手法を比較

	Age-Period-Cohort Analysis	Poisson Rate Regression
分野	Social Epidemiology	Social Epidemiology
系統	Regression model	Regression model
提唱年	1983	1983
提唱者	Theodore R. Holford; Yang Yang & Kenneth C. Land (intrinsic estimator)	E. L. Frome (rate formulation); A. C. Cameron & P. K. Trivedi (modern count-data treatment)
種類	Generalized linear model for rates indexed by age, period, and cohort	Generalized linear model for event rates and counts with log link and person-time offset
原典	Holford, T. R. (1983). The Estimation of Age, Period and Cohort Effects for Vital Rates. Biometrics, 39(2), 311-324.	Frome, E. L. (1983). The Analysis of Rates Using Poisson Regression Models. Biometrics, 39(3), 665-674.
別名	APC Analysis, Age-Period-Cohort Models, Cohort Analysis of Rates, Intrinsic Estimator APC	Poisson Regression for Rates, Log-Linear Rate Model, Incidence-Rate-Ratio Regression, Poisson Regression with Offset
関連	4	3
概要	Age-period-cohort (APC) analysis decomposes variation in disease or mortality rates into three temporal components: the effect of age (biological and accumulated risk), the effect of period (influences hitting everyone alive at a given calendar time, such as a new treatment or a recession), and the effect of cohort (lasting imprints of the conditions into which a birth generation was born). Theodore Holford's 1983 Biometrics paper gave the canonical generalized-linear-model formulation and exposed the method's defining obstacle: because cohort equals period minus age, the three predictors are exactly linearly dependent, so their individual linear slopes cannot be separately identified. A large methodological literature has since proposed constraints, reparameterizations, and estimators to extract whatever the data can legitimately support. Yang, Schulhofer-Wohl, Fu, and Land's 2008 work popularized the intrinsic estimator, a principled choice among the infinitely many fitting solutions. APC analysis is a workhorse of descriptive epidemiology and demography, used to read the temporal fingerprints left on rates of cancer, suicide, obesity, and mortality. Done carefully it separates signal from artifact; done carelessly it manufactures trends that the identification problem makes unknowable.	Poisson rate regression is the standard generalized linear model for analyzing event rates and counts, such as the number of deaths, hospitalizations, or new cases observed over a span of person-time. It models the logarithm of the expected event rate as a linear function of covariates, using a Poisson likelihood and a log link, and accommodates differing amounts of exposure by including the log of person-time as an offset. Because coefficients enter on the log scale, their exponentials are incidence-rate ratios that quantify multiplicative effects on the rate. The rate formulation was crystallized in Frome's 1983 Biometrics paper, and the model sits within the broader count-data framework developed comprehensively by Cameron and Trivedi, who also detail its central practical concern: overdispersion, where the variance exceeds the Poisson assumption and standard errors must be corrected.