Background The sensitivity and specificity of a screening testare biased when disease status is not verified in all subjectsand when the likelihood of confirmation depends on the testresult itself. We assessed the screening characteristics ofthe prostate-specific antigen (PSA) measurement after correctionfor verification bias.
Methods Between 1995 and 2001, 6691 men underwent PSA-basedscreening for prostate cancer. Of these men, 705 (11 percent)subsequently underwent biopsy of the prostate. Under the assumptionthat the chance of undergoing a biopsy depends only on the PSA-testresult and other observed clinical variables, we used a mathematicalmodel to estimate adjusted receiver-operating-characteristic(ROC) curves.
Results Adjusting for verification bias significantly increasedthe area under the ROC curve (i.e., the overall diagnostic performance)of the PSA test, as compared with an unadjusted analysis (0.86vs. 0.69, P<0.001, for men less than 60 years of age; 0.72vs. 0.62, P=0.008, for men 60 years of age or older). If thethreshold PSA value for undergoing biopsy were set at 4.1 ngper milliliter, 82 percent of cancers in younger men and 65percent of cancers in older men would be missed. A digital rectalexamination that is abnormal but not suspicious for cancer doesnot affect the overall performance characteristics of the test.
Conclusions A lower threshold level of PSA for recommendingprostate biopsy, particularly in younger men, may improve theclinical value of the PSA test.
About 75 percent of men in the United States who are 50 yearsof age or older have undergone screening for prostate cancerby measurement of prostate-specific antigen (PSA).1 Controversyexists as to whether the traditional threshold for recommendingprostate biopsy, a PSA level of 4.1 ng per milliliter, shouldbe lowered to improve the sensitivity of the test.2,3 An improvementin sensitivity would, however, reduce the specificity of thetest and thereby lead to an increase in the number of unnecessarybiopsies. Correction for verification bias improves the estimatedsensitivity and specificity of the test and permits better-informeddecisions to be made about recommendations for prostate biopsy.
Verification bias occurs when disease status (e.g., the presenceor absence of biopsy-confirmed prostate cancer) is not determinedin all subjects who are tested and when the probability of verificationdepends on the test result, other clinical variables, or both.When verification of disease status is more likely among menwith positive tests, a bias is introduced that can markedlyincrease the apparent sensitivity of the test and reduce itsapparent specificity (Figure 1). For the PSA test, the probabilitythat disease status will be determined by biopsy depends onthe results of the PSA test and the digital rectal examinationand on age, race, and the presence or absence of a family historyof prostate cancer.6,7,8,9 In an ideal situation, unbiased estimatesof the sensitivity and specificity of the PSA test could beobtained by requiring each man in a randomly selected screeningpopulation to undergo both PSA testing and biopsy. There is,however, a mathematical method to correct for verification bias.10We used this method to obtain more accurate estimates of thediagnostic characteristics of the test for total PSA.
Figure 1. An Example of the Change in Sensitivity and Specificity with Correction for Verification Bias, Based on a Study of Exercise Testing and Confirmation with Coronary Angiography.
Verification bias is evident in the two-by-two table on the left. Only some of the patients with negative test results undergo confirmatory testing, leading to an apparent sensitivity of 67 percent and an apparent specificity of 73 percent. If fewer patients with negative results undergo confirmatory testing, then patients with false negative results are underrepresented, and the sensitivity in the biased sample is overestimated. In the two-by-two table on the right, confirmatory testing in all patients increases the number of patients with negative results. The numbers of patients not included in the analysis on the left are shown in bold; the numbers of patients in the true-negative and false-negative cells each increase by a factor of 2.5 over the totals in the respective cells in the left-hand table. The result is an unbiased estimate of the characteristics of the test. The unbiased sensitivity decreases to 44 percent and the specificity increases to 87 percent. In each table, the number of true positives is shown in cell A and the number of false negatives in cell C. Data are from Froelicher et al.4 and Gianrossi et al.5
Methods
Selection and Evaluation of Patients
Between May 1995 and November 2001, 6691 consecutive eligiblemen were enrolled in a screening study at the Washington UniversitySchool of Medicine, in St. Louis, and underwent both measurementof total PSA and a digital rectal examination. Before May 2000,the PSA tests were performed with an enzyme immunoassay (Tandem-EPSA, Hybritech). Beginning in May 2000, the chemiluminescencemethod on the Access Analyzer (Beckman Coulter) with PSA antibody(Hybritech) was used. To be enrolled, men had to be 50 yearsof age or older; the exceptions were men who had a family historyof prostate cancer or who were black, in which case the minimalage was 40. A previous prostate biopsy or diagnosis of prostatecancer, the use of finasteride, active urinary tract infection,and prostatitis were exclusion criteria. We selected a studyperiod during which the criterion for a recommendation for biopsywas consistent; specifically, biopsy was recommended if PSAvalues were greater than 2.5 ng per milliliter or the findingson digital rectal examination were suspicious for prostate cancer.Neither the patient nor the physician recommending biopsy wasprovided the free PSA value if it was measured.
