Open Access
June 2014 Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint
Jing Qin, Tanya P. Garcia, Yanyuan Ma, Ming-Xin Tang, Karen Marder, Yuanjia Wang
Ann. Appl. Stat. 8(2): 1182-1208 (June 2014). DOI: 10.1214/14-AOAS730


In certain genetic studies, clinicians and genetic counselors are interested in estimating the cumulative risk of a disease for individuals with and without a rare deleterious mutation. Estimating the cumulative risk is difficult, however, when the estimates are based on family history data. Often, the genetic mutation status in many family members is unknown; instead, only estimated probabilities of a patient having a certain mutation status are available. Also, ages of disease-onset are subject to right censoring. Existing methods to estimate the cumulative risk using such family-based data only provide estimation at individual time points, and are not guaranteed to be monotonic or nonnegative. In this paper, we develop a novel method that combines Expectation–Maximization and isotonic regression to estimate the cumulative risk across the entire support. Our estimator is monotonic, satisfies self-consistent estimating equations and has high power in detecting differences between the cumulative risks of different populations. Application of our estimator to a Parkinson’s disease (PD) study provides the age-at-onset distribution of PD in PARK2 mutation carriers and noncarriers, and reveals a significant difference between the distribution in compound heterozygous carriers compared to noncarriers, but not between heterozygous carriers and noncarriers.


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Jing Qin. Tanya P. Garcia. Yanyuan Ma. Ming-Xin Tang. Karen Marder. Yuanjia Wang. "Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint." Ann. Appl. Stat. 8 (2) 1182 - 1208, June 2014.


Published: June 2014
First available in Project Euclid: 1 July 2014

zbMATH: 06333792
MathSciNet: MR3262550
Digital Object Identifier: 10.1214/14-AOAS730

Keywords: Binomial likelihood , Parkinson’s disease , pool adjacent violation algorithm , self-consistency estimating equations

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 2 • June 2014
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