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Table 2 Simulation results, data generated with a Weibull backward recurrence density

From: A new likelihood model for analyses of pharmacoepidemiologic case–control studies which avoids decision rules for determining latent exposure status

  

σ = exp(-0.35)

σ = exp(-0.25)

Analysis method(*)

Relative bias (%)

SE log(OR)

Coverage 95% CI (%)

VIF

Relative bias (%)

SE log(OR)

Coverage 95% CI (%)

VIF

μ = log(1.5/12)

1:1 CC

        

True expo

0.0

0.027

95.7

1.00

0.0

0.027

95.8

1.00

CC WTD

0.9

0.029

94.2

1.15

0.5

0.029

95.1

1.18

WTD prob

22.6

0.040

0.0

2.24

18.0

0.038

0.1

2.05

90 days

-6.0

0.027

33.2

1.06

-8.1

0.028

11.2

1.13

30 days

-11.1

0.035

6.7

1.69

-13.3

0.038

2.4

2.02

1:10 CC

        

True expo

0.0

0.036

95.4

1.00

0.0

0.036

95.2

1.00

CC WTD

0.6

0.038

94.9

1.08

0.5

0.038

95.2

1.10

WTD prob

11.2

0.049

28.7

1.78

8.6

0.047

48.5

1.68

90 days

-6.5

0.037

52.2

1.04

-9.5

0.038

20.6

1.09

30 days

-16.8

0.044

1.1

1.45

-19.6

0.048

0.3

1.70

μ = log(2/12)

1:1 CC

        

True expo

-0.1

0.027

94.2

1.00

0.0

0.027

95.8

1.00

CC WTD

1.7

0.029

90.1

1.21

1.6

0.030

91.5

1.25

WTD prob

18.8

0.039

0.1

2.13

14.4

0.037

0.9

1.97

90 days

-8.0

0.029

13.7

1.16

-10.2

0.030

3.5

1.26

30 days

-13.4

0.038

3.4

2.09

-15.2

0.042

2.6

2.50

1:10 CC

        

True expo

0.0

0.036

94.6

1.00

0.1

0.036

95.3

1.00

CC WTD

1.4

0.038

92.9

1.11

1.7

0.039

92.7

1.14

WTD prob

8.5

0.048

49.2

1.71

5.9

0.046

71.5

1.63

90 days

-9.9

0.038

18.4

1.10

-12.8

0.039

4.7

1.17

30 days

-20.0

0.048

0.4

1.74

-22.1

0.052

0.2

2.05

  1. The datasets had a sample size of 39,600, and on average 80% of patients continue treatment at the index date, 25% of patients have a prescription redemption in the year before the index date and the true OR is 3. For each setting 2,500 datasets were generated and analyzed. The Weibull Backward Recurrence Density used to generate data corresponded to a Weibull distribution with the same mean and variance as a Log-Normal distribution with \(\mu\) and \(\sigma\) as its parameters, see text for details
  2. (*) Analysis methods:
  3. 1:1 CC indicates 1 control per case, 1:10 CC indicates 10 controls per case
  4. True expo – logistic regression with the actual exposure status as covariate (the reference analysis)
  5. CC WTD – estimation based on joint likelihood for case–control status and the reverse WTD, Log-Normal Backward Recurrence Density
  6. WTD prob – a reverse WTD with Log-Normal Backward Recurrence Density is estimated to predict the probability of an individual being exposed and this exposure probability is used as covariate in logistic regression
  7. 90 days – individuals are considered exposed if they have a redemption < 90 days before index date
  8. 30 days – individuals are considered exposed if they have a redemption < 30 days before index date, logistic regression