title: COMBINING ISOTONIC REGRESSION AND EM ALGORITHM TO PREDICT GENETIC RISK UNDER MONOTONICITY CONSTRAINT.
abstract: 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.
authors.affiliation: Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 6700B Rockledge Drive, MSC 7609, Bethesda, MD 20892-7609.
authors.forename: Jing
authors.initials: J
authors.lastname: Qin
authors.affiliation: Department of Epidemiology and Biostatistics, Texas A&M University Health Science Center, TAMU 1266, College Station, TX 77843-1266.
authors.forename: Tanya P
authors.initials: TP
authors.lastname: Garcia
authors.affiliation: Department of Statistics, Texas A&M University, TAMU 3143, College Station, TX 77843-3143.
authors.forename: Yanyuan
authors.initials: Y
authors.lastname: Ma
authors.affiliation: Department of Biostatistics, Columbia University, 630 West 168th Street, New York, New York 10032.
authors.forename: Ming-Xin
authors.initials: MX
authors.lastname: Tang
authors.affiliation: Department of Biostatistics, Columbia University, 630 West 168th Street, New York, New York 10032.
authors.forename: Karen
authors.initials: K
authors.lastname: Marder
authors.affiliation: Department of Biostatistics, Columbia University, 630 West 168th Street, New York, New York 10032.
authors.forename: Yuanjia
authors.initials: Y
authors.lastname: Wang
keywords: Binomial likelihood; Parkinson’s disease; Pool adjacent violation algorithm; Self-consistency estimating equations