Prostate-specific antigen markers

Prostate-specific antigen doubling time is the most popular PSA kinetic measure used to identify those patients on AM who need clinical review. PSADT is calculated from a model of log(PSA) against time:

The doubling time is then calculated as log(2)/β and is interpreted as the estimated time for a man’s PSA to double. Thus, low values of doubling time coincide with rapidly rising PSA and are a cause for concern. Conversely, high values correspond to a steady trend of PSA, and those patients above a threshold of PSADT are advised to remain on monitoring. For a patient’s doubling time to be calculated using the regression method, at least three PSA test results are required. We consider a PSADT of < 3 years to be a marker for rapidly rising PSA.^79,84,86,89

An alternative to PSADT is PSAv. This explicitly measures the rate of change in PSA over time calculated as the slope term (β) from a model of PSA against time on monitoring:

Given that PSAv is the rate of increase of PSA, low positive values refer to steady PSA change and high PSAv equates to sharply increasing PSA. Several studies have used a threshold of PSAv > 1 ng/ml/year^22,71,100 as a trigger for clinical review during monitoring. For this paper, we have calculated each man’s PSAv at each visit beyond their third (calculation of PSAv requires at least three observations of PSA). We have used PSAv > 1 ng/ml/year as a marker for rapidly rising PSA.

Prostate-specific antigen reference ranges have been established as alternatives to these two PSA kinetic measures.³³ A model for such reference ranges has been previously developed⁹³ on a cohort of 512 men enrolled in the AM arm of the ProtecT trial.¹⁵ For example, a 95% reference range, above which the fastest increasing 5% of men with clinically localised PCa lie, is constructed as:

where $\widehat{PSA}$ and $\mathit{var}(\widehat{PSA})$ are found using the ProtecT trial model described in Chapter 3. If subsequent PSA test results fall above this reference range, this implies that the patient’s PSA growth is above what would be expected as a result of normal ageing, such that a recommendation for clinical review could be warranted (e.g. Figure 8). Using the reference range model, we calculate whether or not a man’s PSA result is inside the reference range at each visit; if it falls outside the reference range, this suggests an increasing PSA beyond expected normal changes and that further clinical review may be necessary.

FIGURE 8

An example of a PSARR. The PSA result represented by a triangle would lead to a recommendation for clinical review.

Study populations

The PSA markers were tested on the RMH AS cohort and the SPCG4 and UCHC WW cohorts described in Chapter 4, Methods, Study populations (see also Table 24). The data were again restricted to remove any single PSA test result > 50 ng/ml and any man with a PSA at diagnosis of > 20 ng/ml. Hence, the sample sizes differ (Table 12 and see Table 25).

TABLE 12

Summary of PCa outcomes used for validation in each cohort, with the percentage positive for each outcome during cohort follow-up

Outcomes

All-cause mortality data from UCHC are not used in this analysis to validate reference ranges, because they probably contain many non-PCa-related deaths. Although the data from RMH include PCSM, no such deaths are reported. To exploit these cohorts fully, we introduce outcomes pertaining to a PSA milestone, namely whether or not a man reaches a PSA of 20 ng/ml during follow-up. The outcomes used for validation, along with the proportion of men experiencing these outcomes, are given in Table 12. Given that it is not clinically useful to have an alert (through PSADT, PSAv or PSARRs) close to, say, PCSM, we have only included those alerts occurring at least 5 years prior to PCSM or metastases and 2 years prior to reaching a PSA of 20 ng/ml.

Statistical analysis

Statistical analyses were performed in Stata 12.⁷⁰ We report results solely for men with Gleason score of 3 + 3, because this low-risk group represents the vast majority of modern AM cohorts.¹⁷ We first compared 90%, 95% and 99% PSARRs to choose the optimal cut-off for rapidly rising PSA using the area under the receiver operator characteristic (ROC) curve statistic for onset of metastases and PCSM in SPCG4. Cox proportional hazards (Cox PH) models¹⁰⁵ were used to estimate the association between markers and time-to-event outcomes. Time zero was set to be the date of beginning of monitoring, whereas date of an event or end of monitoring was the time at risk. For each cohort we fit a base model controlling for T-stage (where applicable), baseline PSA and baseline age. We report the HRs for each PSA marker and outcome, together with their 95% CIs. Finally, we compare PSADT, PSAv and PSARR using the difference of deviances from the Cox models using each of these in turn. A better model will have a lower deviance (see Table 16).

TABLE 16

Differences in deviance (predictive ability) between the three PSA marker models

The ability of each PSA marker to discriminate between higher- and lower-risk men is calculated using Harrell’s concordance statistic (or c-statistic) from each Cox PH model.^105,106 This is equivalent to an area under the ROC curve for time-to-event responses, such as those of interest here. The c-statistic estimates the probability that, of two randomly chosen men, the man with the higher-predicted probability of an outcome will reach an outcome before the patient with the lower-risk score. By adding each PSA marker in turn to the baseline models, we can compare the change caused by the marker, by looking at the difference in c-statistic from base model to marker model.

