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. 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 = c("weighted","Holford"),
          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 )

Arguments

data

Data frame with (at least) variables, A (age), P (period), D (cases, deaths) and Y (person-years). Cohort (date of birth) is computed as P-A. If thsi argument is given the arg

Age; numerical vector with mean age at diagnosis for each unit.

Period; numerical vector with mean date of diagnosis for each unit.

Cases, deaths; numerical vector.

Person-years; numerical vector. Also used as denominator for binomial data, see the dist argument.

ref.c

Reference cohort, numerical. Defaults to median date of birth among cases. If used with parm="AdCP" or parm="AdPC", the resdiual cohort effects will be 1 at ref.c

ref.p

Reference period, numerical. Defaults to median date of diagnosis among cases.

dist

Distribution (or more precisely: Likelihood) used for modelling. if a binomial model us ised, Y is assuemd to be the denominator; "binomial" gives a binomial model with logit link.

model

Type of model fitted:

nsfits a model with natural splines for each of the terms, withnparparameters for the terms.
bsfits a model with B-splines for each of the terms, withn

dr.extr

Character. How the drift parameter should be extracted from the age-period-cohort model. "weighted" (default) lets the weighted average (by marginal no. cases, D) of the estimated period and cohort effects have 0 s

parm

Character. Indicates the parametrization of the effects. The first four refer to the ML-fit of the Age-Period-Cohort model, the last four give Age-effects from a smaller model and residuals relative to this. If one of the latter is chosen,

npar

The number of parameters to use for each of the terms in the model. It can be a list of three numerical vectors, in which case these taken as the knots for the age, period and cohort effect, the first and last element in each vector are use

alpha

The significance level. Estimates are given with (1-alpha) confidence limits.

scale

numeric(1), factor multiplied to the rate estimates before output.

print.AOV

Should the analysis of deviance table for the models be printed?

Value

An object of class "apc" (recognized by apc.lines and apc.plot) --- a list with components:
AgeMatrix with 4 colums: A.pt with the ages (equals unique(A)) and three columns giving the estimated rates with c.i.s.
PerMatrix with 4 colums: P.pt with the dates of diagnosis (equals unique(P)) and three columns giving the estimated RRs with c.i.s.
CohMatrix with 4 colums: C.pt with the dates of birth (equals unique(P-A)) and three columns giving the estimated RRs with c.i.s.
DriftA 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. For the sequential parametrizations, only the latter is given.
RefNumerical vector of length 2 with reference period and cohort. If ref.p or ref.c was not supplied the corresponding element is NA.
AOVAnalysis of deviance table comparing the five classical models.
TypeCharacter string explaining the model and the parametrization.
KnotsIf 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 are the boundary knots.

References

The considerations behind the parametrizations used in this function are given in details in a preprint from Department of Biostatistics in Copenhagen: http://www.pubhealth.ku.dk/bs/publikationer/rr-06-1.pdf, later published as: B. Carstensen: Age-period-cohort models for the Lexis diagram. Statistics in Medicine, 10; 26(15):3018-45, 2007.

Examples

Run this code

library( Epi )
data(lungDK)

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

# Two different ways of parametrizing the APC-model, ML
ex.H <- apc.fit( exd, npar=7, model="ns", dr.extr="Holford",  parm="ACP", scale=10^5 )
ex.W <- apc.fit( exd, npar=7, model="ns", dr.extr="weighted", 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.H[["Drift"]]
ex.W[["Drift"]]
ex.S[["Drift"]]

# Plot the effects
fp <- apc.plot( ex.H )
apc.lines( ex.W, frame.par=fp, col="red" )
apc.lines( ex.S, frame.par=fp, col="blue" )

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