Extended Data Fig. 4: Co-occurrence analyses.

a, b, Within-gene co-occurrence among genes identified in the ultra-rare variant burden analyses. The forest plots show the odds-ratio (OR; center) and 95% confidence intervals (CI; error bars), comparing the risk for individuals carrying a single qualifying variant to those carrying multiple variants. The panels depict genes in which co-occurrence of ultra-rare variants was observed (a), as well as genes in which co-occurrence of an ultra-rare variant with a more common variant from the single variant analyses was observed (b). c, d, Cumulative burden of carrying multiple high- or moderate-impact variants among Definitive ALS genes as curated by the GCEP. Shown are the odds-ratios (OR; center) and 95% confidence intervals (CI; error bars) (x-axis), stratified by the number of risk variants carried (y-axis). c, Analysis at the variant level, where each qualifying variant is counted individually. d, Analysis at the gene level, where carrying one or more qualifying variants within the same gene is counted as a single event. e, Forest plots showing the odds ratios (OR; center) and 95% confidence intervals (CI; error bars) for variant pairs. For each low-frequency variant (MAF 0.01-0.05), the odds-ratio is shown for carrying only the index variant (yellow, panel), only the target variant (green, y-axis), and carrying both variants (blue). The interaction odds-ratio (orange) indicates whether the variants act synergistically (OR > 1) or antagonistically (OR < 1). Association statistics are two-tailed and were estimated using Firth’s logistic regression with profile penalized likelihood confidence intervals. P-values are two-tailed and presented uncorrected for multiple testing.