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Unconditional estimands for a single treatment group

Source: R/single_treatment_group_analysis.R
single_treatment_group_analysis.Rd

Estimates 15 descriptive estimands for triplet (treatment group, control group and target age). SEs are calcualted using influence-function (IF) calculations with clustering within id.

Usage

single_treatment_group_analysis(
  data,
  d,
  dp,
  a,
  pre = 1,
  Y_name = "Y",
  age_name = "age",
  D_name = "D",
  id_name = "id",
  female_name = "female"
)

Arguments

data

A data.table with columns:

  • id — cluster identifier (i.e., person)

  • age — integer age

  • female — 0/1 indicator (1 = females)

  • D — treatment group

  • Y — numeric outcome

d

Integer. Treatment group (age at first childbirth)

dp

Integer. Control group (closest not-yet-treated group)

a

Integer. Target age.

pre

Integer, default 1. Offset used for the pre-treatment anchor.

Y_name, age_name, D_name, id_name, female_name

Column name mappings passed to prep_data_table().

Value

A data.frame with one row per estimand/method combination:

  • estimand — one of "APO", "ATE", "theta", "Delta_rho"

  • method — one of "DID_Female", "DID_Male", "TD", "NTD_Conv", "NTD_New", "TD_Null", "NTD_Conv_Null"

  • est — estimate

  • se — cluster-robust standard error

  • n_female_treat, n_female_control, n_male_treat, n_male_control — sample counts

Details

Let \(Y(a, g, d^\star)\) denote the mean outcome at age \(a\) for gender \(g \in \{0,1\}\) (1 = female) when assigned to group \(d^\star\). The core components are:

  • APO(g; d, d', a) \(= Y(d-\mathrm{pre}, g, d) + Y(a, g, d') - Y(d-\mathrm{pre}, g, d')\)

  • ATE(g; d, d', a) \(= Y(a, g, d) - \mathrm{APO}(g; d, d', a)\)

  • \(\theta\)(g) \(= \mathrm{ATE}(g) / \mathrm{APO}(g)\)

From these, the cross-gender contrasts are formed:

  • TD \(= \mathrm{ATE}(F) - \mathrm{ATE}(M)\)

  • NTD_Conv \(= \theta(F) - \theta(M)\)

  • NTD_New \(= \frac{Y(a,F,d)}{Y(a,M,d)} - \frac{\mathrm{APO}(F)}{\mathrm{APO}(M)}\)

  • TD Null and NTD_Conv_Null variants are defined analogously under a null-effect-for-fathers bias-correction.

Internally, influence functions for all pieces are written into temporary columns of a data.table via compute_mean_if(), and cluster-robust standard errors are computed by summing the IFs at the id level via se_cluster().

Note

Requires helper functions compute_mean_if() and se_cluster().

Examples

# \donttest{
set.seed(1)
sim <- simulate_data(n_individuals = 500)
res <- single_treatment_group_analysis(sim, d = 25, dp = 26, a = 26, pre = 1)
head(res)
#>   estimand     method           est           se n_female_treat
#> 1      APO DID_Female  4.741629e+04 2.684547e+03             58
#> 2      APO   DID_Male  6.658594e+04 3.135801e+03             58
#> 3      ATE DID_Female -1.229815e+03 2.447360e+03             58
#> 4      ATE   DID_Male  5.422312e+02 2.761787e+03             58
#> 5    theta DID_Female -2.593655e-02 5.039948e-02             58
#> 6    theta   DID_Male  8.143329e-03 4.176981e-02             58
#>   n_female_control n_male_treat n_male_control
#> 1               36           59             55
#> 2               36           59             55
#> 3               36           59             55
#> 4               36           59             55
#> 5               36           59             55
#> 6               36           59             55
# }