All biopsies were ultrasound-guided, and in 89 percent of biopsies,five to eight cores were removed. Although prospective studieshave indicated that increasing the number of cores improvesthe detection of cancer,11,12,13 a randomized trial showed thatincreasing the number of cores from 6 to 12 did not improvecancer detection.14 We therefore did not expect the variationin the number of cores to affect our analyses significantly.Moreover, to compensate for any missed cancers, a diagnosisof prostate cancer up to 18 months after the first PSA testwas considered evidence that prostate cancer was present atthe time of the initial biopsy. Of the 705 men who underwentprostate biopsy (11 percent of the total), 182 received a diagnosisof prostate cancer. We used the PSA value from the initial enrollmentvisit to determine the sensitivity and specificity of the testat various cutoff values. Comparison of the characteristicsof the men who underwent biopsy with the characteristics ofthe men who did not was performed with the use of t-tests fornormal continuous variables, Wilcoxon tests for non-normal variables,and chi-square tests for categorical covariates; two-sided Pvalues are reported.
Estimation of Receiver-Operating-Characteristic Curves
Receiver-operating-characteristic (ROC) curves are plots ofthe sensitivity versus 1 minus the specificity; each point alongthe curve is specific for a particular threshold value for biopsy.We estimated unadjusted ROC curves calculated for the sampleof 705 men who underwent biopsy. PSA levels were categorizedinto ranges that resulted in adequate separation between thepoints on the ROC curve (for men less than 60 years of age,the categories were 0.8 ng per milliliter or less, 0.9 to 1.3ng per milliliter, 1.4 to 2.5 ng per milliliter, 2.6 to 4.0ng per milliliter, 4.1 to 6.0 ng per milliliter, and 6.1 ngper milliliter or greater; for men aged 60 years of age or older,they were 1.0 ng per milliliter or less, 1.1 to 2.0 ng per milliliter,2.1 to 4.0 ng per milliliter, 4.1 to 6.0 ng per milliliter,6.1 to 10.0 ng per milliliter, and 10.1 ng per milliliter orgreater).
ROC-curve analyses were performed with ROC Analyzer software(developed by Centor and Keightley, University of Alabama, Birmingham).Areas under the curve were calculated by the trapezoidal (nonparametric)method and compared by methods proposed by Hanley and McNeil,15with two-sided P values. An area under the curve of 1.0 indicatesa test with perfect discrimination between subjects with diseaseand those without disease, whereas an area under the curve of0.5 indicates a test with no discriminatory power.
Correction for Verification Bias
We used the method of Begg and Greenes,10 which corrects forverification bias by adjusting for the verification process,to estimate the sensitivity and specificity of the PSA testin the entire population undergoing the test and not just inthe subgroup in which disease status was verified by prostatebiopsy. The key assumption of this method is that the chancethat a man will undergo prostate biopsy depends only on observedvariables (e.g., the PSA level or the results of digital rectalexamination) and not on the presence or absence of cancer, whichcannot be directly observed.
