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Graduate (smooth and gap-fill) empirical decrement rates

smooth_decrement_rates.Rd

Takes the pooled output of estimate_decrement_rates() and returns a version with no age gaps and much less small-cell noise – both prerequisites for compute_service_table()'s age-chaining recursion, which needs a complete, stable qx curve to run at all.

Each exit cause (every status_col value other than active_value) is graduated independently via .smooth_rate_curve(), weighted by exposure (pop) so ages with more data pull their local curve harder than thin, noisy ages. active_value (the "stayed" outcome) is deliberately never smoothed on its own – it is derived afterward as 1 - the sum of the smoothed exit rates, which is what guarantees every age/group's rates still sum to exactly 1 after smoothing (independently smoothing every outcome type would not preserve that).

Usage

smooth_decrement_rates(
  decrements,
  age_col,
  status_col,
  group_cols,
  active_value = "active",
  span = 0.75,
  decrement_dt = NULL
)

Arguments

decrements

A data.table (or coercible) shaped like the output of estimate_decrement_rates(): one row per age / group_cols / status_col, with a pop (exposure) and decrement_rate column.

age_col

A single string naming the age column.

status_col

A single string naming the outcome-type column.

group_cols

A character vector of stratifying columns (e.g. gender), or NULL for no stratification.

active_value

A single string giving the status_col value that represents "stayed" rather than an exit. Defaults to "active".

span

Numeric. The loess() smoothing span passed through to .smooth_rate_curve(). Defaults to 0.75.

decrement_dt

Deprecated. Use decrements instead.

Value

A data.table with one row per age / group_cols / status_col, spanning the full observed age range within each group with no gaps:

age_col, group_cols

As supplied.

status_col

The outcome type, including active_value.

decrement_rate

The graduated rate, clipped to [0, 1]. Sums to 1 across outcome types for a given age/group (up to the clamping caveat below).

pop, exits, and n_periods from decrement_dt are not carried forward: an interpolated age never had a real headcount, so those columns would be fabricated rather than meaningful.

Details

Age grid. Each group's target age grid (min(age) to max(age)) is computed once across all outcome types in decrement_dt, not separately per status_col, so every exit cause ends up graduated onto exactly the same set of ages within a group.

Clamping caveat. If the smoothed exit rates for a given age/group happen to sum to slightly more than 1 (possible when several causes are each pushed up near a sparse edge), the derived active_value rate is clamped to 0 rather than going negative. In that edge case the row then sums to slightly less than 1 rather than exactly 1 – a known imperfection that is not further corrected.

See also

.smooth_rate_curve, estimate_decrement_rates, compute_service_table