11-12-2012, 01:42 PM
Introduction to Meta-Analysis
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INTRODUCTION
Figure 1.1 illustrates a meta-analysis that shows the impact of high dose versus
standard dose of statins in preventing death and myocardial infarction (MI). This
analysis is adapted from one reported by Cannon et al. and published in the Journal
of the American College of Cardiology (2006).
Our goal in presenting this here is to introduce the various elements in a
meta-analysis (the effect size for each study, the weight assigned to each effect
size, the estimate of the summary effect, and so on) and show where each fits into
the larger scheme. In the chapters that follow, each of these elements will be
explored in detail.
INDIVIDUAL STUDIES
The first four rows on this plot represent the four studies. For each, the study name is
shown at left, followed by the effect size, the relative weight assigned to the study
for computing the summary effect, and the p-value. The effect size and weight are
also shown schematically.
Effect size
The effect size, a value which reflects the magnitude of the treatment effect or (more
generally) the strength of a relationship between two variables, is the unit of
currency in a meta-analysis. We compute the effect size for each study, and then work with the effect sizes to assess the consistency of the effect across studies and to
compute a summary effect.
The effect size could represent the impact of an intervention, such as the impact of
medical treatment on risk of infection, the impact of a teachingmethod on test scores,
or the impact of a new protocol on the number of salmon successfully returning
upstream. The effect size is not limited to the impact of interventions, but could
represent any relationship between two variables, such as the difference in test scores
for males versus females, the difference in cancer rates for persons exposed or not
exposed to second-hand smoke, or the difference in cardiac events for persons with
two distinct personality types. In fact, what we generally call an effect size could refer
simply to the estimate of a single value, such as the prevalence of Lyme disease.
Precision
In the schematic, the effect size for each study is bounded by a confidence
interval, reflecting the precision with which the effect size has been estimated
in that study. The confidence interval for the last study (Ideal) is noticeably
narrower than that for the first study (Prove-it), reflecting the fact that the Ideal
study has greater precision. The meaning of precision and the factors that affect
precision are discussed in Chapter 8.
Study weights
The solid squares that are used to depict each of the studies vary in size, with the size
of each square reflecting the weight that is assigned to the corresponding study
when we compute the summary effect. The TNT and Ideal studies are assigned
relatively high weights, while somewhat less weight is assigned to the A to Z study
and still less to the Prove-it study.
As one would expect, there is a relationship between a study’s precision and that
study’s weight in the analysis. Studies with relatively good precision (TNT and
Ideal) are assigned more weight while studies with relatively poor precision (Proveit)
are assigned less weight. Since precision is driven primarily by sample size, we
can think of the studies as being weighted by sample size.
However, while precision is one of the elements used to assign weights, there are
often other elements as well. In Part 3 we discuss different assumptions that one can
make about the distribution of effect sizes across studies, and how these affect the
weight assigned to each study.
p - values
For each study we show the p-value for a test of the null. There is a necessary
correspondence between the p-value and the confidence interval, such that the
p-value will fall under 0.05 if and only if the 95% confidence interval does not
include the null value. Therefore, by scanning the confidence intervals we can
easily identify the statistically significant studies. The role of p-values in the
analysis, as well as the relationship between p-values and effect size, is discussed
in Chapter 32.