform well in controlling the overall type I error. This paper presents an approach $-$ motivated by the Law of Iterated Logarithm $-$ that ``penalizes" the Z-value of the test statistic to account for multiple tests. It also can account for estimation of heterogeneity in treatment effects across studies and for the unpredictable nature of information from trials in a cumulative meta-analysis. Our extensive simulation studies show that this method controls the overall type I error for a very broad range of practical situations for up to 25 inspections. An example based on data from the Stroke Unit Trialists' Collaboration is used to illustrate the method.

Key words and phrases: Cumulative meta-analysis, fixed effects model, law of iterated logarithm, multiple inspections, random effects model, sequential analysis, type I error.