Interpreting the beta geometric in comparative fecundability studies

The beta distribution has often been used to describe variation in fecundability between couples when modelling the number of menstrual cycles required for a couple to achieve pregnancy. Groups are often compared for a condition or factor that could affect conception rates. However, when heterogeneity is present in each group, comparing group-specific parameters is not very informative on what any differences might imply for the individual couples. We present a quantile ratio that provides an individual level interpretation of any between-group differences in the beta distribution. Our results are illustrated on the two examples of Ridout and Morgan (1991, Biometrics 47, 1423-1433). The quantile ratio suggests a simplification in one of the examples.