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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