Powerful Haplotype-Based Hardy-Weinberg Equilibrium Tests for Tightly Linked Loci

<div><p>Recently, there have been many case-control studies proposed to test for association between haplotypes and disease, which require the Hardy-Weinberg equilibrium (HWE) assumption of haplotype frequencies. As such, haplotype inference of unphased genotypes and development of haplotype-based HWE tests are crucial prior to fine mapping. The goodness-of-fit test is a frequently-used method to test for HWE for multiple tightly-linked loci. However, its degrees of freedom dramatically increase with the increase of the number of loci, which may lack the test power. Therefore, in this paper, to improve the test power for haplotype-based HWE, we first write out two likelihood functions of the observed data based on the Niu's model (NM) and inbreeding model (IM), respectively, which can cause the departure from HWE. Then, we use two expectation-maximization algorithms and one expectation-conditional-maximization algorithm to estimate the model parameters under the HWE, IM and NM models, respectively. Finally, we propose the likelihood ratio tests LRT and LRT for haplotype-based HWE under the NM and IM models, respectively. We simulate the HWE, Niu's, inbreeding and population stratification models to assess the validity and compare the performance of these two LRT tests. The simulation results show that both of the tests control the type I error rates well in testing for haplotype-based HWE. If the NM model is true, then LRT is more powerful. While, if the true model is the IM model, then LRT has better performance in power. Under the population stratification model, LRT is still more powerful. To this end, LRT is generally recommended. Application of the proposed methods to a rheumatoid arthritis data set further illustrates their utility for real data analysis.</p></div

Mean and standard deviation (SD) of and estimates, mean of sum of absolute differences (SAD) of haplotype frequency estimates for EM, ECM and IEM algorithms, simulated size and powers of two HWE tests for different values of and , under Niu's model.

<p>Mean and standard deviation (SD) of and estimates, mean of sum of absolute differences (SAD) of haplotype frequency estimates for EM, ECM and IEM algorithms, simulated size and powers of two HWE tests for different values of and , under Niu's model.</p

Haplotype distribution for population stratification model.

<p>Haplotype distribution for population stratification model.</p

Haplotype LD display for the seventh haplotype block on chromosome 15.

<p>The red box denotes that the LOD value between any two loci is larger than or equal to 2.0. The numbers in the red boxes are the corresponding values of and the empty box denotes that .</p

Mean and standard deviation (SD) of and estimates, mean of sum of absolute differences (SAD) of haplotype frequency estimates for EM, ECM and IEM algorithms, simulated size and powers of two HWE tests for different values of and , under inbreeding model.

<p>Mean and standard deviation (SD) of and estimates, mean of sum of absolute differences (SAD) of haplotype frequency estimates for EM, ECM and IEM algorithms, simulated size and powers of two HWE tests for different values of and , under inbreeding model.</p

Haplotype distribution for Niu's model and inbreeding model.

<p>Haplotype distribution for Niu's model and inbreeding model.</p

Results of application to North American Rheumatoid Arthritis Consortium data set.

<p>Chr., chromosome; SNP, single nucleotide polymorphism; N. of SNPs, number of SNPs.</p

Excess Winter Mortality and Cold Temperatures in a Subtropical City, Guangzhou, China

<div><p>Background</p><p>A significant increase in mortality was observed during cold winters in many temperate regions. However, there is a lack of evidence from tropical and subtropical regions, and the influence of ambient temperatures on seasonal variation of mortality was not well documented.</p> <p>Methods</p><p>This study included 213,737 registered deaths from January 2003 to December 2011 in Guangzhou, a subtropical city in Southern China. Excess winter mortality was calculated by the excess percentage of monthly mortality in winters over that of non-winter months. A generalized linear model with a quasi-Poisson distribution was applied to analyze the association between monthly mean temperature and mortality, after controlling for other meteorological measures and air pollution.</p> <p>Results</p><p>The mortality rate in the winter was 26% higher than the average rate in other seasons. On average, there were 1,848 excess winter deaths annually, with around half (52%) from cardiovascular diseases and a quarter (24%) from respiratory diseases. Excess winter mortality was higher in the elderly, females and those with low education level than the young, males and those with high education level, respectively. A much larger winter increase was observed in out-of-hospital mortality compared to in-hospital mortality (45% vs. 17%). We found a significant negative correlation of annual excess winter mortality with average winter temperature (r_s=-0.738, P=0.037), but not with air pollution levels. A 1 °C decrease in monthly mean temperature was associated with an increase of 1.38% (95%CI:0.34%-2.40%) and 0.88% (95%CI:0.11%-1.64%) in monthly mortality at lags of 0-1 month, respectively.</p> <p>Conclusion</p><p>Similar to temperate regions, a subtropical city Guangzhou showed a clear seasonal pattern in mortality, with a sharper spike in winter. Our results highlight the role of cold temperature on the winter mortality even in warm climate. Precautionary measures should be strengthened to mitigate cold-related mortality for people living in warm climate.</p> </div

The dose-response relationship between average monthly temperature and monthly mortality using a natural spline function with a degree freedom of 3.

<p>The dose-response relationship between average monthly temperature and monthly mortality using a natural spline function with a degree freedom of 3.</p

A map of Guangzhou showing the location of Guangzhou weather station (marked by triangles) and seven air pollution monitoring stations (marked by a star).

<p>The six urban districts included in the present study are labeled by number 1-6.</p