time_exposed_stock: Data frame of time exposed at risk for a stock of...

In qlifetable: Managing and Building of Quarterly Life Tables

Data frame of time exposed at risk for a stock of general/insured population

Description

Computes for each integer age and each combination of age and seasonal quarter the total time exposed at risk (in years) of a (stock) population of survivors (expected survivors) during a given year.

Usage

time_exposed_stock(
  date.birth,
  year,
  type,
  random.b = TRUE,
  constant.age.year = FALSE
)

Arguments

date.birth	A character vector with the dates of birth in format either "yyyy-mm-dd" or "yyyy-mm-dd hour:min:secs" (for instance, "2016-01-20 12:00:00") of the members of the population. If "hour:min:secs" is omitted the function imputes either "12:00:00", if 'random.b = FALSE', or a random hour by default.
year	A numeric vector indicating the year for which the total time exposed at risk (by quarter) of the population is to be computed.
type	A character argument informing if the total time exposed to risk is computed either since the beginning of the year or from the end of the year, depending when the census (stock) of population (portfolio) has been made. Only two values are allowed: '"forward"' and '"backward"'. If 'type = "forward"' the time exposed to risk is computed since the beginning of the year (i.e., it is assumed that the population counting has been performed at the beginning of the year of interest). If 'type = "backward"' the time exposed to risk is computed from the end of the year (i.e., it is assumed that the population counting has been performed at the end of the year of interest).
random.b	A 'TRUE/FALSE' argument indicating whether the exact moment ("hour:min:secs") when the birth occurs within the day is randomly selected. If TRUE, this overwrites "hour:min:secs" in 'date.birth' even if those have been declared. By default, TRUE.
constant.age.year	A 'TRUE/FALSE' argument indicating whether the length of the year should be constant, 365.25 days, or variable, depending on the time lived for the person in each year since her/his dates of birth and event. By default, FALSE. The advantage of using a non-constant (person-dependent) length of year is congruence when estimating time exposed at risk: in each year the time exposed along the time and age axes will coincide.

Value

A data frame with the time exposed at risk for each (potential) combination of integer age and age and season/calendar quarter of the population. The data frame has the following components:

age	Integer age to which the time exposed at risk corresponds.
quarter.age	Age quarter to which the time exposed at risk corresponds.
quarter.calendar	Calendar (time, season) quarter to which the time exposed at risk corresponds.
time.exposed	Total time (in years) exposed at risk of the population during the quarter determined for the combination of 'age', 'quarter.age' and 'quarter.calendar'.

Note

Using the notation of a general population, denoting by P the stock of population counted either at the beginning or the end of the year, and by E, I, D and B the emigrants, immigrants, deaths and births recorded during the year, to compute the total time exposed to risk they relate as follows:

If the census (stock) of the population is performed at the beginning of the year of interest, it is initially assumed that all the people is going to survive (is going to be at risk) up to the end of the year. In this case 'type = "forward"' should be used and the total time exposed at risk, in each age a and (r, s) quarter, is through: T(a, r, s) = time_exposed_stock(P) + time_exposed_ins(I) - time_exposed_ins(E) - time_exposed_ins(D) + time_exposed_newborns(B).

If the census (stock) of population is performed at the end of the year of interest, only the people who survives up to that date is included in the counting. In this case 'type = "backward"' should be used and the total time exposed at risk, in each age a and (r, s) quarter, is computed using the expression: T(a, r, s) = time_exposed_survivors(P) - time_exposed_outs(I) + time_exposed_outs(E) + time_exposed_outs(D).

Author(s)

Jose M. Pavia [e-mail]

Josep Lledo [e-mail]

References

Pavia, JM and Lledo, J (2022). Estimation of the Combined Effects of Ageing and Seasonality on Mortality Risk. An application to Spain. *Journal of the Royal Statistical Society, Series A (Statistics in Society)*, 185(2), 471-497. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssa.12769")}

See Also

time_exposed_ins, time_exposed_outs, time_exposed_newborns

Examples

dates.b <- c("1920-05-13", "1999-04-12", "2019-01-01")
out <- time_exposed_stock(dates.b, year = 2019, type = "backward")

qlifetable documentation built on April 19, 2023, 5:09 p.m.