Epi (version 2.34)

N2Y: 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.

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 res.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.

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. 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 the period. This is the method used.

References

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

See Also

splitLexis, apc.fit

Examples

# NOT RUN {
# 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 number 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")
# }