1. Biostatistics Case Studies Peter D. Christenson Biostatistician http://gcrc.humc.edu/Biostat Session 2: Diagnostic Classification

2. Case Study

3. PSA Background PSA secreted by prostatic epithelial cells; test developed in the late 1970s. Currently, usually screen PSA>4.0 ng/ml. Why 4.0? Unclear; early studies of CaP patients showed many PSA > 4.0? Hesitant to unnecessarily take biopsies with lower PSA. A few studies did suggest substantial CaP with lower PSA. Prostate Cancer Prevention Trial specified biopsy at study end, regardless of PSA.

4. Issues and Goals Over-diagnosis in men over 50: Microscopic evidence in 33% of autopsy / cystoprostatectomy specimens. 9-16% currently diagnosed with CaP. 3% CaP mortality. Screening (early diagnosis): Maximize curable CaP detection and exclude as many men as possible from unnecessary biopsies. Prognosis (predicting outcome): Predict mortality using pre- and post-biopsy info.

5. Catalona, et al (1991) Men ≥ 50 years of age with PSA ≥ 4.0. Biopsy those with abnormal DRE or ultrasound. N=1653 N=1516 N=107 (6.5%)N=30 (1.8%) N=85N=27 N=19/85=22%N=18/27=67% PSA<4.0PSA≥10 4.0≤PSA<10 ? Abnormal DRE / US CaP in biopsy

6. Krumholtz, at al (2002) Prostate screening program. Recommend biopsy if high PSA and/or abnormal DRE. PSA cutoff changed from 4.0 to 2.6 mid-study. CaP in 156/601=26% with 2.6≤PSA≤4.0 and 97/309=31% with 4.0<PSA≤10.0. Report on 94 with embedded prostatectomy specimens. PSA≤4.0  more organ-confined; not greater over- detection.

7. Prostate Cancer Prevention Trial (PCPT) 18,882 men randomized to finasteride or placebo; up to 7 years follow-up. Annual DRE and PSA. Biopsy recommended if PSA>4.0 or abnormal DRE. End of study biopsy planned for all men without during-study diagnosis of CaP. Primary outcome = biopsy CaP positive or negative. Main result: finasteride had 25% efficacy; 18% CaP in finasteride vs. 24.4% CaP in placebo.

8. Current Paper: Thompson et al, 2004.

9. Main Results Overall, 449/2950 = 15.2% with CaP detected in biopsy.

10. Conclusions and Issues There is substantial CaP with low PSA values, and the rate appears to have a dose-response relationship with PSA. Is it a good screening tool? Does it have prognostic ability, at least for CaP in biopsy, since mortality was not studied. What do we make of the reported sensitivity and specificity? We first examine several “what if” scenarios with artificial data.

11. Scenario 1: PSA is useless

12. Scenario 2: PSA is a perfect test

13. Scenario 3: Almost perfect association

14. PSA Prognostic Ability in Scenario 3 Predict P(CaP) = Probability(CaP) using PSA: P(CaP if PSA = 3) = 33 ± 2 % (CI) P(CaP if PSA = 8) = 88 ± 2 % (CI) Since ±2% is very small, this study is very precise at measuring the prevalence of biopsy-evident CaP according to PSA intervals. PSA would be a decent prognostic factor for biopsy-detected CaP (but of course we actually want to predict clinical outcomes).

15. PSA Screening Ability Sensitivity= True positive rate = % identified among CaP +. Specificity= True negative rate = % not identified among CaP -. For screening, sensitivity is usually more important than specificity.

16. PSA Screening Ability in Scenario 3 using PSA>4.0 Sensitivity= 820/(820+449) = 65% Specificity= 2501/(2501+367) = 87%

17. PSA Screening Ability in Scenario 3 using PSA>2.0 Sensitivity= 987/(987+282) = 78% Specificity= 1993/(1993+875) = 55%

18. Conclusions from Scenarios Association ≠ screening accuracy. Good* screening needs something more like: *Few unnecessary biopsies, but detect most serious CaP.

19. Back to Actual Results: Overall, 449/2950 = 15.2% with CaP detected in biopsy.

20. Revised Table 2: Prevalence of CaP and its Precision 95% CI for CaP Prevalence PSA RangeAny GradeHigh Grade ≤ 0.50 6.6 ± 2.2%0.8 + 0.8% 0.6 – 1.010.1 ± 2.1%1.0 ± 0.7% 1.1 – 2.017.0 ± 2.4%2.0 ± 0.9% 2.1 – 3.023.9 ± 3.9%4.6 ± 1.9% 3.1 – 4.026.9 ± 6.4%6.7 ± 3.6% ≤ 4.015.2 ± 1.3%2.3 ± 0.5%

21. Table 2: Sensitivity and Specificity Sensitivity at PSA=1.1 of 0.75 = (170+115+52)/449 Specificity at PSA=1.1of 0.33=(486-32 +791-80)/(2950-449) Relative to only PSA≤4.0. Not useful without PSA>4.0 info.

22. Figure 2: Models P(CaP)=function(PSA) Risk= P(CaP)

23. Figure 2 Models Table 2 Data Dotted line is only to show form of model; do not extrapolate. Logistic model is not very useful with so much data, unless adjustment for other factors (e.g., family hx of CaP) is desired.

24. Logistic Regression Uses odds of disease = P(CaP)/[1-P(CaP)]. Log(odds) are linear in PSA  sigmoidal curve in previous graph, common for bounded outcomes. Increase in odds for a given change in PSA is proportional to PSA. For this study, log(odds)= -2.70 + 0.507(PSA) and P(CaP) = exp(logodds)/(1+exp(logodds) Can include other adjusting factors. Usually used for prediction (prognosis); but can define, e.g., Prob(CaP)=fixed number such as 0.22 to classify and obtain sensitivity and specificity.

25. Logistic Regression in Software SPSS: Select Analyze > Regression > Binary Logistic Specify CaP (1=Yes;0=N0) as dependent variable. Specify PSA as covariate. Select Options > CI for exp(B). OK SAS: proc logistic descending; class CaP; model CaP = PSA; run;

26. Software Output: SAS Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits PSA 1.66 1.50 1.85 Analysis of Maximum Likelihood Estimates Parameter DF Estimate Intercept 1 -2.700 PSA 1 0.507

27. Combined Screening and Prognosis ? PSA Other Pre- Biopsy 1 Biopsy Character- istics 2 Risk of CaP Death Biopsy Moderate Low High Neg Pos 1 Such as PSA velocity 2 Such as prostate volumeSee NEJM 2004(Jul 8);351:125-135.

28. Summary This paper does not address PSA screening ability. Demonstrates substantial CaP even with very low PSA. Study in progress with mortality as outcome (Ref 29). Studies in progress using additional markers for early detection and of CaP (Ref 30). Possible prediction error in any study due to lab error in measuring PSA. Here, if large, say 20%, 20% error =~ 10% error in Prob(CaP).