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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: 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.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.

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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Estimated IL10 survival curves based on genotypes and based on haplotypes.
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Figure 2: Estimated IL10 survival curves based on genotypes and based on haplotypes.

Mentions: To validate our model we calculated the survival curves of all 23 subgroups with different genotype combinations according to equation (3) and compared these with the Kaplan-Meier curves. These curves are given in Figure 2 for the subgroup of 233 patients who were homozygous for the most common allele of IL10 -2849G > A and IL10 4251A > G, and heterozygous for IL10 -1082G > A and IL10 -592C > A (Figure 2). These two curves are comparable, indicating that our haplotype method produces valid results.


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)

Estimated IL10 survival curves based on genotypes and based on haplotypes.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Estimated IL10 survival curves based on genotypes and based on haplotypes.
Mentions: To validate our model we calculated the survival curves of all 23 subgroups with different genotype combinations according to equation (3) and compared these with the Kaplan-Meier curves. These curves are given in Figure 2 for the subgroup of 233 patients who were homozygous for the most common allele of IL10 -2849G > A and IL10 4251A > G, and heterozygous for IL10 -1082G > A and IL10 -592C > A (Figure 2). These two curves are comparable, indicating that our haplotype method produces valid results.

Bottom Line: 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.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.

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