The 10 commandments of APC-models Bendix Carstensen Senior statistician, Steno Diabetes Center, Gentofte, Denmark External lecturer, Department of Biostatistics, University of Copenhagen [email protected] http://www.biostat.ku.dk/˜bxc Age-Period-Cohort models are descriptive models for rates from disease registers: Data are cases and person-years observed in subsets of a Lexis-diagram (figure 1). Model is a piecewise constant intensity model — likelihood proportional to Poisson likelihood. Result is a description of rates by age, period and cohort effects (figure 2). 15 ● ● 30 6 15 3 10 2 ● ● Cases per 100,000 PY ● ● 10 ● ● ● Age ● ● ● ● ● ● ● 5 ● 5 1 ● 3 0.6 1.5 0.3 Rate ratio ● ● ● Denmark 0 1985 0 1990 1995 2000 5 10 Age 15 1980 1990 Calendar time Calendar time Figure 1: Lexis diagram showing the sampling scheme for the childhood diabetes register in Denmark with tabulation by age, period and cohort in 1-year classes. Figure 2: Estimates from an age×sex-period-cohort model for childhood diabetes rates in Denmark, using natural splines for the effects. Red: Females; Blue: Males; Black: M/F rate ratio; Green: Cohort; Magenta: Period. 1.Tabulate cases and person-years as detailed as possible, preferably by age, period and cohort. 2.Compute risk time from population data using correct formulae for converting population figures to risk time in the subsets of the Lexis diagram (figure 1). 3.Use the mean age, period and cohort in each cell of the table as continuous covariates. a = p − c must be met for all analysis units (figure 1). 4.Use parametric functions of age, period and cohort to describe the effects. Choose the parametrization (splines, fractional polynomials,. . . ) so that relevant features are captured, but modelling of random noise is avoided. 5.Report estimates of the three effects that can be combined to the predicted rates. 6.Age should be the primary variable: Report age-specific rates, i.e. include the absolute level with the age-parameters. 7.Make informed choices of the other aspects of parametrization (figure 2): •How is the drift extracted (weighted by no. cases). •Where is the drift allocated (included with the cohort effect). •How are the RRs for period and cohort fixed (reference cohort: 1985). 8.Report estimates as line-graphs with confidence limits. 9.Be careful with firm interpretation of formal tests for period and cohort effects — significant effects may represent clinically/epidemiologically irrelevant effects. 10.Do not report goodness of fit tests — they are largely meaningless for demographic data. Carstensen, B.: Demography and epidemiology: Age-Period-Cohort models in the computer age. Research report 1, 2006, Department of Biostatistics, University of Copenhagen, http://www.pubhealth.ku.dk/bs/publikationer/rr-06-1.pdf.