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Fitting Proportional Odds Model to Case-Control data with Incorporating Hardy-Weinberg Equilibrium.

Zhang W, Zhang Z, Li X, Li Q - Sci Rep (2015)

Bottom Line: On the basis of it, we construct a score test statistic to test whether the genetic variant is associated with the diseases.Simulation studies show that the proposed estimator has smaller mean squared error than the existing methods when the genetic effect size is away from zero and the proposed test statistic has a good control of type I error rate and is more powerful than the existing procedures.Application to 45 single nucleotide polymorphisms located in the region of TRAF1-C5 genes for the association with four-level anticyclic citrullinated protein antibody from Genetic Analysis Workshop 16 further demonstrates its performance.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Systems Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.

ABSTRACT
Genetic association studies have been proved to be an efficient tool to reveal the aetiology of many human complex diseases and traits. When the phenotype is binary, the logistic regression model is commonly employed to evaluate the association strength of the genetic variants predispose to human diseases because the maximum likelihood estimator of the odds ratio based on case-control data is equivalent to that from the same model by taking the data as being arisen prospectively. This equivalence does not hold for the proportional odds model and using it to analyze the case-control data directly often results in a substantial bias. Through putting a parameter of the minor allele frequency in the modified likelihood function under the condition that the Hardy-Weinberg equilibrium law holds within controls, a consistent estimator is obtained. On the basis of it, we construct a score test statistic to test whether the genetic variant is associated with the diseases. Simulation studies show that the proposed estimator has smaller mean squared error than the existing methods when the genetic effect size is away from zero and the proposed test statistic has a good control of type I error rate and is more powerful than the existing procedures. Application to 45 single nucleotide polymorphisms located in the region of TRAF1-C5 genes for the association with four-level anticyclic citrullinated protein antibody from Genetic Analysis Workshop 16 further demonstrates its performance.

No MeSH data available.


Related in: MedlinePlus

The empirical powers of proT and hweT for β = In 1.2, In 1.4, In 1.6 and In 1.8 under the significant level α = 0.001.
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f6: The empirical powers of proT and hweT for β = In 1.2, In 1.4, In 1.6 and In 1.8 under the significant level α = 0.001.

Mentions: In this part, we explore the power performances of proT and hweT. For the convenience, we assume . In order to make the power comparable, we set the small sample size for large β. In details, we set n = 1,000, 500, 300, and 200 for β = ln 1.2, ln 1.4, ln 1.6 and ln 1.8, respectively, under the nominal significance level of 0.05, and n = 2,400, 1,000, 600, and 400 for β = ln 1.2, ln 1.4, ln 1.6 and ln 1.8, respectively, under the nominal significance level of 0.001. We conduct 1,000 and 50,000 replicates for the significance level of 0.05 and 0.001. Figures 5 and 6 show the power results. Both figures indicate that the proposed hweT is more powerful than the proT. In some cases, there is 6% power increase. For example, when n = 1,000, MAF = 0.35, and β = ln 1.4, the power of hweT is 0.582, which is much larger than that 0.522 of proT under the significance level of 0.001.


Fitting Proportional Odds Model to Case-Control data with Incorporating Hardy-Weinberg Equilibrium.

Zhang W, Zhang Z, Li X, Li Q - Sci Rep (2015)

The empirical powers of proT and hweT for β = In 1.2, In 1.4, In 1.6 and In 1.8 under the significant level α = 0.001.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4660314&req=5

f6: The empirical powers of proT and hweT for β = In 1.2, In 1.4, In 1.6 and In 1.8 under the significant level α = 0.001.
Mentions: In this part, we explore the power performances of proT and hweT. For the convenience, we assume . In order to make the power comparable, we set the small sample size for large β. In details, we set n = 1,000, 500, 300, and 200 for β = ln 1.2, ln 1.4, ln 1.6 and ln 1.8, respectively, under the nominal significance level of 0.05, and n = 2,400, 1,000, 600, and 400 for β = ln 1.2, ln 1.4, ln 1.6 and ln 1.8, respectively, under the nominal significance level of 0.001. We conduct 1,000 and 50,000 replicates for the significance level of 0.05 and 0.001. Figures 5 and 6 show the power results. Both figures indicate that the proposed hweT is more powerful than the proT. In some cases, there is 6% power increase. For example, when n = 1,000, MAF = 0.35, and β = ln 1.4, the power of hweT is 0.582, which is much larger than that 0.522 of proT under the significance level of 0.001.

Bottom Line: On the basis of it, we construct a score test statistic to test whether the genetic variant is associated with the diseases.Simulation studies show that the proposed estimator has smaller mean squared error than the existing methods when the genetic effect size is away from zero and the proposed test statistic has a good control of type I error rate and is more powerful than the existing procedures.Application to 45 single nucleotide polymorphisms located in the region of TRAF1-C5 genes for the association with four-level anticyclic citrullinated protein antibody from Genetic Analysis Workshop 16 further demonstrates its performance.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Systems Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.

ABSTRACT
Genetic association studies have been proved to be an efficient tool to reveal the aetiology of many human complex diseases and traits. When the phenotype is binary, the logistic regression model is commonly employed to evaluate the association strength of the genetic variants predispose to human diseases because the maximum likelihood estimator of the odds ratio based on case-control data is equivalent to that from the same model by taking the data as being arisen prospectively. This equivalence does not hold for the proportional odds model and using it to analyze the case-control data directly often results in a substantial bias. Through putting a parameter of the minor allele frequency in the modified likelihood function under the condition that the Hardy-Weinberg equilibrium law holds within controls, a consistent estimator is obtained. On the basis of it, we construct a score test statistic to test whether the genetic variant is associated with the diseases. Simulation studies show that the proposed estimator has smaller mean squared error than the existing methods when the genetic effect size is away from zero and the proposed test statistic has a good control of type I error rate and is more powerful than the existing procedures. Application to 45 single nucleotide polymorphisms located in the region of TRAF1-C5 genes for the association with four-level anticyclic citrullinated protein antibody from Genetic Analysis Workshop 16 further demonstrates its performance.

No MeSH data available.


Related in: MedlinePlus