Fig. 4.
Comparison of MFM analysis and single disease analysis. Causal variants were simulated for two diseases with models defined by SNP groups from the IL2RA region. MFM is shown by solid lines and independent analyses by dashed lines. Throughout, disease 1 has causal variants A + D, while causal variants for disease 2 vary. a, b Disease 2 has causal variants A + C and the odds ratio of A, ORA, is the same for both diseases; a A has a stronger effect than C and D; ORA = 1.4 (both), ORD = 1.25 (disease 1), ORC = 1.25 (disease 2). b A has a weaker effect than C and D; ORA = 1.25 (both), ORD = 1.4 (disease 1), ORC = 1.4 (disease 2). c Disease 2 has only C causal; ORA = ORD = 1.25 (disease 1), ORC = 1.25 (disease 2). d Disease 2 has no causal variants (no association). Potential models include A (red), B (green), C (blue), D (yellow), A + D (orange), A + C (purple) and null (black); any other models are grouped together as grey. The y-axis shows the average posterior probabilities for each model. a, b MFM can identify the true two causal variant model at smaller sample sizes than independent analysis in simulated data when there is sharing between diseases. c, d When there is no sharing (c) or one disease has no true associations (d), no information is gained by using MFM but there is only minimal loss in accuracy in doing so. Source data are provided in Supplementary Data 5–8