Bootstrap variance of a matching-weight treatment effect

Estimates the weighted difference in means, group 1 minus group 0, for each outcome, with a bootstrap standard deviation, percentiles, z and p. A port of the CCF %mw_var SAS macro (Rajeswaran 2014), for matching weights as described by Li and Greene (2013).

Usage

ps_mw_var(
  data,
  treatment_col = "tavr",
  outcomes,
  weight_col,
  n_rep = 1000L,
  seed = NULL,
  treated_level = NULL
)

Arguments

data: A data frame.
treatment_col: Name of the group column, coded 0/1 or logical, with both groups present. Default "tavr".
outcomes: Character vector of numeric outcome columns.
weight_col: Name of the column of matching weights, which must be positive and finite.
n_rep: Number of bootstrap replicates. Default 1000, the macro's RESAMPL=.
seed: NULL (default) or one whole number. With a seed, the random number stream is set to abs(seed) immediately before the draws, the result is reproducible whatever ran earlier in the session, the caller's stream is restored afterwards, and the seed is kept in $meta$seed. With NULL the draws come from the caller's stream and advance it, and $meta$seed is NA.
treated_level: The value of treatment_col that is treated. NULL (default) requires a 0/1 or logical column and takes 1 or TRUE. Give a value, for example "transcatheter", to use a column holding any two values.

Value

An object of class c("ps_mw_var", "ps_data") with:

$data: The input data frame, unchanged.
$meta: Named list: treatment_col, weight_col, outcomes, method, n_rep, seed, n_total, n_dropped.
$tables: Named list with mw_var, one row per outcome: outcome, label, sumwgt_0, mean_0, sd_0, sumwgt_1, mean_1, sd_1, estimate, n_rep, sd, p2_5, p16, p50, p84, p97_5, z and p.

Details

With the Li-Greene matching weight (mt_wt from ps_logistic() or ps_forest()) the estimate targets the ATM, the average treatment effect among the matched: the population that 1:1 matching on the propensity score would keep. With other weights it targets whatever estimand those weights define.

Estimate. For each group, PROC MEANS weighted summaries: the mean sum(w y) / sum(w), the SD with an n - 1 denominator, and the sum of weights. The macro labels the sum of weights N; it is reported here as sumwgt_0 and sumwgt_1 because it is not a count. For a 0/1 outcome the means are weighted proportions.

Bootstrap. Each replicate resamples rows with replacement within each group, to that group's size, and recomputes the weighted means. The treatment group is the only stratum, as in the macro. sd is the standard deviation of the replicate differences, and the percentiles use quantile(type = 4), which is SAS PCTLDEF=1 as the macro sets it. Replicates where an outcome has no non-missing value in a group are left out for that outcome, and n_rep counts those that remain.

The weights are held fixed. Each resampled row keeps its original weight; the propensity model and the weights are not re-estimated. This reproduces the macro, and it ignores the uncertainty in estimating the weights, so sd can be too small.

Missing values. Rows with a missing group are dropped. A missing outcome is dropped for that outcome only.

Random numbers. With seed, the result is reproducible and the caller's random number stream is restored afterwards.

References

Li L, Greene T. A weighting analogue to pair matching in propensity score analysis. The International Journal of Biostatistics. 2013;9(2):215-234. doi:10.1515/ijb-2012-0030

Examples

dta <- sample_ps_data(n = 200, seed = 42)
dta$mt_wt <- pmin(dta$prob_t, 1 - dta$prob_t) /
  ifelse(dta$tavr == 1, dta$prob_t, 1 - dta$prob_t)
obj <- ps_mw_var(dta, treatment_col = "tavr", outcomes = c("age", "ef"),
                 weight_col = "mt_wt", n_rep = 200, seed = 1)
obj$tables$mw_var
#>   outcome label sumwgt_0   mean_0     sd_0 sumwgt_1   mean_1     sd_1
#> 1     age  <NA> 116.0528 74.50040 5.446871 115.3951 74.37045 5.632652
#> 2      ef  <NA> 116.0528 54.52772 6.903189 115.3951 54.55226 7.246387
#>      estimate n_rep        sd      p2_5        p16         p50       p84
#> 1 -0.12994823   200 0.8665785 -1.939877 -0.9633344 -0.14053587 0.6971630
#> 2  0.02453471   200 1.0395746 -2.040412 -1.1955832 -0.05329846 0.9746622
#>      p97_5           z         p
#> 1 1.442813 -0.14995552 0.8807997
#> 2 1.780236  0.02360072 0.9811711