MAPLES (version 1.0)

ageprofile: Computes smoothed transition rates by respondent's age (age profiles).

Description

Computes age profiles for a specific transition between two states according to a set of time-fixed or time-varying covariates. It needs an micro-level episode-data structure, i.e. a longitudinal dataset containing the following variables: start : starting date of observation; Tstop : ending date of observation; Status : is 0 if right censored; 1 if event occurred; 2 if left censored; 3 if interval censored. Status is equal to 1 if and only if the date of the event precedes the date of right censoring. Agestart - ages at starting date (Start) Agestop Age at the ending date (Stop) An episode-data structure can be obtained through the command epdata.

Usage

ageprofile(formula, epdata, tr.name = "Transition", win,  method = "car", agelimits = c(0, 100),  outfile = FALSE, tails = c(FALSE, FALSE),  subset = TRUE, weight,  sig.eff = TRUE, sig.lev = 0.05)

Arguments

formula

a formula object specifying the ~ operator and factors variables separated by '+' operators. Response variable on the left is not required. The expression ~1 implies that only the baseline (age profile for the whole sample) will be provided. Note that interaction terms are not recognized by the formula: ~v1:v2 or ~v1*v2 gives the same results as ~v1+v2.

epdata

a dataframe containing episode-data prepared by epdata command optionally with time-varying factor variables created by splitter command.

tr.name

a string containing the name of the considered transition

win

a matrix with two columns containing the initial and final calendar date specifiyng a restricted window of observation. Only events and exposure times referring to this window will be considered in the analysis. If win argument is not specified, the whole episode is considered. For example, let us consider an episode data structure coming from a retrospective survey held on January 1, 2010. Since we want to compute transition rates according to behaviours experienced in the last 10 years, we can restrict our window ob observation to the decade January 1, 2000 - January 1, 2010. Thus, the win argument would be a matrix with two columns, the first containing the exact data 2000 and the second the exact date 2010. Window of observation may be also limited to specific ages or events. For example, win=cbind(date_at_birth+15,date_at_birth+20) restricts observations within the age group 15-19 (completed) years of age and win=cbind(date_at_marriage,date_at_the_interview) restricts observatins between marriage and the interview.

Note that in the win matrix no missing data are allowed.

method

specifies the type of rates to compute. There are three alternatives: 'cpr' for Cohort Period Rates 'car' for Cohort Age Rates 'cap' for Cohort Age Probabilities

agelimits

a couple of values indicating the lower and the upper limit of age interval to be considered. It can be useful to restrict age interval when the transition is never or almost never experienced outside a specific age interval. For example, the transition rates for the first child birth may be limited to the age interval (15-50).

outfile

if TRUE writes the output on a file named 'trname.txt' where 'trname' is the string specified in the tr.name argument.

tails

a vector of two logical elements indicating respectively if the left and the right tails must be flattened. This option may be useful if we can assume that the transition rate is approximately zero at the borders of the considered age interval.

subset

an optional vector specifying a subset of observations to be used in the estimation process.

weight

an optional vector containing (post-sampling) weights.

sig.eff

if TRUE the age profile for a specific subgroup defined by factor levels is fixed as identical to the baseline if the relative risk (for aech specific age-subinterval) is not statistically significant at the level specified by sig.lev. In other words, the relative risk in a specific age subinterval is zero if the pvalue is higher than sig.lev (see details).

sig.lev

specifies the maximum level significance under which the relative risk in a specific age-subinterval is non-zero (if sig.eff=TRUE). The default value is 0.05.

Value

Gives a list of objects:

profiles

a matrix containing the smoothed age profiles for the whole sample (baseline) and for each factor level considered

unsmoothed

a matrix containing the unsmoothed transition rates, i.e. the ratio between occurences and exposures for each age and factor level

knot

a matrix with the two knots (in column) for each factor level (rows)

event

a matrix with the number of event occured in the three age sub-intervals defined by knots (columns) for each factor level (rows)

rrisk

a matrix with the estimated relative risks in the three age sub-intervals (columns) for each factor level (rows)

se

a matrix with the standard error related to the relative risk computed in the three age sub-intervals (columns) for each factor level (rows)

pvalue

a matrix with the pvalues related to the hypothesis that the relative risk in each age sub-interval is different from zero (columns) for each factor level (rows)

factors

a vector of names containing the factors specified in the formula argument

trname

the name of the transition in analysisi as specified in the tr.name argument.

ANOVAtest

pvalues anova test for each factor covariate

factors

vector of string containing the names of factor covariates as specified in the formula argument.

method

the method used for the computaion of rates as speficied in the method argument.

agelimits

the age interval as specified in the agelimits argument.

tails

tails argument.

Details

p-values for the null hypothesis that the corresponding parameter is zero is calculated with reference to the t distribution with the estimated residual degrees of freedom for the model fit if the dispersion parameter has been estimated, and the standard normal if not.

References

Impicciatore R. and Billari F.C., (2010), MAPLES: a general method for the estimation of age profiles from standard demographic surveys (with an application to fertility),DEAS WP, http://ideas.repec.org/p/mil/wpdepa/2010-40.html

See Also

epdata, splitter, plotap

Examples

# creates an episode-data structure relating to the transition 
# childless-->first child
ep1<-with(demogr,epdata(start=dbirth, event=dch1, rcensor=dint, 
        birth=dbirth,id=id,
        addvar=subset(demogr,select=c(-id,-dbirth)))) 

# creates a new episode-data structure with a time-varying factor 
# variable relating to the status "never married" (not_marr) or 
# "ever married"(marr)  
ep2<-splitter(ep1,split=ep1$d1marr,tvar.lev=c("not_marr","marr"),
              tvar.name="mar")

# Estimates age profiles for the transition to the first birth 
# according to the following factors: 
# sex (respondent'sex w/2 levels: 'Male', 'Female');
# edu ('Level of education w/3 levels: 'low_sec','upp_sec', 'tert');
# mar (ever married w/2 levels: 'not_marr', 'marr')  
ch1.ap<-ageprofile(formula=~sex+edu+mar, epdata=ep2, 
                   tr.name="First child", agelimits=c(15,50))

# The estimates are obtained under the hypothesis of independence among 
# factors. We can relax this hp by considering the interaction between 
# factors. The following commands add the interaction between sex and edu. 
ep2$inter<-ep2$sex:ep2$edu
ch1.ap<-ageprofile(formula=~sex+edu+mar+inter, epdata=ep2, 
                   tr.name="First child", agelimits=c(15,50))