Epi (version 2.63)

apc.fit: Fit an Age-Period-Cohort model to tabular data.

Description

Fits the classical five models to tabulated rate data (cases, person-years) classified by two of age, period, cohort: Age, Age-drift, Age-Period, Age-Cohort and Age-Period-Cohort. There are no assumptions about the age, period or cohort classes being of the same length, or that tabulation should be only by two of the variables. Only requires that mean age and period for each tabulation unit is given.

Usage

apc.fit( data,
            A,
            P,
            D,
            Y,
        ref.c,
        ref.p,
          dist = c("poisson","binomial"),
         model = c("ns","bs","ls","factor"),
       dr.extr = "Y",
          parm = c("ACP","APC","AdCP","AdPC","Ad-P-C","Ad-C-P","AC-P","AP-C"),
          npar = c( A=5, P=5, C=5 ),
         scale = 1,
         alpha = 0.05,
     print.AOV = TRUE )

Value

An object of class "apc" (recognized by apc.plot and

apc.lines) --- a list with components:

Type

Text describing the model and parametrization returned.

Model

The model object(s) on which the parametrization is based.

Age

Matrix with 4 columns: A.pt with the ages (equals unique(A)) and three columns giving the estimated rates with c.i.s.

Per

Matrix with 4 columns: P.pt with the dates of diagnosis (equals unique(P)) and three columns giving the estimated RRs with c.i.s.

Coh

Matrix with 4 columns: C.pt with the dates of birth (equals unique(P-A)) and three columns giving the estimated RRs with c.i.s.

Drift

A 3 column matrix with drift-estimates and c.i.s: The first row is the ML-estimate of the drift (as defined by drift), the second row is the estimate from the Age-drift model. The first row name indicates which type of inner product were used for projections. For the sequential parametrizations, only the latter is given.

Ref

Numerical vector of length 2 with reference period and cohort. If ref.p or ref.c was not supplied the corresponding element is NA.

Anova

Analysis of deviance table comparing the five classical models.

Knots

If model is one of "ns" or "bs", a list with three components: Age, Per, Coh, each one a vector of knots. The max and the min of the vectors are the boundary knots.

Details

Each record in the input data frame represents a subset of a Lexis diagram. The subsets need not be of equal length on the age and period axes, in fact there are no restrictions on the shape of these; they could be Lexis triangles for example. The requirement is that A and P are coded with the mean age and calendar time of observation in the subset. This is essential since A and P are used as quantitative variables in the models.

This approach is different from to the vast majority of the uses of APC-models in the literature where a factor model is used for age, period and cohort effects. The latter can be obtained by using model="factor". Note however that the cohort factor is defined from A and P, so that it is not possible in this framework to replicate the Boyle-Robertson fallacy.

References

The considerations behind the parametrizations used in this function are given in detail in: B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 10; 26(15):3018-45, 2007.

Various links to course material etc. is available through http://bendixcarstensen.com/APC/

See Also

apc.frame, apc.lines, apc.plot, LCa.fit, apc.LCa.

Examples

library( Epi )
data(lungDK)

# Taylor a dataframe that meets the requirements for variable names
exd <- lungDK[,c("Ax","Px","D","Y")]
names(exd)[1:2] <- c("A","P")

# Three different ways of parametrizing the APC-model, ML
ex.1 <- apc.fit( exd, npar=7, model="ns", dr.extr="1", parm="ACP", scale=10^5 )
ex.D <- apc.fit( exd, npar=7, model="ns", dr.extr="D", parm="ACP", scale=10^5 )
ex.Y <- apc.fit( exd, npar=7, model="ns", dr.extr="Y", parm="ACP", scale=10^5 )

# Sequential fit, first AC, then P given AC.
ex.S <- apc.fit( exd, npar=7, model="ns", parm="AC-P", scale=10^5 )

# Show the estimated drifts
ex.1[["Drift"]]
ex.D[["Drift"]]
ex.Y[["Drift"]]
ex.S[["Drift"]]

# Plot the effects
lt <- c("solid","22")[c(1,1,2)]
apc.plot( ex.1, lty=c(1,1,3) )
apc.lines( ex.D, col="red", lty=c(1,1,3) )
apc.lines( ex.Y, col="limegreen", lty=c(1,1,3) )
apc.lines( ex.S, col="blue", lty=c(1,1,3) )