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Estimating effects of rare haplotypes on failure time using a penalized Cox proportional hazards regression model.

Souverein OW, Zwinderman AH, Jukema JW, Tanck MW - BMC Genet. (2008)

Bottom Line: Estimation is performed with an EM algorithm.These steps are iterated until the parameter estimates converge.Two penalty functions are considered, namely the ridge penalty and a difference penalty, which is based on the assumption that similar haplotypes show similar effects.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Clinical Epidemiology, Biostatistics and Bioinformatics, Academic Medical Center, University of Amsterdam, P.O. Box 22700, 1100 DE, Amsterdam, The Netherlands. olga.souverein@wur.nl

ABSTRACT

Background: This paper describes a likelihood approach to model the relation between failure time and haplotypes in studies with unrelated individuals where haplotype phase is unknown, while dealing with the problem of unstable estimates due to rare haplotypes by considering a penalized log-likelihood.

Results: The Cox model presented here incorporates the uncertainty related to the unknown phase of multiple heterozygous individuals as weights. Estimation is performed with an EM algorithm. In the E-step the weights are estimated, and in the M-step the parameter estimates are estimated by maximizing the expectation of the joint log-likelihood, and the baseline hazard function and haplotype frequencies are calculated. These steps are iterated until the parameter estimates converge. Two penalty functions are considered, namely the ridge penalty and a difference penalty, which is based on the assumption that similar haplotypes show similar effects. Simulations were conducted to investigate properties of the method, and the association between IL10 haplotypes and risk of target vessel revascularization was investigated in 2653 patients from the GENDER study.

Conclusion: Results from simulations and real data show that the penalized log-likelihood approach produces valid results, indicating that this method is of interest when studying the association between rare haplotypes and failure time in studies of unrelated individuals.

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Related in: MedlinePlus

Frequencies and log TVR hazard ratios with 95% confidence intervals of the IL10 haplotypes.
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Figure 1: Frequencies and log TVR hazard ratios with 95% confidence intervals of the IL10 haplotypes.

Mentions: With 4 biallelic SNPs, 16 different haplotypes are possible, but seven had zero frequency in the current sample. Of the remaining nine haplotypes, there were four major haplotypes with substantial frequencies 27% (0000), 24% (0001), 21% (0100), and 27% (1110), while the relative frequencies of the remaining five haplotypes varied between 0.46% and 0.02%. The estimated haplotype frequencies and log hazard ratios at the optimal CVL (ridge penalty) are given in Figure 1. The hazard ratios of the four major haplotypes were not different from each other, but of the five rare haplotypes two had decreased (0010, and 0101), and three had increased (0110, 1000, and 1100) hazard ratios, although all had very wide confidence intervals, and none were statistically significantly associated with TVR risk.


Estimating effects of rare haplotypes on failure time using a penalized Cox proportional hazards regression model.

Souverein OW, Zwinderman AH, Jukema JW, Tanck MW - BMC Genet. (2008)

Frequencies and log TVR hazard ratios with 95% confidence intervals of the IL10 haplotypes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2254440&req=5

Figure 1: Frequencies and log TVR hazard ratios with 95% confidence intervals of the IL10 haplotypes.
Mentions: With 4 biallelic SNPs, 16 different haplotypes are possible, but seven had zero frequency in the current sample. Of the remaining nine haplotypes, there were four major haplotypes with substantial frequencies 27% (0000), 24% (0001), 21% (0100), and 27% (1110), while the relative frequencies of the remaining five haplotypes varied between 0.46% and 0.02%. The estimated haplotype frequencies and log hazard ratios at the optimal CVL (ridge penalty) are given in Figure 1. The hazard ratios of the four major haplotypes were not different from each other, but of the five rare haplotypes two had decreased (0010, and 0101), and three had increased (0110, 1000, and 1100) hazard ratios, although all had very wide confidence intervals, and none were statistically significantly associated with TVR risk.

Bottom Line: Estimation is performed with an EM algorithm.These steps are iterated until the parameter estimates converge.Two penalty functions are considered, namely the ridge penalty and a difference penalty, which is based on the assumption that similar haplotypes show similar effects.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Clinical Epidemiology, Biostatistics and Bioinformatics, Academic Medical Center, University of Amsterdam, P.O. Box 22700, 1100 DE, Amsterdam, The Netherlands. olga.souverein@wur.nl

ABSTRACT

Background: This paper describes a likelihood approach to model the relation between failure time and haplotypes in studies with unrelated individuals where haplotype phase is unknown, while dealing with the problem of unstable estimates due to rare haplotypes by considering a penalized log-likelihood.

Results: The Cox model presented here incorporates the uncertainty related to the unknown phase of multiple heterozygous individuals as weights. Estimation is performed with an EM algorithm. In the E-step the weights are estimated, and in the M-step the parameter estimates are estimated by maximizing the expectation of the joint log-likelihood, and the baseline hazard function and haplotype frequencies are calculated. These steps are iterated until the parameter estimates converge. Two penalty functions are considered, namely the ridge penalty and a difference penalty, which is based on the assumption that similar haplotypes show similar effects. Simulations were conducted to investigate properties of the method, and the association between IL10 haplotypes and risk of target vessel revascularization was investigated in 2653 patients from the GENDER study.

Conclusion: Results from simulations and real data show that the penalized log-likelihood approach produces valid results, indicating that this method is of interest when studying the association between rare haplotypes and failure time in studies of unrelated individuals.

Show MeSH
Related in: MedlinePlus