88 CHAPTER 6 Hypothesis Testing
Rubin ( 2002 ) are my recommendations. Little and Rubin deal specifi -
cally with missing data and the various approaches to handling them
based on the type of missing data. Hardin and Hilbe ( 2003 ) take the
generalized estimating function approach, which is an alternative way
of dealing with longitudinal data that we did not cover. The book gives
a thorough and very readable treatment even for nonstatisticians.
6.13 META - ANALYSIS
Two problems may occur when conducting clinical trials.
- Often a study may not have suffi cient sample size to reach
defi nitive conclusions. - Two or more studies may have confl icting results (not because
there was anything wrong with any of the studies, but rather
because type I and type II errors can occur even when the study
is well powered).
A technique called meta - analysis is being used more often recently to
combine information in order to reach stronger conclusions that are
also more likely to be correct than what any single study might tell us.
This can be done either by combining estimates or p - values in an
appropriate way. Care is required in the choice of studies to be com-
bined. Also publication bias (the bias due to a tendency to only publish
positive results) is a common problem. To remedy this, for FDA regu-
lated trials, the FDA requires posting trial information on the Internet
(for all phase III trials), including all trial results and data after the trial
is completed. This certainly will help to eliminate publication bias.
Hedges and Olkin ( 1985 ) was the pioneering work on formal sta-
tistical approaches to meta - analysis using frequentist approaches.
Stangl and Berry ( 2000 ) provide thorough coverage of the Bayesian
approach to meta - analysis. In this section, we will illustrate the use of
Fisher ’ s test for combining p - values to strengthen inference from
several tests.
Fisher ’ s test is based on the following results: Under the null
hypothesis in each of k hypothesis tests, the individual p - values have
a uniform distribution on [0, 1]. If we let U represent a random variable
with this uniform distribution, then let L = − 2 ln( U ) where “ ln ” denotes