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For testing a group of hypotheses, tremendous $p$-value combination methods have been developed and widely applied since 1930's. Some methods (e.g., the minimal $p$-value) are optimal for sparse signals, and some others (e.g., Fisher's combination) are optimal for dense signals. To address a wide spectrum of signal patterns, this paper proposes a unifying family of statistics, called TFisher, with general $p$-value truncation and weighting schemes. Analytical calculations for the $p$-value and the statistical power of TFisher under general hypotheses are given. Optimal truncation and weighting parameters are studied based on Bahadur Efficiency (BE) and the proposed Asymptotic Power Efficiency (APE), which is superior to BE for studying the signal detection problem. A soft-thresholding scheme is shown to be optimal for signal detection in a large space of signal patterns. When prior information of signal pattern is unavailable, an omnibus test, oTFisher, can adapt to the given data. Simulations evidenced the accuracy of calculations and validated the theoretical properties. The TFisher tests were applied to analyzing a whole exome sequencing data of amyotrophic lateral sclerosis. Relevant tests and calculations have been implemented into an R package $TFisher$ and published on the CRAN., Comment: 46 pages, 15 figures

Genome-wide association studies have been successful in identifying common variants that influence the susceptibility to complex diseases. From these studies, it has emerged that there is substantial overlap in susceptibility loci between diseases. In line with those findings, we hypothesized that shared genetic pathways may exist between multiple sclerosis (MS) and amyotrophic lateral sclerosis (ALS). While both diseases may have inflammatory and neurodegenerative features, epidemiological studies have indicated an increased co-occurrence within individuals and families. To this purpose, we combined genome-wide data from 4088 MS patients, 3762 ALS patients and 12 030 healthy control individuals in whom 5 440 446 single-nucleotide polymorphisms (SNPs) were successfully genotyped or imputed. We tested these SNPs for the excess association shared between MS and ALS and also explored whether polygenic models of SNPs below genome-wide significance could explain some of the observed trait variance between diseases. Genome-wide association meta-analysis of SNPs as well as polygenic analyses fails to provide evidence in favor of an overlap in genetic susceptibility between MS and ALS. Hence, our findings do not support a shared genetic background of common risk variants in MS and ALS.

Superoxide dismutase (SOD1) gene variants may cause amyotrophic lateral sclerosis, some of which are associated with a distinct phenotype. Most studies assess limited variants or sample sizes. In this international, retrospective observational study, we compare phenotypic and demographic characteristics between people with SOD1-ALS and people with ALS and no recorded SOD1 variant. We investigate which variants are associated with age at symptom onset and time from onset to death or censoring using Cox proportional-hazards regression. The SOD1-ALS dataset reports age of onset for 1122 and disease duration for 883 people; the comparator population includes 10,214 and 9010 people respectively. Eight variants are associated with younger age of onset and distinct survival trajectories; a further eight associated with younger onset only and one with distinct survival only. Here we show that onset and survival are decoupled in SOD1-ALS. Future research should characterise rarer variants and molecular mechanisms causing the observed variability. Analysis of age of onset and disease duration in a large, international cohort of people with SOD1-ALS shows that there is a distinct phenotype and that onset and progression are decoupled., United Kingdom, Medical Research Council; Economic and Social Research Council; European Community’s Health Seventh Framework Programme; European Research Council (ERC); Horizon 2020; Framework Programme; Programme Grants for Applied Research; Research and Innovation Programme; Avexis/Novartis; United Kingdom Dementia Research Institute; National Institute for Health Research (NIHR) Maudsley Biomedical Research Centre at South London Maudsley Foundation Trust; King’s College London; Motor Neurone Disease Association; ALS Association; Psychiatry Research Trust; Health Holland, Top Sector Life Sciences & Health; ALS Foundation Netherlands