May 10, 2011 § Leave a comment
Hypothesis: The common odds ratio is not what you really want, or at least not enough.
Study here. It combines a previous study from Iceland with replications across Europe. Let’s just look at their first marker, rs9321501, and ignore dependence. How is this marker associated with schizophrenia?
Stratifying across 12 locations, the 41 named authors come up with a common odds ratio of 1.09 (1.04 to 1.15). I only have data for 11 locations. With the data I have I get a common odds ratio of 1.096. The odds ratio on the aggregated data, however, is 0.96. What explains the difference?
The high common odds ratio is almost entirely due to two locations: Holland and Iceland. Both have large sample sizes and odds ratios over 1.2.
The low odds ratio is almost entirely due to… Iceland again! In the Iceland study, 71% of schizophrenic alleles are in the test group, while 67% of control alleles are in the test group. In the replications, 62% of schizophrenic alleles are in the test group, while 59% of control alleles are in the test group. When we add Iceland, along comes Simpson’s paradox. Iceland had a huge control group, so it actually lifts the control percentage above the schizophrenic percentage.
Clearly the common odds ratio is better than the odds ratio of the aggregate. Is the common odds ratio informative enough? I’ll get back to you!