To apply this method, we first estimated the probability ofcancer as a function of clinical variables, using a logistic-regressionmodel, in the sample in which disease status was verified bybiopsy. The variables included in the model were the resultsof digital rectal examination (prostate abnormal or enlarged,suspicious for cancer, or normal), race (black vs. other), familyhistory with respect to prostate cancer (present vs. absent),and category of PSA-test result. Separate models were constructedfor men under the age of 60 years (4556 men, with disease statusverified in 316) and those 60 years of age or older (2108 men,with disease status verified in 388), because the higher incidenceof benign prostatic hyperplasia in older men is hypothesizedto reduce the specificity of the test in this group.16,17,18(Data on age were not available for 27 men.) We then used thefitted logistic-regression model obtained from the subgroupundergoing biopsy to predict the probability of prostate cancerin the entire group, according to the specified covariates.From this analysis, we derived an adjusted ROC curve by calculatingthe probability of being in a particular PSA test-result categoryfor men in the entire sample with and without prostate cancer.We then compared the adjusted ROC curves with the unadjustedcurves, using the methods proposed by Hanley and McNeil,15 withtwo-sided P values and standard errors based on the number ofmen undergoing biopsy (316 younger men and 388 older men).
Results
As compared with the men who did not undergo biopsy, those whodid were on average 5.4 years older and had a median PSA valuethat was 2.4 ng per milliliter higher, and were 1.6 and 6.7times as likely to have an abnormal or suspicious digital-examinationresult, respectively (Table 1).
Table 1. Characteristics of Men According to Whether the Results of the PSA Test Were Verified by Biopsy.
After adjustment for the results of the PSA test and digitalrectal examination, we found that within the subgroup of menwho had a biopsy, black race was significantly associated withprostate cancer for those under the age of 60 years (odds ratio,2.75; P=0.004) but not for those 60 years of age or older (oddsratio, 1.56; P=0.19). Having a family history of prostate cancerwas not significantly associated with prostate cancer amongeither the younger men (odds ratio, 0.79; P=0.49) or the oldermen (odds ratio, 1.17; P=0.62).
Figure 2 shows the estimates of the ROC curves, both adjustedand unadjusted for verification bias. For a particular PSA valueused as the threshold for the recommendation of prostate biopsy,the points on the adjusted ROC curve were to the lower leftof the corresponding points on the unadjusted curve (indicatinglower sensitivity and higher specificity). In addition, theareas under the ROC curves were significantly greater (indicatingbetter diagnostic accuracy) for the adjusted curves. In menunder the age of 60 years, the adjustment increased the areaunder the curve from 0.69 to 0.86 (P<0.001). For men 60 yearsof age or older, the area under the curve increased from 0.62without adjustment to 0.72 after adjustment (P=0.008). The PSAtest performed significantly better in men under the age of60 years than in older men (P<0.001).
Figure 2. Adjusted and Unadjusted Receiver-Operating-Characteristic (ROC) Curves for Men under 60 Years of Age and Men 60 Years of Age or Older.
Sensitivity and 1 minus specificity (ROC curves) are shown at various threshold values of prostate-specific antigen (PSA) for the recommendation of biopsy in men under the age of 60 years (Panel A) and men 60 years of age or older (Panel B). The numbers in boxes are the PSA threshold values in nanograms per milliliter. A perfect test would have 100 percent sensitivity and 100 percent specificity and would include a point at the upper left-hand corner. The curve for a test with no discriminatory power would appear as a diagonal line from the lower left to the upper right corner. Correcting for verification bias improves the overall characteristics of the PSA test by bringing the curve closer to the upper left-hand corner.
The sensitivity and specificity of the PSA test at selectedthreshold PSA levels, after adjustment for verification bias,are shown in Table 2. The sensitivity and specificity for thresholdvalues not used in the analysis can be approximated by linearinterpolation from the reported values. For men under 60 yearsof age, if a PSA value of 4.1 ng per milliliter were used asthe threshold for a recommendation of biopsy, the test wouldhave a sensitivity of 0.18, so that 82 percent of prostate cancerswould be missed, but it would have a specificity of 0.98, sothat only 2 percent of men without prostate cancer would undergobiopsy. The unadjusted estimates of sensitivity and specificitywere 0.43 and 0.77, respectively, at this threshold value inthe younger age group. In men 60 years of age or older, a testwith the same threshold of 4.1 ng per milliliter used for arecommendation of biopsy would have a sensitivity of 0.35, sothat 65 percent of prostate cancers would be missed, but itwould have a specificity of 0.88, so that 12 percent of menwithout prostate cancer would undergo biopsy. The unadjustedestimates for this threshold in older men were 0.57 for sensitivityand 0.60 for specificity.
Table 2. Characteristics of the PSA Test after Adjustment for Verification Bias, According to Age.
