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Table 1 Design of the simulation data

From: Comparing performance between log-binomial and robust Poisson regression models for estimating risk ratios under model misspecification

Scenario

Scenario

Models to generate simulation datasetsb

Model misspe-cified?c

Max P of exposeda

Beta of Z2

Link Function

% of exposed at Max P

I-1

0.75

3

log

0

log (P (Y1 = 1| X = 0, Z1, Z2)) = −1.38 – Z1–3 * Z2

No

I-2

0.75

3

log

1.4

log (P (Y2 = 1| X = 0, Z1, Z2)) = − 1.23 – max (Z1 + 3 * Z2, 0.15)

Yes

I-3

0.75

3

log

2.8

log (P (Y3 = 1| X = 0, Z1, Z2)) = − 1.08 – max (Z1 + 3 * Z2, 0.30)

Yes

I-4

0.75

3

log

5.8

log (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.78 – max (Z1 + 3 * Z2, 0.60)

Yes

II-1

0.85

3

log

0

log (P (Y1 = 1| X = 0, Z1, Z2)) = − 1.26 – Z1–3 * Z2

No

II-2

0.85

3

log

1.4

log (P (Y2 = 1| X = 0, Z1, Z2)) = − 1.11 – max (Z1 + 3 * Z2, 0.15)

Yes

II-3

0.85

3

log

2.8

log (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.96 – max (Z1 + 3 * Z2, 0.30)

Yes

II-4

0.85

3

log

5.8

log (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.66 – max (Z1 + 3 * Z2, 0.60)

Yes

III-1

0.95

3

log

0

log (P (Y1 = 1| X = 0, Z1, Z2)) = − 1.15 – Z1–3 * Z2

No

III-2

0.95

3

log

1.4

log (P (Y2 = 1| X = 0, Z1, Z2)) = − 1.00 – max (Z1 + 3 * Z2, 0.15)

Yes

III-3

0.95

3

log

2.8

log (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.85 – max (Z1 + 3 * Z2, 0.30)

Yes

III-4

0.95

3

log

5.8

log (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.55 – max (Z1 + 3 * Z2, 0.60)

Yes

IV-1

0.95

2

log

0

log (P (Y1 = 1| X = 0, Z1, Z2)) = − 1.15 – Z1–2 * Z2

No

IV-2

0.95

2

log

1.4

log (P (Y2 = 1| X = 0, Z1, Z2)) = − 1.05 – max (Z1 + 2 * Z2, 0.10)

Yes

IV-3

0.95

2

log

2.8

log (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.95 – max (Z1 + 2 * Z2, 0.20)

Yes

IV-4

0.95

2

log

5.8

log (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.75 – max (Z1 + 2 * Z2, 0.40)

Yes

V-1

0.95

4

log

0

log (P (Y1 = 1| X = 0, Z1, Z2)) = − 1.15 – Z1–4 * Z2

No

V-2

0.95

4

log

1.4

log (P (Y2 = 1| X = 0, Z1, Z2)) = − 0.95 – max (Z1 + 4 * Z2, 0.20)

Yes

V-3

0.95

4

log

2.8

log (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.75 – max (Z1 + 4 * Z2, 0.40)

Yes

V-4

0.95

4

log

5.8

log (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.35 – max (Z1 + 4 * Z2, 0.80)

Yes

VI-1

0.95

3

logit

0

logit (P (Y1 = 1| X = 0, Z1, Z2)) = − 0.76 – Z1–3 * Z2

Yes

VI-2

0.95

3

logit

1.4

logit (P (Y2 = 1| X = 0, Z1, Z2)) = − 0.61 – max (Z1 + 3 * Z2, 0.15)

Yes

VI-3

0.95

3

logit

2.8

logit (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.46 – max (Z1 + 3 * Z2, 0.30)

Yes

VI-4

0.95

3

logit

5.8

logit (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.16 – max (Z1 + 3 * Z2, 0.60)

Yes

VII-1

0.95

3

probit

0

probit (P (Y1 = 1| X = 0, Z1, Z2)) = − 0.48 – Z1–3 * Z2

Yes

VII-2

0.95

3

probit

1.4

probit (P (Y2 = 1| X = 0, Z1, Z2)) = − 0.33 – max (Z1 + 3 * Z2, 0.15)

Yes

VII-3

0.95

3

probit

2.8

probit (P (Y3 = 1| X = 0, Z1, Z2)) = − 0.18 – max (Z1 + 3 * Z2, 0.30)

Yes

VII-4

0.95

3

probit

5.8

probit (P (Y4 = 1| X = 0, Z1, Z2)) = − 0.12 – max (Z1 + 3 * Z2, 0.60)

Yes

  1. aMaximum P (Y k  = 1| X = 1, Z1, Z2)
  2. bModels to generate Y k for unexposed subjects. For exposed subjects, P (Yk = 1| X = 1, Z1, Z2) =3*P (Yk = 1| X = 0, Z1, Z2). k = 1, 2, 3, and 4
  3. cModel was defined as misspecified when the link function was not ‘log’ or the % of exposed at maximum P (Yk = 1| X = 0, Z1, Z2) was greater than 0
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BMC Medical Research Methodology

ISSN: 1471-2288

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