COMBINING ISOTONIC REGRESSION AND EM ALGORITHM TO PREDICT GENETIC RISK UNDER MONOTONICITY CONSTRAINT

• Published in: The annals of applied statistics Vol. 8; no. 2; p. 1182
• Main Authors: Qin, Jing, Garcia, Tanya P, Ma, Yanyuan, Tang, Ming-Xin, Marder, Karen, Wang, Yuanjia
• Format: Journal Article
• Language: English
• Published: United States 2014
• Subjects: Self-consistency estimating equations; Pool adjacent violation algorithm; Binomial likelihood; Parkinson’s disease
• ISSN: 1932-6157
• 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, nor non-negative. 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 non-carriers, and reveals a significant difference between the distribution in compound heterozygous carriers compared to non-carriers, but not between heterozygous carriers and non-carriers.