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. Author manuscript; available in PMC: 2022 Aug 11.
Published in final edited form as: J R Stat Soc Ser C Appl Stat. 2022 Mar 17;71(3):669–697. doi: 10.1111/rssc.12550

TABLE 2.

Estimated within-trial sample average treatment effect (SATE) and target population average treatment effects (PATE) on change in CD4 cell counta and corresponding 95% confidence intervals based on proposed sandwich variance estimators. Trial data are from ACTG 320b and ACTG A5202c; the WIHS and CNICS cohorts are used to create random samples from two target populations (all people N = 1.1 million and all women living with HIV in the USA N = 280,000). The three sets of results correspond to generalizability estimators that use (i) the true propensity score among trial participants ei = 1/2; (ii) the estimated propensity score using a logistic regression model with main effects for all covariates and a quadratic term for age; and (iii) the estimated propensity score using a more complex logistic regression model with main effects for all covariates, a quadratic term for age, and all pairwise interactions between covariates

PATE PATE PATE PATE PATE
Cohort m Trial n SATE IPSW1 IPSW2 REG DR1 DR2
True propensity scores
CNICS 6,158 320 1,040 19 (12, 25) 20 (11, 29) 18 (10, 26) 14 (5, 23) 15 (6, 24) 15 (7, 24)
CNICS 12,302 A5202 1,440 6 (−8, 20) 5 (−27, 36) 1 (−26, 28) −2 (−27, 24) −3 (−29, 24) −3 (−29, 24)
WIHS 493 320 173 24 (7, 41) 52 (19, 86) 42 (15, 69) 32 (−2, 65) 37 (1, 73) 37 (2, 72)
WIHS 1,012 A5202 255 1 (−35, 37) 106 (−44, 256) 31 (−44, 105) 0.04 (−103, 104) 4 (−84, 92) 4 (−85, 92)
Estimated propensity scores with main-effects logistic model
CNICS 6,158 320 1,040 19 (12, 25) 18 (10, 26) 17 (9, 25) 14 (5, 23) 15 (7, 24) 15 (7, 24)
CNICS 12,302 A5202 1,440 6 (−8, 20) −2 (−26, 31) 0.33 (−24, 25) −1 (−27, 25) −1 (−27, 25) −1 (−27, 25)
WIHS 493 320 173 24 (7, 41) 41 (13, 69) 47 (21, 73) 35 (3, 68) 40 (6, 74) 40 (6, 74)
WIHS 1,012 A5202 255 1 (−35, 37) 81 (−49, 211) 37 (−37, 111) 10 (−90, 110) 11 (−75, 96) 11 (−75, 96)
Estimated propensity scores with full logistic model
CNICS 6,158 320 1,040 19 (12, 25) 18 (10, 25) 18 (10, 25) 14 (5, 23) 15 (6, 24) 15 (6, 24)
CNICS 12,302 A5202 1,440 6 (−8, 20) 0.24 (−21, 22) −1 (−24, 22) −3 (−27, 23) −4 (−29, 22) −4 (−29, 22)
WIHS 493 320 173 24 (7, 41) 38 (16, 60) 39 (17, 61) 25 (−6, 55) 28 (−3, 60) 28 (−3, 60)
WIHS 1,012 A5202 255 1 (−35, 37) 52 (−39, 144) 24 (−28, 75) −9 (−75, 57) −8 (−75, 58) −8 (−75, 59)
a

For ACTG 320, the outcome is change in CD4 cell count from baseline to week 4. For ACTG A5202, the outcome is change in CD4 cell count from baseline to week 48.

b

For ACTG 320, the treatment contrast is protease inhibitor (X = 1) versus no protease inhibitor (X = 0).

c

For ACTG A5202, the treatment contrast is abacavir-lamivudine (X = 1) versus tenofovir disoproxil fumarate-emtricitabine (X = 0) plus efavirenz or ritonavir-boosted atazanavir.