Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics

The Decay of Disease Association with Declining Linkage Disequilibrium: A Fine Mapping Theorem

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise linkage disequilibrium, r2. A complete derivation of this relationship from a general disease model is shown. Quite interestingly, this relationship holds across all modes of inheritance. Extensive Monte Carlo simulations using a disease genetics model applied to chromosomes subjected to a standard model of recombination are employed to better understand the variation around this fine mapping theorem due to sampling effects. We also use this relationship to provide a framework for estimating properties of a non-interrogated causal site using data at closely linked markers. Lastly, we apply this way of examining association data from high-density genotyping in a large, publicly-available data set investigating extreme BMI. We anticipate that understanding the patterns of disease association decay with declining linkage disequilibrium from a causal site will enable more powerful fine mapping methods and provide new avenues for identifying causal sites/genes from fine-mapping studies

The Decay of Disease Association with Declining Linkage Disequilibrium: A Fine Mapping Theorem

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise linkage disequilibrium, r2. A complete derivation of this relationship from a general disease model is shown for very large sample sizes. Quite interestingly, this relationship holds across all modes of inheritance. Extensive Monte Carlo simulations using a disease genetics model applied to chromosomes subjected to a standard model of recombination are employed to better understand the variation around this fine mapping theorem due to sampling effects. We also use this relationship to provide a framework for estimating properties of a non-interrogated causal site using data at closely linked markers. Lastly, we apply this way of examining association data from high-density genotyping in a large, publicly-available data set investigating extreme BMI. We anticipate that understanding the patterns of disease association decay with declining linkage disequilibrium from a causal site will enable more powerful fine mapping methods and provide new avenues for identifying causal sites/genes from fine-mapping studies