*Relative Efficiencies of Using Summary Statistics vs Individual
Level Data in Meta-analysis*

**Description**

In this project, we study the relative
efficiencies of using summary statistics vs using individual level data in a
two-arm clinical trial. We simulate K trials of size n from a logisic
regression model with one binary treatment factor. For both meta-analysis of
summary statistics and meta-analysis of individual level data, the K
intercepts may be assumed to be the same or allowed to be different. The
former analysis estimates the effects using the weighted average of the
effect estimates from each
individual trial, where the weight is the inverse of the estimated variance
from each trial. The latter analysis estimates the effects using a
logistic regression model with all the individual level data.

**Programs**

The codes in both MatLab and R-format
are available in this file. "EffSim1.m" and "EffSim1.R"
are the functions for the relative efficiencies summarized from 10,000 replicates
when one half of the subjects are assigned to placebo and the other half are
assigned to treatment within each trial (Fixed Group Sizes). "EffSim2.m" and "EffSim2.R"
are the functions for the relative efficiencies summarized from 10,000
replicates when the treatment assignement is random with equal probability
(Random Group Sizes).
When an empty cell appears for a particular trial, this trial is
discarded and a new one is generated.

**Input** To use the programs, one needs to input the number of
trials (K), the size of each trial (n), the intercept (beta0) and the effect
(beta1).

**Output** The output from the programs is a 5 by 4 matrix.

Row 1: the
first row is the ratios of the sample variances between the meta-analysis of
individual level data with a common intercept and the meta-analysis of
summary statistics with a common intercept,
between the meta-analysis of
individual level data with different intercepts and the meta-analysis of
summary statistics with a common intercept,
between the meta-analysis of
individual level data with a common intercept and the meta-analysis of
summary statistics with different intercepts,
between the meta-analysis of
individual level data with different intercepts and the meta-analysis of
summary statistics with different intercepts;

Row 2: the second row is the average of the ratios between the estimated
variances of these estimators;

Row 3: the third row is the sample variances of the estimators from the
meta-analysis of
summary statistics with a common intercept, the meta-analysis of
individual level data with different intercepts, the meta-analysis of
summary statistics with a common intercept, and the meta-analysis of
summary statistics with different intercepts;

Row 4: the fourth row is the average of the estimated variances for these
estimators;

Row 5:
the fifth row is the standard deviations of the ratios between the
estimated variances.