Abstract
BackgroundThe 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.Methodology/Principal FindingsWe 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/SignificanceWe 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.
Highlights
APC analysisIn this work, using the long-term observational data, we determine the APC effects in the frame of the Log-Linear Age-PeriodCohort (LLAPC) model [2]
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
The incidence rate is defined as a ratio of the number of events divided by the total person-years experience
Summary
In this work, using the long-term observational data, we determine the APC effects in the frame of the LLAPC model [2]. Either three effects (one of the TP effects, one of the BP effects, and the corresponding Age effect) are set to zero and used as reference levels or the sums of these effects are equated to zero These settings are still insufficient for solving the identifiability problem [2] and required the use of additional constraints on a set of the parameter estimates to be determined. These effects are used as reference levels and are usually set to zero In such a case, the solution of the APC problem is reduced to determining one parameter – the identification parameter. When the exact value of d is a priori known, the system (3) can be corrected for this effect by moving this parameter to the left side of
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