Metastases

Using an alert based on PSARR alone to recommend clinical review would miss 15 out of 30 future metastatic cancers (sensitivity 50%, 95% CI 31% to 69%) while causing 38 unnecessary rebiopsies to be performed in the 107 men with non-life-threatening disease (specificity 65%,95% CI 55% to 74%). The PSADT < 3-year marker would lead to 13 missed metastatic cancers out of 30 (sensitivity 57%, 95% CI 37% to 75%; Table 13) and would unnecessarily biopsy 42 of the 107 men with disease that would not progress to metastases during the follow-up of the cohort (specificity 61%, 95% CI 51% to 70%). Finally, the PSAv > 1 ng/ml/year marker alone would miss just eight of the 30 future metastatic cancers (sensitivity 73%, 95% CI 54% to 88%) but would cause 70 unnecessary biopsies (specificity 35%, 95% CI 26% to 45%).

TABLE 13

Sensitivity and specificity comparing the PSA markers in alerting men with onset of metastases

Initial age, PSA and T-stage were not useful to identify those men developing metastases (c-statistic = 0.58, see Table 15). There was weak evidence of positive associations between the PSADT marker (HR 2.1, 95% CI 0.97 to 4.4) and PSARR (HR 2.4, 95% CI 0.9 to 6.7) and development of metastases (see Table 15), and no evidence that men alerted by the PSAv > 1 ng/ml/year marker were more likely to develop metastases in the future (HR 1.1, 95% CI 0.5 to 2.7; see Table 15). However, the PSA markers slightly improved the discriminative ability of the baseline model, with increases in c-statistic of 9% (PSADT), 7% (PSARRs) and 2% (PSAv). Comparing the PSA marker models, there was some weak evidence of a better predictive ability using doubling time over velocity (p = 0.06; see Table 16).

TABLE 15

Hazard ratio and c-statistic improvements for the three PSA markers on each of the four outcomes

Prostate cancer-specific mortality

The PSARR marker led to 56% sensitivity (95% CI 31% to 79%; Table 14) and 61% specificity (95% CI 52% to 70%) when used alone to determine which men would die from PCa. This would mean that 8 out of 18 men with lethal cancer would be missed by the PSARR, and 48 unnecessary biopsies would be performed. Using the PSADT marker alone would miss 6 out of 18 lethal cancers (sensitivity 67%, 95% CI 41% to 87%) and cause 52 unnecessary rebiopsies to be performed in the 124 men without lethal cancer (specificity 58%, 95% CI 49% to 67%). If the PSAv marker were used as a standalone recommendation for clinical review, just three of the 18 lethal cancers would be missed (sensitivity 83%, 95% CI 59% to 96%), but 83 unnecessary biopsies would be performed in the 124 men with non-life-threatening disease (specificity 33%, 95% CI 25 to 42%).

TABLE 14

Sensitivity and specificity comparing the PSA markers in alerting men with PCa specific mortality

A model using baseline characteristics of PSA, T-stage and age was not useful to discriminate between those who died as a result of PCa and those who did not (c-statistic = 0.53; Table 15). Those men with a PSADT < 3 years were more likely to die from PCa (HR 3.2, 95% CI 1.1 to 9.2) and this improved the c-statistic from the baseline model by 0.13 (25%). There was some weak evidence for an association between PSARR (HR 3.3, 95% CI 0.9 to 12.1) and little evidence for an association between PSAv (HR 2.1, 95% CI 0.6 to 7.7) and death from PCa. There was some weak evidence that the PSADT model was a better predictor of outcome than the PSAv (p = 0.05; Table 16) model.

Reaching a prostate-specific antigen of 20 ng/ml during surveillance

In the RMH cohort, baseline age, PSA and T-stage had a moderate discriminative ability in separating men who would reach a PSA of 20 ng/ml (c-statistic = 0.74; see Table 15). There was no evidence that those men with a PSA outside their reference ranges were more likely to reach a PSA of 20 ng/ml (HR 1.5, 95% CI 0.5 to 4.1), and including PSARR only trivially improved the c-statistic. There was some evidence that men with a PSADT < 3 years were more likely to reach a PSA of 20 ng/ml (HR 2.2, 95% CI 1.0 to 4.6); including PSADT improved the c-statistic by 0.03 (5%). Those who would have been alerted by a PSAv > 1 ng/ml/year were more likely to reach a PSA of 20 ng/ml (HR 10.8, 95% CI 1.5 to 80.8). The PSAv marker led to an increase of 0.05 (7%) in the c-statistic from the baseline model. Comparing these models, the PSAv marker model was preferred to those including PSARR (p = 0.001; see Table 16) and PSADT (p = 0.006), with some weak evidence that the PSADT model improved on the PSARR model (p = 0.06).

For the UCHC data, baseline age and PSA were highly discriminative of reaching PSA 20 ng/ml in at least 2 years, with a c-statistic for the baseline model of 0.82 (see Table 15). Men with a PSA result over their PSARR were more likely to reach 20 ng/ml (HR 12, 95% CI 5.4 to 26.9; see Table 15). Given that there are very few men in the Gleason score of 3 + 3 category who reach a PSA of 20 ng/ml, the CI is very imprecise. Including PSARR led to an increase in c-statistic of 0.03 (4%) over the baseline model. Associations were found between both PSADT (HR 6.0, 95% CI 2.8 to 12.8) and PSAv (HR 4.3, 95% CI 2.5 to 7.5) and reaching a PSA of 20 ng/ml in the UCHC cohort. The inclusion of each of these markers led to increases of 0.02 over the baseline model, or 3%. There was strong evidence that the PSARR model had a higher predictive ability than both the PSAv and PSADT models (both p < 0.0001; see Table 16).