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. 2019 Jul 31;26(12):1664–1674. doi: 10.1093/jamia/ocz094

Table 1.

Examples showing that an overall outcome PPV may not be indicative of the presence, magnitude or direction of outcome misclassification bias

Example True RR and exposure-outcome counts, without misclassification Levels of outcome misclassification Observed RR and exposure-outcome counts, with misclassification Observed outcome PPVs and consequence of misclassification
1a True RR: 0.86 (95% CI, 0.75-0.98)

  • SN1= 95.00%

  • SN0= 95.00%

  • SP1= 99.85%

  • SP0= 99.85%

 Observed RR: 0.87 (95% CI, 0.76-0.99)

  • Overall PPV = 94%

  • PPV1= 93%

  • PPV0= 94%

  • Consequence of misclassification:

  • Negligible bias
With outcome Without outcome
With outcome Without outcome Exposed 219 9781
Unexposed 10 085 389 915
Exposed 215 9785
Unexposed 10 000 390 000
1b True RR: 0.70 (95% CI, 0.60-0.81)

  • SN1= 95.00%

  • SN0= 90.00%

  • SP1= 99.55%

  • SP0= 99.82%

 Observed RR: 0.87 (95% CI, 0.76-0.99)

  • Overall PPV = 93%

  • PPV1= 79%

  • PPV0= 93%

  • Consequence of misclassification:

  • The conclusion is that exposed individuals have 13% lower risk of the outcome, when they really have 30% less risk.
With outcome Without outcome
With outcome Without outcome
Exposed 175 9825
Exposed 210 9790
Unexposed 10 000 390 000
Unexposed 9702 390 298
1c True RR: 1.00 (95% CI, 0.88-1.13)

  • SN1= 85.00%

  • SN0= 95.00%

  • SP1= 99.90%

  • SP0= 99.81%

 Observed RR: 0.87 (95% CI, 0.76-0.99)

  • Overall PPV = 93%

  • PPV1= 96%

  • PPV0= 93%

  • Consequence of misclassification:

  • A type I error occurs. The conclusion is that exposed individuals have 13% lower risk of the outcome, when there is no true difference in risk between exposed and unexposed individuals.
With outcome Without outcome With outcome Without outcome
Exposed 223 9777
Exposed 250 9750
Unexposed 10 241 389 759
Unexposed 10 000 390 000

The data are from a hypothetical cohort study of 10 000 exposed individuals, 400 000 unexposed individuals, and a baseline outcome prevalence of 2.5%.

CI, confidence interval; PPV0: outcome positive predictive value among unexposed; PPV1: outcome positive predictive value among exposed; RR: relative risk; SN0: sensitivity among unexposed; SN1: sensitivity among exposed; SP1: specificity among exposed; SP0: specificity among unexposed; PPV: overall outcome positive predictive value;.