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

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1182-1208
Number of pages27
JournalAnnals of Applied Statistics
Issue number2
StatePublished - Jun 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


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