title: A heuristic solution of the identifiability problem of the age-period-cohort analysis of cancer occurrence: lung cancer example.
abstract: BACKGROUND
  The Age-Period-Cohort (APC) analysis is aimed at estimating the following effects on disease incidence: (i) the age of the subject at the time of disease diagnosis; (ii) the time period, when the disease occurred; and (iii) the date of birth of the subject. These effects can help in evaluating the biological events leading to the disease, in estimating the influence of distinct risk factors on disease occurrence, and in the development of new strategies for disease prevention and treatment.
  
  
  RESULTS
  We developed a novel approach for estimating the APC effects on disease incidence rates in the frame of the Log-Linear Age-Period-Cohort (LLAPC) model. Since the APC effects are linearly interdependent and cannot be uniquely estimated, solving this identifiability problem requires setting four redundant parameters within a set of unknown parameters. By setting three parameters (one of the time-period and the birth-cohort effects and the corresponding age effect) to zero, we reduced this problem to the problem of determining one redundant parameter and, used as such, the effect of the time-period adjacent to the anchored time period. By varying this identification parameter, a family of estimates of the APC effects can be obtained. Using a heuristic assumption that the differences between the adjacent birth-cohort effects are small, we developed a numerical method for determining the optimal value of the identification parameter, by which a unique set of all APC effects is determined and the identifiability problem is solved.
  
  
  CONCLUSIONS
  We tested this approach while estimating the APC effects on lung cancer occurrence in white men and women using the SEER data, collected during 1975-2004. We showed that the LLAPC models with the corresponding unique sets of the APC effects estimated by the proposed approach fit very well with the observational data.
authors.affiliation: Eppley Institute, University of Nebraska Medical Center, Omaha, Nebraska, United States of America.
authors.forename: Tengiz
authors.initials: T
authors.lastname: Mdzinarishvili
authors.forename: Simon
authors.initials: S
authors.lastname: Sherman
mesh_terms: D000230:Adenocarcinoma / Q000453:epidemiology*; D000293:Adolescent; D000328:Adult; D000367:Age Factors; D000368:Aged; D000369:Aged, 80 and over; D002648:Child; D002675:Child, Preschool; D015988:Cohort Effect; D015331:Cohort Studies; D005260:Female; D006801:Humans; D015994:Incidence; D007223:Infant; D007231:Infant, Newborn; D008175:Lung Neoplasms / Q000453:epidemiology*; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D011379:Prognosis; D012107:Research Design; D012307:Risk Factors; D018426:SEER Program; D013997:Time Factors; D055815:Young Adult