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Lin K, Croswell JM, Koenig H, et al. Prostate-Specific Antigen-Based Screening for Prostate Cancer: An Evidence Update for the U.S. Preventive Services Task Force [Internet]. Rockville (MD): Agency for Healthcare Research and Quality (US); 2011 Oct. (Evidence Syntheses, No. 90.)

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# Appendix 5Model to Adjust for Contamination and Compliance in the PLCO Trial

## Model Assumptions

1. Mortality due to cancer after 7 years is the primary endpoint.
2. All of the information that is necessary to model the correct ratio of the screened group’s prostate cancer mortality rate to the control group’s prostate cancer mortality rate is in the PLCO trial. Key parameters reported in this trial:
1. Prostate cancer mortality rate in the screened arm: 2.0 prostate cancer deaths per 10,000 person-years
2. Prostate cancer mortality rate in the control arm: 1.7 prostate cancer deaths per 10,000 person-years
3. Prostate cancer mortality rate ratio: 1.13 (95% CI, 0.75–1.70)
4. Compliance rate in the screened arm: 85%
5. Contamination rate in the controlled arm: varied by trial year; range, 40%–52%
3. There is a true underlying prostate cancer mortality rate per 10,000 person-years in a completely screened group, denoted as “x.”
4. There is a true underlying prostate cancer mortality rate per 10,000 person-years in a completely unscreened group, denoted as “y.”
5. Adjusting for compliance in the screened arm: the reported compliance implies that the rate of 2.0 prostate cancer deaths per 10,000 person-years is 0.85x + 0.15y.
6. Adjusting for contamination in the control arm:
1. To calculate the effect of the lowest rate of contamination: the 40% contamination rate in the control group implies that the observed rate of 1.7 deaths per 10,000 person-years is 0.4x + 0.6y.
2. To calculate the effect of the highest rate of contamination: the 52% contamination rate in the control group implies that the observed rate of 1.7 deaths per 10,000 person-years is 0.52x + 0.48y.
7. Estimating the lower bound of the confidence interval after adjustment: the lower confidence interval bound of 0.75 for the observed prostate cancer mortality rate ratio of 1.13 gives a lower width of 0.38 (1.13–0.75 = 0.38). Due to the large sample size of this trial, it is assumed that the maximum increase in the confidence interval lower width would be no greater than 20%. Therefore, under this assumption, the lower confidence interval bound will not be more than 0.46 (0.38 × 0.2 = 0.076; 0.38 + 0.076 = 0.46) below the modeled ratio.

## Calculation of Adjusted Prostate Cancer Mortality Estimate and Lower Confidence Interval Bound

• Given the lowest rate of contamination (40%):
• The system of linear equations to solve is: 0.85x + 0.15y = 2.0 and 0.40x + 0.60y = 1.7
• Solving for these equations gives x = 2.10 and y = 1.43
• The adjusted prostate cancer mortality rate ratio is x/y, or 2.10/1.43 = 1.47
• The estimated lower confidence bound (see assumption #7) is 1.47 − 0.46 = 1.01
• Given the highest rate of contamination (52%):
• The system of linear equations to solve is: 0.85x + 0.15y = 2.0 and 0.52x + 0.48y = 1.7.
• Solving for these equations gives x = 2.13 and y = 1.24
• The adjusted prostate cancer mortality rate ratio is x/y, or 2.13/1.24 = 1.72
• The estimated lower confidence bound (see assumption #7) is 1.72 − 0.46 = 1.26
Bookshelf ID: NBK82308