N2Y {Epi}

Create risk time ("Person-Years") in Lexis triangles from population count data.

Description

Data on population size at equidistant dates and age-classes are used to estimate person-time at risk in Lexis-triangles, i.e. classes classified by age, period AND cohort (date of birth). Only works for data where age-classes have the same width as the period-intervals.

Usage

N2Y( A, P, N,
     data = NULL,
     return.dfr = TRUE)

Arguments

A

Name of the age-variable, which should be numeric, corresponding to the left endpoints of the age intervals.

P

Name of the period-variable, which should be numeric, corresponding to the date of population count.

N

The population size at date P in age class A.

data

A data frame in which arguments are interpreted.

return.dfr

Logical. Should the results be returned as a data frame (default TRUE) or as a table.

Details

The calculation of the risk time from the population figures is done as described in: B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 26: 3018-3045, 2007.

The number of periods in the result is one less than the number of dates (nP=length(table(P))) in the input, so the number of distinct values is 2*(nP-1), because the P in the output is coded differently for upper and lower Lexis triangles.

The number of age-classes is the same as in the input (nA=length(table(A))), so the number of distinct values is 2*nA, because the A in the output is coded differently for upper and lower Lexis triangles.

In the paper "Age-Period-Cohort models for the Lexis diagram" I suggest that the risk time in the lower triangles in the first age-class and in the upper triangles in the last age-class are computed so that the total risk time in the age-class corresponds to the average of the two population figures for the age-class at either end of a period multiplied with the period length. This is the method used.

Value

A data frame with variables A, P and Y, representing the mean age and period in the Lexis triangles and the person-time in them, respectively. The person-time is in units of the distance between population count dates.

If return.dfr=FALSE a three-way table classified by the left end point of the age-classes and the periods and a factor wh taking the values up and lo corresponding to upper (early cohort) and lower (late cohort) Lexis triangles.

Author(s)

Bendix Carstensen, http://bendixcarstensen.com

References

B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 26: 3018-3045, 2007.

See Also

splitLexis, apc.fit

Examples

# Danish population at 1 Jan each year by sex and age
data( N.dk )
# An illustrative subset
( Nx <- subset( N.dk, sex==1 & A<5 & P<1975 ) )
# Show the data in tabular form
xtabs( N ~ A + P, data=Nx )
# Lexis triangles as data frame
Nt <- N2Y( data=Nx, return.dfr=TRUE )
xtabs( Y ~ round(A,2) + round(P,2), data=Nt )
# Lexis triangles as a 3-dim array
ftable( N2Y( data=Nx, return.dfr=FALSE ) )

# Calculation of PY for persons born 1970 in 1972
( N.1.1972 <- subset( Nx, A==1 & P==1972)$N )
( N.2.1973 <- subset( Nx, A==2 & P==1973)$N )
N.1.1972/3 + N.2.1973/6
N.1.1972/6 + N.2.1973/3
# These numbers can be found in the following plot:

# Blue numbers are population size at 1 January
# Red numbers are the computed person-years in Lexis triangles:
Lexis.diagram(age=c(0,5), date=c(1970,1975), int=1, coh.grid=TRUE )
with( Nx, text(P,A+0.5,paste(N),srt=90,col="blue") )
with( Nt, text(P,A,formatC(Y,format="f",digits=1),col="red") )
text( 1970.5, 2, "Population count 1 January", srt=90, col="blue")
text( 1974.5, 2, "Person-\nyears", col="red")