title: Estimating haplotype effects on dichotomous outcome for unphased genotype data using a weighted penalized log-likelihood approach.
abstract: OBJECTIVE
  To develop a method to estimate haplotype effects on dichotomous outcomes when phase is unknown, that can also estimate reliable effects of rare haplotypes.
  
  
  METHODS
  In short, the method uses a logistic regression approach, with weights attached to all possible haplotype combinations of an individual. An EM-algorithm was used: in the E-step the weights are estimated, and the M-step consists of maximizing the joint log-likelihood. When rare haplotypes were present, a penalty function was introduced. We compared four different penalties. To investigate statistical properties of our method, we performed a simulation study for different scenarios. The evaluation criteria are the mean bias of the parameter estimates, the root of the mean squared error, the coverage probability, power, Type I error rate and the false discovery rate.
  
  
  RESULTS
  For the unpenalized approach, mean bias was small, coverage probabilities were approximately 95%, power ranged from 15.2 to 44.7% depending on haplotype frequency, and Type I error rate was around 5%. All penalty functions reduced the standard errors of the rare haplotypes, but introduced bias. This trade-off decreased power.
  
  
  CONCLUSIONS
  The unpenalized weighted log-likelihood approach performs well. A penalty function can help to estimate an effect for rare haplotypes.
authors.affiliation: Department of Clinical Epidemiology and Biostatistics, Academic Medical Center, Amsterdam, The Netherlands. o.w.souverein@amc.uva.nl
authors.forename: Olga W
authors.initials: OW
authors.lastname: Souverein
authors.forename: Aeilko H
authors.initials: AH
authors.lastname: Zwinderman
authors.forename: Michael W T
authors.initials: MW
authors.lastname: Tanck
mesh_terms: D000465:Algorithms; D005787:Gene Frequency; D005838:Genotype; D006239:Haplotypes; D006801:Humans; D016013:Likelihood Functions; D008957:Models, Genetic; D015233:Models, Statistical; D012044:Regression Analysis