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Table 1 Type I errors, Bias and Mean Square Error (MSE) for non parsimonious PS model according to the method used (PS matching (PSm) or IPTW) and to the strength of the association between baseline covariates, treatment/outcome

From: Evaluation of the Propensity score methods for estimating marginal odds ratios in case of small sample size

N

 

OR(a) = 1.5, OR(b) = 1.5

OR(a) = 2.5, OR(b) =1.5

OR(a) = 1.5, OR(b) = 2.5

OR(a) = 2.5, OR(b) = 2.5

  

PSm

IPTW

PSm

IPTW

PSm

IPTW

PSm

IPTW

40

Type I error

0.055

0.048

0.053

0.056

0.052

0.039

0.052

0.047

 

Bias

0.05

0.057

0.049

0.07

0.059

0.055

0.048

0.079

 

%

5.6

6.5

5.4

7.8

7.1

6.6

5.7

9.4

 

Variance

0.875

0.593

0.918

0.694

0.873

0.576

0.903

0.683

 

MSE

0.878

0.597

0.92

0.699

0.876

0.579

0.905

0.690

60

Type I error

0.045

0.046

0.047

0.046

0.044

0.039

0.044

0.039

 

Bias

0.058

0.036

0.058

0.049

0.048

0.022

0.05

0.033

 

%

6.4

4

6.4

5.4

5.7

2.6

6

3.9

 

Variance

0.511

0.36

0.553

0.414

0.484

0.329

0.516

0.388

 

MSE

0.514

0.362

0.556

0.416

0.486

0.33

0.519

0.389

100

Type I error

0.049

0.046

0.047

0.046

0.047

0.034

0.04

0.036

 

Bias

0.023

0.018

0.02

0.022

0.021

0.015

0.025

0.016

 

%

2.6

2

2.2

2.5

2.5

1.8

2.9

1.9

 

Variance

0.254

0.194

0.282

0.223

0.242

0.177

0.261

0.204

 

MSE

0.255

0.194

0.283

0.223

0.243

0.177

0.262

0.204

500

Type I error

0.049

0.046

0.05

0.048

0.041

0.038

0.042

0.037

 

Bias

0.01

0.007

0.012

0.008

0.01

0.005

0.013

0.005

 

%

1.1

0.8

1.3

0.9

1.2

0.6

1.5

0.6

 

Variance

0.04

0.034

0.045

0.038

0.037

0.032

0.042

0.035

 

MSE

0.04

0.034

0.045

0.038

0.037

0.032

0.042

0.035

  1. This table specially details the sample sizes ranging from 40 to 500. Prevalence of the treatment was set at 0.5. Conditional treatment effect was set at log(2.5) except for Type I errors estimations (log(1)). (N: number of subjects; PS: propensity score; IPTW: inverse probability of treatment weighting, OR(a) and OR(b): strengths of the association between baseline covariates and treatment or outcome respectively, as defined on an odds ratio scale).