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. 2010 Aug 17;172(7):843–854. doi: 10.1093/aje/kwq198

Table 2.

Mean Incidence Rates and Rate Ratios as a Function of Estimated Asymmetric Propensity Score Percentiles From 1,000 Simulated Data Sets in the Presence of Unmeasured Confounding Due to “Last Resort Treatment” and “Treatment Withheld”

PS “Percentile”a Treatment Prevalence = 0.2
 Treatment Prevalence = 0.05
Treated
 Untreated
 RRb Treated
 Untreated
 RRb
No. IRc No. IRc No. IRc No. IRc
“Last resort treatment”
    <0d 63 11 261 12
    0–1 19 133 561 22 6.68 4 117 635 24 5.51
    1–2.5 29 188 528 34 5.85 7 181 685 38 5.07
    2.5–5 49 219 659 45 5.04 12 244 771 53 4.75
    5–25 18 207 201 52 4.58 3 231 117 59 4.68
    25–50 242 160 2,007 67 2.40 62 287 2,283 81 3.56
    50–75 451 221 2,010 108 2.06 112 259 2,376 120 2.17
    75–95 719 360 1,608 172 2.10 182 399 1,901 190 2.10
    95–97.5 163 514 201 256 2.06 42 579 238 282 2.09
    97.5–99 129 607 121 301 2.10 34 673 143 335 2.06
    99–100 137 834 80 406 2.14 36 949 95 455 2.15
    >100d 5 1,679 1 1,772
“Treatment withheld”
    <0d 91 6 321 10
    0–1 19 33 718 15 2.48 4 39 705 19 2.08
    1–2.5 29 54 601 27 2.18 7 66 712 32 2.13
    2.5–5 49 79 683 40 2.06 12 96 813 47 2.12
    5–25 2 99 19 44 2.54 1 97 44 48 2.30
    25–50 239 136 1,914 66 2.07 57 151 2,160 74 2.06
    50–75 474 222 2,014 108 2.06 117 242 2,378 119 2.04
    75–95 767 367 1,611 183 2.01 188 408 1,903 233 1.76
    95–97.5 160 591 201 554 1.10 41 618 238 526 1.20
    97.5–99 114 830 121 1,058 0.81 31 777 143 803 1.00
    99–100 92 1,623 80 2,348 0.71 29 1,296 95 1,673 0.80
    >100d 2 5,662 1 4,726
“Last resort treatment” and “treatment withheld”
    <0d 61 11 261 12
    0–1 19 125 550 21 6.75 5 103 627 22 5.25
    1–2.5 29 173 516 31 5.99 7 159 651 35 4.87
    2.5–5 49 199 650 41 5.01 12 219 754 49 4.65
    5–25 21 200 238 48 4.84 3 238 150 55 4.75
    25–50 248 148 2,013 64 2.35 65 261 2,308 77 3.44
    50–75 466 212 2,013 104 2.05 117 241 2,375 114 2.12
    75–95 752 349 1,611 173 2.03 188 389 1,900 222 1.76
    95–97.5 158 562 201 500 1.16 41 591 238 500 1.21
    97.5–99 112 778 121 978 0.82 31 742 143 760 1.01
    99–100 91 1,518 80 2,197 0.71 29 1,236 95 1,592 0.80
    >100d 2 5,219 1 4,170

Abbreviations: IR, incidence rate; PS, propensity score; RR, rate ratio.

a

Asymmetric PS percentiles according to PS distribution in treated and untreated persons separately (to allow closer assessment of persons treated contrary to prediction). Percentiles between 0 and 5 are derived from the PS distribution in the treated patients; all other percentiles are derived from the PS distribution in the untreated patients.

b

Controlled for measured covariates based on PS stratification; inconsistencies with the incidence rates in the treated and untreated are due to rounding.

c

Per 1,000 person-years (repeated events).

d

Untreated patients in the <0 asymmetric PS percentile stratum are those with a lower PS than the lowest one observed in the treated patients (nonoverlap). Treated patients in the >100 asymmetric PS percentile stratum are those with a higher PS than the highest one observed in the untreated patients (nonoverlap).