iterate_ax: Ax iteration method from dx
In ihmeuw-demographics/demCore: Core Functions for Demography

iterate_ax

R Documentation

Ax iteration method from dx

Description

Implement iteration method to minimize the difference across initialized ax and its expected relationship with dx. This method can be used to start with naive values of ax (like age_length/2) and arrive at more informed ax values based on an approximation that assumes a relationship between ax and the age pattern of deaths (dx) in a cohort. Since dx is often calculated using the mx –> ax –> qx method in the first place, initialization and iteration is required.

Usage

iterate_ax(dt, id_cols, n_iterations = 30L, threshold = 0.01, quiet = F)

gen_ax_from_dx(dt, id_cols, validate_arguments = T)

Arguments

`dt`	[`data.table()`] Life tables with columns: all `id_cols`, 'age_start', 'age_end', 'dx', 'ax', 'qx', 'mx'.
`id_cols`	[`character()`] Columns that uniquely identify each row of `dt`. Must include 'age_start' and 'age_end'.
`n_iterations`	[`integer(1)`] Maximum number of iterations to run.
`threshold`	[`numeric(1)`] How far apart should ax and the implied ax from dx be before removal from iteration.
`quiet`	[`logical(1)`] Whether to omit messages about iteration progress. Default is F and progress messages are given.
`validate_arguments`	[`logical(1)`] Whether to validate that the input arguments are formatted correctly. Default is 'TRUE'.

Details

iterate_ax: Implement ax iteration.

gen_ax_from_dx: Calculate ax from dx without iteration. This is used as a helper function within iterate_ax but can also be used independently when dx is believed to be accurate. The complete relationship is:

_na_x = \frac{-\frac{n}{24} {_nd_{x-n}} + \frac{n}{2} {_nd_x} + \frac{n}{24} {_nd_{x+n}}}{_nd_x}

See the references page for the formatted equation.

Limitations: this method relies on initialized ax and dx values, and cannot produce estimates for the first and last age groups. Preston pg 45.

Note: this is not the best method for ages under 5 years. See gen_u5_ax_from_mx().

Value

[data.table()]
Input life tables with ax, dx, qx modified. Input mx is unchanged. iterate_ax makes a copy while gen_ax_from_dx modifies in place.

References

Preston Samuel H, Patrick H, Michel G. Demography: measuring and modeling population processes. MA: Blackwell Publishing. 2001.

Examples

data("austria_1992_lt")
dt <- austria_1992_lt[,.(age_start, age_end, age_length, mx, ax, qx, dx, lx)]
new_dt <- iterate_ax(dt, id_cols = c("age_start", "age_end"))

# plot change in qx, ax, lx, dx, mx
dt <- merge(dt, new_dt, by = c("age_start", "age_end"))
data.table::setnames(dt, c("ax.x", "ax.y"), c("ax.initial", "ax.iterated"))
plot(data = dt, ax.iterated/ax.initial ~ age_start)

ihmeuw-demographics/demCore documentation built on Feb. 24, 2024, 11:05 p.m.