title: Multi-state models for investigating possible stages leading to bipolar disorder.
abstract: BACKGROUND
  It has been proposed that bipolar disorder onsets in a predictable progressive sequence of clinical stages. However, there is some debate in regard to a statistical approach to test this hypothesis. The objective of this paper is to investigate two different analysis strategies to determine the best suited model to assess the longitudinal progression of clinical stages in the development of bipolar disorder.
  
  
  METHODS
  Data previously collected on 229 subjects at high risk of developing bipolar disorder were used for the statistical analysis. We investigate two statistical approaches for analyzing the relationship between the proposed stages of bipolar disorder: 1) the early stages are considered as time-varying covariates affecting the hazard of bipolar disorder in a Cox proportional hazards model, 2) the early stages are explicitly modelled as states in a non-parametric multi-state model.
  
  
  RESULTS
  We found from the Cox model thatthere was evidence that the hazard of bipolar disorder is increased by the onset of major depressive disorder. From the multi-state model, in high-risk offspring the probability of bipolar disorder by age 29 was estimated as 0.2321. Cumulative incidence functions representing the probability of bipolar disorder given major depressive disorder at or before age 18 were estimated using both approaches and found to be similar.
  
  
  CONCLUSIONS
  Both the Cox model and multi-state model are useful approaches to the modelling of antecedent risk syndromes. They lead to similar cumulative incidence functions but otherwise each method offers a different advantage.
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, N1G 2W1 Canada.
authors.forename: Charles Dg
authors.initials: CD
authors.lastname: Keown-Stoneman
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, N1G 2W1 Canada.
authors.forename: Julie
authors.initials: J
authors.lastname: Horrocks
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, N1G 2W1 Canada.
authors.forename: Gerarda A
authors.initials: GA
authors.lastname: Darlington
authors.affiliation: Department of Epidemiology Dalla Lana School of Public Health, University of Toronto, 155 College St., Toronto, M5T 3M7.
authors.forename: Sarah
authors.initials: S
authors.lastname: Goodday
authors.affiliation: Mood Disorders Centre of Ottawa, University of Ottawa Health Services, 1 Nicholas Street, Suite 302, Ottawa, K1N 7B7 Canada.
authors.forename: Paul
authors.initials: P
authors.lastname: Grof
authors.affiliation: Department of Psychiatry and Hotchkiss Brain Institute (HBI), University of Calgary, TRW Building, 3280 Hospital Drive, NW, Room 4D6, Calgary, AB, Calgary, T2N 4Z6 Canada.
authors.forename: Anne
authors.initials: A
authors.lastname: Duffy
keywords: Bipolar disorder; High-risk; Multi-state model; Survival analysis