You can calculate/approximate the standard errors via the p-values. First, convert the two-sided p-values into one-sided p-values by dividing them by 2. So you get $p = .0115$ and $p = .007$. Then convert these p-values to the corresponding z-values. For $p = .0115$, this is $z = -2.273$ and for $p = .007$, this is $z = -2.457$ (they are negative, since the odds ratios are below 1). These z-values are actually the test statistics calculated by taking the log of the odds ratios divided by the corresponding standard errors (i.e., $z = log(OR) / SE$). So, it follows that $SE = log(OR) / z$, which yields $SE = 0.071$ for the first and $SE = .038$ for the second study.
Now you have everything to do a meta-analysis. I'll illustrate how you can do the computations with R, using the metafor package:
library(metafor)
yi <- log(c(.85, .91)) ### the log odds ratios
sei <- c(0.071, .038) ### the corresponding standard errors
res <- rma(yi=yi, sei=sei) ### fit a random-effects model to these data
res
Random-Effects Model (k = 2; tau^2 estimator: REML)
tau^2 (estimate of total amount of heterogeneity): 0 (SE = 0.0046)
tau (sqrt of the estimate of total heterogeneity): 0
I^2 (% of total variability due to heterogeneity): 0.00%
H^2 (total variability / within-study variance): 1.00
Test for Heterogeneity:
Q(df = 1) = 0.7174, p-val = 0.3970
Model Results:
estimate se zval pval ci.lb ci.ub
-0.1095 0.0335 -3.2683 0.0011 -0.1752 -0.0438 **
Note that the meta-analysis is done using the log odds ratios. So, $-0.1095$ is the estimated pooled log odds ratio based on these two studies. Let's convert this back to an odds ratio:
predict(res, transf=exp, digits=2)
pred se ci.lb ci.ub cr.lb cr.ub
0.90 NA 0.84 0.96 0.84 0.96
So, the pooled odds ratio is .90 with 95% CI: .84 to .96.
With regards to common control groups, you may want to check out 16.5.4 of the Cochrane Handbook. To quote a subset of this page:
Approaches to overcoming a unit-of-analysis error for a study that
could contribute multiple, correlated, comparisons include the
following.
- Combine groups to create a single pair-wise comparison
(recommended).
- Select one pair of interventions and exclude the
others.
- Split the ‘shared’ group into two or more groups with smaller
sample size, and include two or more (reasonably independent)
comparisons.
- Include two or more correlated comparisons and account
for the correlation.
- Undertake a multiple-treatments meta-analysis
(see Section 16.6).
The recommended method in most situations is to
combine all relevant experimental intervention groups of the study
into a single group, and to combine all relevant control intervention
groups into a single control group. As an example, suppose that a
meta-analysis of ‘acupuncture versus no acupuncture’ would consider
studies of either ‘acupuncture versus sham acupuncture’ or studies of
‘acupuncture versus no intervention’ to be eligible for inclusion.
Then a study comparing ‘acupuncture versus sham acupuncture versus no
intervention’ would be included in the meta-analysis by combining the
participants in the ‘sham acupuncture’ group with participants in the
‘no intervention’ group. This combined control group would be compared
with the ‘acupuncture’ group in the usual way. For dichotomous
outcomes, both the sample sizes and the numbers of people with events
can be summed across groups. For continuous outcomes, means and
standard deviations can be combined using methods described in Chapter
7 (Section 7.7.3.8).
With regards to pooling effect sizes for performing moderator meta analysis. There is a list of SPSS resources here. You might want to get a book like Introduction to Meta-Analysis to provide an overview of some of the many issues and calculations involved.
References
- Borenstein, M., Hedges, L.V., Higgins, J.P.T. & Rothstein, H.R. (2011). Introduction to meta-analysis. John Wiley \& Sons
Best Answer
The chapter on stochastically dependent effect sizes by Gleser and Olkin (2009) in The handbook of research synthesis and meta-analysis (2nd ed.) describes how multiple-treatment and multiple-endpoint studies can be meta-analyzed. Your case can be covered by the "multiple-treatment" part -- that is, you can look at the two disease stages as two different 'treatments' that are both compared against a common control group. In essence, you will have to compute the covariance between the two (log) ORs and take that into consideration when you want to include the two ORs in your meta-analysis.
If you work with R, you may find the
metaforpackage useful. On the metafor package website, you can find code that will reproduce the methods described in the Gleser and Olkin chapter: http://www.metafor-project.org/doku.php/analyses:gleser2009. That should help to get you started.