Biostatistics Case Studies

Peter D. Christenson

Biostatistician

http://gcrc.humc.edu/Biostat

Session 2: Diagnostic Classification

Case Study

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.

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.

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=85 N=27

N=19/85=22% N=18/27=67%

PSA<4.0 PSA≥104.0≤PSA<10

?

Abnormal DRE / US

CaP in biopsy

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.

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.

Current Paper: Thompson et al, 2004.

Main Results

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

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.

Scenario 1: PSA is useless

420

PSA

Ca

P

No

Yes

24.4% 24.4%

Scenario 2: PSA is a perfect test

420

Yes

No

PSA

Ca

P

0 / 2950 = 0%

1187 / 1187 = 100%

Scenario 3: Almost perfect association

% C

aP

PSA4.02.0

90

70

50

30

10

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).

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.

PSA Screening Ability in Scenario 3using PSA>4.0

Sensitivity = 820/(820+449) = 65%

Specificity = 2501/(2501+367) = 87%

% C

aP

PSA4.02.0

90

70

50

30

10

+ CaP: N= 449- CaP: N=2501

+ CaP: N=820- CaP: N=367

PSA Screening Ability in Scenario 3using PSA>2.0

Sensitivity = 987/(987+282) = 78%

Specificity = 1993/(1993+875) = 55%

% C

aP

PSA4.02.0

90

70

50

30

10

+ CaP: N= 282- CaP: N=1993

+ CaP: N=987- CaP: N=875

Conclusions from ScenariosAssociation ≠ screening accuracy.

Good* screening needs something more like:

*Few unnecessary biopsies, but detect most serious CaP.

% C

aP

PSA4.02.0

75

55

35

15

Back to Actual Results:

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

Revised Table 2:Prevalence of CaP and its Precision

95% CI for CaP Prevalence

PSA Range Any Grade High Grade

≤ 0.50 6.6 ± 2.2% 0.8 + 0.8%

0.6 – 1.0 10.1 ± 2.1% 1.0 ± 0.7%

1.1 – 2.0 17.0 ± 2.4% 2.0 ± 0.9%

2.1 – 3.0 23.9 ± 3.9% 4.6 ± 1.9%

3.1 – 4.0 26.9 ± 6.4% 6.7 ± 3.6%

≤ 4.0 15.2 ± 1.3% 2.3 ± 0.5%

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.

Figure 2: Models P(CaP)=function(PSA)

Risk=

P(CaP)

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.

109876543210

80

60

40

20

0

PSA

P(

Ca

P )

Figure 2 Logistic Model

Table 2 CIs? after PSA>4

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.

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;

Software Output: SAS

Odds Ratio Estimates

Point 95% WaldEffect 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

Combined Screening and Prognosis ?

PSAOtherPre-

Biopsy1

BiopsyCharacter-

istics2

Risk ofCaP

Death

Biopsy

Biopsy

Moderate

Low

High

Neg

Neg

Pos

Pos

1 Such as PSA velocity2 Such as prostate volume See NEJM 2004(Jul 8);351:125-135.

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).