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Estimate empirical decrement rates from a personnel panel

estimate_decrement_rates.Rd

Estimates, for each age (and any grouping columns you supply), the empirical probability that a person active in one snapshot ends up in each possible employment status by the next snapshot – retirement, another kind of exit, or simply staying active. These are the raw ingredients (qx-style decrement rates) for building an actuarial life table, e.g. with a life-table function that chains them across age.

The function walks every consecutive pair of snapshots in personnel_dt, tracks the same individuals from one snapshot to the next, and pools the results into one stable rate per age/group/outcome using all of the data available, rather than relying on any single pair of snapshots (which can be noisy for ages with few people).

Usage

estimate_decrement_rates(
  personnel,
  age_col,
  status_col,
  personnel_id_col,
  ref_date_col,
  group_cols,
  personnel_dt = NULL
)

Arguments

personnel

A data.table (or data.frame/tibble, coerced automatically) containing the personnel panel: multiple snapshots of the same population over time, identified by ref_date_col. Must contain at least two distinct, non-missing reference dates.

age_col

A single string naming the (integer, or coercible to integer) age column.

status_col

A single string naming the employment status column, e.g. "employment_status". The value "active" identifies who is exposed to risk in each snapshot; every other value your data uses (e.g. "pensioner", "deceased") is picked up automatically as its own outcome type – nothing needs to be hardcoded or registered in advance.

personnel_id_col

A single string naming the personnel identifier column, used to track the same person across snapshots.

ref_date_col

A single string naming the reference date column that identifies each snapshot.

group_cols

A character vector of additional columns (e.g. gender, occupation, service type) to estimate separate rates by, alongside age.

personnel_dt

Deprecated. Use personnel instead.

Value

A data.table with one row per age / group_cols / outcome type, pooled across every consecutive snapshot pair in personnel_dt:

age_col, group_cols

The age and grouping columns, as supplied.

status_col

The outcome type this row's rate applies to – "active" (stayed), an observed exit status (e.g. "pensioner"), or the synthetic "non-retirement-exit" (someone who dropped out of the panel without an explicit exit status). For a given age/group, these rows sum to 1.

pop

Total exposure: the number of person-periods active at the start of a snapshot pair, summed across every pair that contributed to this age/group.

exits

Total number of people in that exposure who had this outcome by the next snapshot, summed the same way.

decrement_rate

The pooled rate, exits / pop. This is the empirical qx (or px, for the "active" row) to feed into a life table.

n_periods

Number of distinct snapshot pairs that contributed to this age/group/outcome cell – a quick way to spot ages resting on very little data.

Details

This section is for readers who want to know exactly how the rate is computed, not just what it means.

Two collapsing steps. Estimating a life-table-ready rate means collapsing two different axes, and this function only ever does the first one:

  • Time, here: every consecutive snapshot pair in personnel_dt (2015-2016, 2016-2017, ...) is walked via roll_snapshot_pairs(), and each pair's exposure/outcome counts are pooled into one age-indexed rate. This function never chains anything across age – that is a separate step (a life-table function operating purely on this function's output).

Pooling is exposure-weighted, not a mean of rates. For a given age/group/outcome, pop and exits are summed across every contributing snapshot pair before dividing. A period-pair with 500 people at risk therefore contributes proportionally more than one with 2 people at risk. A plain average of the per-period rates would let a noisy, thin period swing the estimate just as much as a large one – this deliberately avoids that.

Cohort tracking, not independent aggregation. Within each snapshot pair, exposure and outcomes are computed by joining the same individuals from T0 to T1 on personnel_id_col (see .compute_decrement_pair()), not by aggregating each snapshot separately and matching on age afterward. This matters: someone who was already a pensioner at T0 and remains one at T1 is never miscounted as a newly observed exit, and each person's age/group is taken from T0, so there is no fragile assumption that snapshots are exactly one year apart.

The outcome vocabulary is derived from the data. Aside from the synthetic "non-retirement-exit" (assigned to anyone who drops out of the panel between snapshots without an explicit status change), every outcome type reported is simply whatever value status_col takes on in your data – including "active" itself, so you get a stay probability alongside every exit-type probability. This means the function keeps working unmodified if your data's status vocabulary differs from what was used to build or test it (e.g. adding a "deceased" status requires no code change).

Caveat. The literal string "active" is currently hardcoded as the value of status_col that defines who is exposed to risk – unlike the exit-side vocabulary, this one value is assumed rather than derived.

See also

.compute_decrement_pair, roll_snapshot_pairs

Examples

if (FALSE) { # \dontrun{
library(data.table)

personnel_dt <- data.table(
  personnel_id = c("P1", "P2", "P1", "P2"),
  ref_date = as.Date(c("2020-01-01", "2020-01-01", "2021-01-01", "2021-01-01")),
  age = c(60L, 45L, 61L, 46L),
  employment_status = c("active", "active", "pensioner", "active"),
  gender = c("M", "F", "M", "F")
)

estimate_decrement_rates(
  personnel_dt = personnel_dt,
  age_col = "age",
  status_col = "employment_status",
  personnel_id_col = "personnel_id",
  ref_date_col = "ref_date",
  group_cols = "gender"
)
} # }