Concordance odds ratios and approximate rate ratios in longitudinal twin studies

Odds ratios derived from probandwise concordance rates are usually interpreted as increased risks in twins. Though the odds ratios in case-control studies have been shown to reflect rate ratios, few studies focused on such relationships in twin studies. The authors derived an approximate formula for the ratios of person-time incidence rates after the random assignment of twins into index twins and co-twins, i.e., incidence rate ratios. The resulting rate ratio was estimated as the product of the concordance odds ratio and a term that reflect the follow-up duration and the average time to occurrence of disease. Odds ratios coincide with rate ratios when the average time to occurrence of disease is half the duration of follow-up, although in studies spanning several decades these two measures might be different. The authors illustrated that when the incidence rate is not constant over the follow-up period as in longitudinal twin studies, the conventional odds ratio should not be used as an estimator of rate ratio.