simul_confusion/catalogue.md

Scenario catalogue

Scenarios without DIF

	J		Epsilon
	4	7	0.2	0.5
Scenario 101	X		X
Scenario 102	X			X
Scenario 103		X	X
Scenario 104		X		X

Each scenario has 5 subscenarios:

• A - H₀ true
• B - H₁ true, effect size 0.2
• C - H₁ true, effect size 0.4
• D - H₁ true, effect size -0.2
• E - H₁ true, effect size -0.4

Scenarios with DIF

	J		Epsilon		Nb items DIF			DIF size
	4	7	0.2	0.5	1	2	3	0.3	0.5
Scenario 105	X		X		X			X
Scenario 106	X			X	X			X
Scenario 107	X		X		X				X
Scenario 108	X			X	X				X
Scenario 109	X		X			X		X
Scenario 110	X			X		X		X
Scenario 111	X		X			X			X
Scenario 112	X			X		X			X
Scenario 113		X	X			X		X
Scenario 114		X		X		X		X
Scenario 115		X	X			X			X
Scenario 116		X		X		X			X
Scenario 117		X	X				X	X
Scenario 118		X		X			X	X
Scenario 119		X	X				X		X
Scenario 120		X		X			X		X

Each scenario has 7 subscenarios:

• A - H₀ true, DIF -0.3/0.5 on traitement group
  • MPR example
• B - H₁ true, effect size 0.2, DIF +0.3/0.5 on traitement group
  • BDI example
• C - H₁ true, effect size 0.2, DIF -0.3/0.5 on traitement group
  • Dentistry example
• D - H₁ true, effect size 0.4, DIF +0.3/0.5 on traitement group
  • BDI example
• E - H₁ true, effect size 0.4, DIF -0.3/0.5 on traitement group
  • Dentistry example
• F - H₁ true, effect size -0.2, DIF -0.3/0.5 on traitement group
  • Adverse effects example
• G - H₁ true, effect size -0.4, DIF -0.3/0.5 on traitement group
  • Adverse effects example

Confusion simulation details

8 covariates are simulated for each scenario, each defined by their odds ratio on treatment and odds ratio on outcome:

OR_TT^X: Odds ratio describing the increase in probability of patients being treated when covariate X is positive.
OR_Y^X: Odds ratio describing the increase in average outcome when covariate X is positive.

Covariates are simulated as in Sturmer et al, 2021:

Variables	OR_TT^X	OR_Y^X
X_1	2.0	1.0
X_2	1.5	1.0
X_3	1.0	2.0
X_4	1.0	1.5
X_5	Epsilon	Epsilon
X_6	1.5 x Epsilon	1.5 x Epsilon
X_7	1.0 / 10	1.0 / 10
X_8	1.0 / 0.1	1.0 / 10

X_1 and X_2 are thus Instrumental variables, X_3 and X_4 are Risk factors for the outcome and X_5 and X_6 are Confounders.

X_7 and X_8 are unobserved tail-end cofounders indicating rare treatment decisions for extreme propensity score values in each group. Untreated patients with very high propensity of treatment will be very likely to have X_7=1 (patients that should have been treated but weren't due to frailty). Treated patients with very low propensity of treatment will be very likely to have X_8=1 (patients that should not have been treated but were due to severe condition).

For each replication, observed covariates explained treatment with an AUC drawn randomly between 0.65 and 0.85 (average: 0.75).