Scales the cohort initiation curves from init_est() so that the cumulative probability of ever smoking at the reference age matches the trend in ever smoking estimated by ever_smoke(). init_est() gives us the shape of the curve (the distribution of starting ages among people who ever start); this function pins down the level.
Usage
init_adj(
init_data,
ever_smoke_data,
ref_age = 30,
fix_ref_age = FALSE,
min_ref = 18,
cohorts = 1973:2020,
period_start = 2003,
period_end = 2018,
n_completion_cohorts = 10
)Arguments
- init_data
Data table - raw estimates from init_est().
- ever_smoke_data
Data table - trend targets from ever_smoke().
- ref_age
Integer - the index age for calibration (default 30).
- fix_ref_age
Logical. If TRUE, forces ref_age even if data is sparse.
- min_ref
Integer - youngest reference age a truncated cohort may calibrate at. With the completion step this can sit lower than it used to: the old guard against truncation bias was to refuse cohorts seen only to their early twenties, whereas now the bias is corrected rather than avoided. It should not go so low that F(r) is a small and noisy fraction of F(ref_age).
- cohorts
Integer vector - cohorts to adjust.
- period_start
Integer - first year of data.
- period_end
Integer - last year of data.
- n_completion_cohorts
Integer - how many of the most recent fully observed cohorts to average the completion ratios over.
Details
The trend target is the level of ever smoking at age ref_age: ever_smoke() estimates it on 25-34 year olds and we map each year's value to the cohort that is ref_age in that year. For cohorts old enough to have been surveyed at ref_age, the raw curve and the target refer to the same age and the scalar is simply target / raw.
Younger cohorts have not been seen that far. Their raw curve stops at whatever age the surveys last observed them, and its value there is missing the initiation that happens between that age and ref_age. Dividing the age-30 target by, say, an age-21 curve quietly assumes nobody starts between 21 and 30 - and the cohorts we did see all the way say that is wrong by about 5 21 and 2 multiplying it by F(ref_age) / F(r) averaged over the most recent fully observed cohorts within sex and IMD quintile. That trades the "initiation stops dead at the truncation age" assumption for "the timing of initiation, conditional on ever starting, is stable across adjacent cohorts", which is a much weaker thing to assume and one we can check in the data.
Initiation is still assumed to stop after ref_age: the curve is carried forward flat from there.