I am trying to combine response data (i.e. proportions) from multiple studies where each study has only one arm of interest i.e. arm A or arm B. Because in each study I don’t have both arms I cannot perform a classic meta-analysis. The data are percentage of responders. I would like to estimate the percent responders for each arm, the difference and the relative risk between the groups with 95% confidence intervals for each. I thought of using a logistic regression with a random effect (i.e. the individual studies) using Proc GLIMMIX. The confidence intervals are important because I will use these to define a non-inferiority margin. Questions are 1) how can I get confidence intervals for the difference between the arms and 2) how do I get the relative risk?
Sample data and code looks something like this:
data a;
input studyno arm $ n_total n_responders;
cards;
1 B 107 42
2 B 73 41
3 B 75 41
4 B 77 49
5 B 199 123
6 B 201 122
7 B 221 123
8 A 16 4
9 A 47 16
10 A 767 107
11 A 170 20
12 A 51 13
13 A 128 20
14 A 19 5
15 A 14 1
16 A 47 13
17 A 118 23
18 A 58 11
;
run;
proc glimmix data=a;
class arm studyno;
model N_responders/n_total = arm /solution cl dist=binomial link=logit;
random intercept/subject=studyno;
lsmeans arm / cl ilink;
estimate 'A vs B' arm 1 -1 / cl ilink exp;
run;
Thanks in advance for any suggestions.