Figure 3 shows the adjusted ROC curves for men with a normaldigital rectal examination and men with a digital rectal examinationindicating benign hyperplasia (suspicious results were excludedfrom this analysis). Among men under the age of 60 years, theROC areas under the curve were 0.86 for those with a normaldigital rectal examination and 0.84 for those with an abnormaldigital rectal examination (P=0.82). Likewise, for men 60 yearsof age or older, the areas under the curve did not differ significantlywhen the data were stratified according to the results of thedigital rectal examination, with a value of 0.71 for men withnormal results and 0.72 for men with abnormal results (P=0.94).
Figure 3. Adjusted Receiver-Operating-Characteristic (ROC) Curves for Men under 60 Years of Age and Men 60 Years of Age or Older, According to the Results of Digital Rectal Examination.
The ROC curves are shown for men with abnormal results on digital rectal examination (DRE) (enlarged prostate, but not suspicious for cancer) and those with normal results, after correction for verification bias. Panel A shows the results for men under 60 years of age, and Panel B shows the results for older men. The numbers in boxes are the threshold values of prostate-specific antigen (PSA) in nanograms per milliliter for the recommendation of biopsy. In each age group, the overall shape of the ROC curve did not differ significantly according to the results of the digital rectal examination. However, the sensitivity and 1 minus specificity of the PSA test at a given threshold value did change. At each threshold value, the test had a lower sensitivity and a higher specificity in the group with a normal digital rectal examination than in the group with an abnormal examination.
Although the curves did not change significantly after datafrom men with abnormal results of the digital rectal examinationand data from those with normal results were separated, thecutoff points differed between these groups, with increasedsensitivity and decreased specificity for each PSA thresholdin the group of men who had abnormal examination results ascompared with the group of men who had normal results. Thisdifference can be explained by a shift toward higher PSA levelsin all men with abnormal results on digital rectal examination.
Discussion
We found that correction for verification bias improved theestimated sensitivity and specificity of the PSA test for ascreened population. Unadjusted estimates of areas under theROC curve for the PSA test have been reported to be as low as0.52.19 Our analysis showed that, after adjustment for verificationbias, the area under the ROC curve increased, providing evidenceof an increase in the discriminatory power of the PSA test.The estimated geometric mean of PSA levels derived from theadjusted ROC curves for men with prostate cancer ranged from2.1 to 3.9 ng per milliliter, depending on age and the resultsof the digital rectal examination. These values are significantlylower than the levels of 6.3 and 7.5 ng per milliliter reportedin a previous study.20 The discrepancy between these valuessuggests a strong selection bias in the latter study, the resultsof which were unadjusted, and in which men with higher PSA valueswere more likely to receive a diagnosis of prostate cancer,resulting in inflation of the sensitivity of the test. Thisbias led to the incorrect assumption that the PSA test has nearlyperfect discriminatory power, with the area under the curvein that study ranging from 0.91 to 0.94.20 The adjusted estimatesof specificity from our analysis are similar to the ranges reportedby Oesterling et al.21 However, in that study, men without diseasewere randomly selected to undergo biopsy, thereby avoiding verificationbias.
Analyses according to the results of the digital rectal examination(an abnormal or enlarged prostate vs. a normal prostate, excludingsuspicious results) revealed that the ROC curves have the sameoverall diagnostic performance, but with altered cutoff points.This result is consistent with a constant shift to higher PSAlevels in all men with abnormal results on the digital rectalexamination, regardless of disease status, and suggests thatthe threshold value for recommending biopsy should be higheramong men with abnormal findings on digital rectal examination.The use of PSA density, in which increased values of PSA areadjusted for prostate size, follows the same principle.
Our study was limited by the use of prostate biopsy as the goldstandard; this choice may have resulted in underestimation ofthe adjusted sensitivity of the test because the small amountof tissue removed may have introduced sampling error. To reducethis possibility, we used all diagnoses of cancer made within18 months after PSA screening in calculating outcomes. Thismethod may have introduced bias, however, because patients withrising PSA levels may be more likely to have additional biopsies.We therefore removed such men from the analysis (78 men, 44of whom had cancer) and reestimated the adjusted ROC curves.A rising PSA level did not alter the ROC curves (results notshown), but the shift in the adjusted cutoff points to the lowerleft of the unadjusted points was less for younger men. Moreover,there may be variables besides age, PSA level, results on digitalrectal examination, race, and family history that both predictthe chance of undergoing prostate biopsy and are related tounderlying disease status. This is a problem with retrospectivestudies. In addition, although our analysis was based on 705men with verified disease status from a subgroup of 6691 men,the results may be applicable only to a volunteer population.
