title: Modeling biological rhythms in failure time data.
abstract: BACKGROUND
  The human body exhibits a variety of biological rhythms. There are patterns that correspond, among others, to the daily wake/sleep cycle, a yearly seasonal cycle and, in women, the menstrual cycle. Sine/cosine functions are often used to model biological patterns for continuous data, but this model is not appropriate for analysis of biological rhythms in failure time data.
  
  
  METHODS
  We adapt the cosinor method to the proportional hazards model and present a method to provide an estimate and confidence interval of the time when the minimum hazard is achieved. We then apply this model to data taken from a clinical trial of adjuvant of pre-menopausal breast cancer patients.
  
  
  RESULTS
  The application of this technique to the breast cancer data revealed that the optimal day for pre-resection incisional or excisional biopsy of 28-day cycle (i. e. the day associated with the lowest recurrence rate) is day 8 with 95% confidence interval of 4-12 days. We found that older age, fewer positive nodes, smaller tumor size, and experimental treatment were predictive of longer relapse-free survival.
  
  
  CONCLUSIONS
  In this paper we have described a method for modeling failure time data with an underlying biological rhythm. The advantage of adapting a cosinor model to proportional hazards model is its ability to model right censored data. We have presented a method to provide an estimate and confidence interval of the day in the menstrual cycle where the minimum hazard is achieved. This method is not limited to breast cancer data, and may be applied to any biological rhythms linked to right censored data.
authors.affiliation: Department of Biostatistics, Epidemiology, and Scientific Computing, King Faisal Specialist Hospital & Research Center, Riyadh 11211, Saudi Arabia. nkum@kfshrc.edu.sa
authors.forename: Naser B
authors.initials: NB
authors.lastname: Elkum
authors.forename: James D
authors.initials: JD
authors.lastname: Myles