The prospective Prostate Cancer Prevention Trial conducted bythe Southwest Oncology Group may provide unbiased estimatesof the sensitivity and specificity of the PSA test that arenot limited by verification bias, since all men in the trialunderwent biopsy at the completion of the study.22 We studiedonly total PSA measurements, which are commonly used in theprimary care setting for screening.23 Measurements other thantotal PSA, such as PSA velocity, PSA density, and free PSA,may provide more discriminatory power and further improve thetest. Nevertheless, an analysis of data from the Physicians'Health Study showed that a single measurement of total PSA hadrelatively high sensitivity and specificity for the detectionof prostate cancer diagnosed within four years after the test.24That study sought to minimize verification bias by assessingthe relation between PSA levels in base-line serum samples andthe subsequent diagnosis of prostate cancer. For a populationwith a mean age of 63 years at the time of PSA testing, thesensitivity and specificity of a threshold value of 4.1 ng permilliliter were 0.46 and 0.91, respectively.24 The latter valueis close to the 88 percent specificity found for the adjustedestimates with a threshold value of 4.1 ng per milliliter inour analysis for men who were at least 60 years old. The sensitivityof 0.35 for the threshold value of 4.1 ng per milliliter inour study may be lower than 0.46, since the Physicians' HealthStudy used a casecontrol design and included only clinicallyevident cancers, whereas we sought to account for all prostatecancers.
The ideal threshold value for a recommendation of prostate biopsydepends on the tradeoff between false positive and false negativeresults. Our analysis therefore did not address which PSA thresholdis optimal, but it does show the implications of following currentscreening recommendations. We found that lowering the thresholdfor biopsy from 4.1 to 2.6 ng per milliliter in men youngerthan 60 years would double the cancer-detection rate from 18percent to 36 percent, whereas the specificity would fall onlyfrom 0.98 to 0.94. Other studies of men who underwent biopsyshowed that the use of PSA cutoff values between 2.6 and 4.1ng per milliliter yielded a positive predictive value of 22to 25 percent, findings that are similar to the positive predictivevalue for higher PSA levels and consistent with the doublingin sensitivity in our analysis resulting from lowering the thresholdfor biopsy to 2.6 ng per milliliter.2,21,25
In conclusion, we found that prior estimates of unadjusted sensitivityare significantly higher than adjusted estimates. Moreover,unadjusted values for specificity underestimate the true specificityof the PSA test. Both of these findings support the use of alower threshold PSA value for a recommendation of biopsy. Earlydetection may increase the probability that the disease is confinedto the prostate,3,26 and patients with such confined diseasemay be more likely to be free from PSA failure after treatment.27These findings, as well as recent data from a randomized trialshowing that prostate-cancer treatment improves disease-freesurvival,28 indicate that reduction of the threshold PSA levelat which biopsy is recommended to 2.6 ng per milliliter, atleast in men under 60 years of age, may be reasonable.
Supported in part by a fellowship from the Agency for HealthcareResearch and Quality, Department of Health and Human Services(T32 HS00020-16) and by a grant from Beckman Coulter.
We are indebted to Dr. Marc Sabatine for his invaluable guidanceon the manuscript, to Dr. Jerome Richie and Dr. Andrew K. Leefor helping us to establish our collaboration, and to Dr. JayHarris and Dr. Akila Viswanathan for their critical reviewsof the manuscript.
Source Information
From the Joint Center for Radiation Therapy, Harvard Medical School, Boston (R.S.P.); the Department of Radiation Oncology, Brigham and Women's Hospital and the DanaFarber Cancer Institute, Boston (A.V.D.); the Division of Urologic Surgery, Washington University School of Medicine, St. Louis (W.J.C., K.A.R.); the Department of Urology, Northwestern University, Fineberg School of Medicine, Chicago (W.J.C.); and the Department of Health Policy and Management, Harvard School of Public Health, Boston (K.M.K.).
Address reprint requests to Dr. Kuntz at the Center for Risk Analysis, Harvard School of Public Health, 718 Huntington Ave., Boston, MA 02115-5924, or at kmk{at}hsph.harvard.edu.
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