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Review |
1 Department of Clinical Biochemistry, Hillerød Hospital, Hillerød, Denmark.
2 Department of Urology, Prostate Center, University of Münster, Münster, Germany.
3 Euro/DPC Limited, Gwynedd, United Kingdom.
4 Department of Medicine II, Grosshadern Hospital, University of Munich, Munich, Germany.
5 NOKLUS, Norwegian Quality Improvement of Primary Care Laboratories, Division For General Practice, University of Bergen, Bergen, Norway.
6 Department of Urology, Rudolfstiftung, Vienna, Austria.
7 Roche Diagnostics GmbH, Mannheim, Germany.
8 Centre for the Study of Biological Markers of Malignancy, General Regional Hospital Campo SS., Venice, Italy.
9 Department of Urology, Cantonal Hospital, St. Gallen, Switzerland.
10 Department of Urology, University Hospital of Leuven, Leuven, Belgium.
aAddress correspondence to this author at: Department of Clinical Biochemistry, Hillerød Hospital, Helsevej 2, 3400 Hillerød, Denmark. Fax 45-4824-0067; e-mail geso{at}fa.dk.
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Abstract |
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Methods: The survey yielded 27 studies addressing the topic, and estimates for the biological variation of tPSA could be derived from 12 of these studies.
Results: The mean biological variation was 20% in the concentration range 0.1–20 µg/L for men over 50 years. The biological variation means that the one-sided 95% confidence interval (CI) of the dispersion for a single tPSA result is 
33%. Three replicate samples with one analysis on each narrow the one-sided 95% CI for the mean concentration to 20% and facilitate decisions on prostate biopsy. During monitoring of serial measurements, the change needed for significance is 50% (P <0.05).
Conclusions: The biological variation of tPSA has implications for screening, diagnosis, and monitoring. Single measurements may not be sufficiently precise for screening and diagnosis. Replicate samples and calculation of the mean concentration may improve precision by reducing the dispersion. Monitoring of tPSA requires an estimate of either the change needed for significance or, alternatively, of the significance of the change.
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Introduction |
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In conducting this review, the goals of the European Group on Tumor Markers (EGTM) were (a) to determine whether a sound estimate for the biological variation of tPSA could be derived from a survey of published studies; (b) to illustrate, by examples, how biological variation can affect the interpretation of single, replicate, and serial tPSA results; and (c) to provide guidance and recommendations for interpretation of single, replicate, and serial tPSA measurements in urologic practice.
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Methods |
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statistics
The statistical definitions and calculation procedures to estimate the impact of CVa and CVb on tPSA results are mentioned in the text when appropriate and are based on a recent review (7). The arithmetic mean CVb values compiled in different groups were compared with ANOVA supplied with the 2-sided t-test for further comparison. The weighted average CVb for a group was weighted by the degrees of freedom (DF) calculated from the number of persons in each subgroup as well as the number of samples per person. For example, where 3 subgroups are considered, the formula used is:
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where DF is the number of persons x (number of samples per person – 1) (11).
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Results |
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biological variation estimates
The literature survey identified 27 original articles addressing the biological variation concept of tPSA (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47). Three studies reported data for biological variation directly, rendering further calculations unnecessary (23)(24)(25). Nine studies reported the CVt for tPSA, i.e., the sum of the analytical and biological variation, as well as the CVa (21)(22)(26)(27)(28)(29)(30)(31)(32). We subsequently back-calculated the CVb by subtracting CVa from CVt: CVb = 
(7). Fifteen studies reported considerable variability of serial tPSA concentrations, but it was impossible to derive the CVb because of sufficient information on CVt and CVa was lacking (33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47).
The CVb estimates are listed in Table 1
in descending order by length of monitoring period. The monitoring periods clustered into 3 main groups: days, weeks, and months. For days monitoring, the arithmetic mean CVb was 10% (range, 2.1%–19.6%) and derived from 303 individuals. For weeks monitoring, the arithmetic mean CVb was 15% (range, 14%–16.1%) and derived from 131 individuals. For months monitoring, the arithmetic mean CVb was 20% (range, 18.1%–22.9%) and derived from 890 individuals. All 3 groups included patients with prostate cancer as well as persons without malignant prostatic disease.
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The difference in CVb among study groups with days, weeks, and months monitoring was significant (ANOVA, P <0.05). Supplementary 2-sided t-tests showed a significant increment of CVb among all 3 groups (P <0.05). The increasing CVb results cannot be explained solely by population heterogeneity of the compared groups. For example, the CVb from similar subpopulations increased with the length of the monitoring periods, e.g., for healthy persons, the mean CVb was 9.6% (range, 8.6%–10.5%) for days monitoring (32) (1 study, 2 populations), 15% (range, 14%–16.1%) for weeks monitoring (21)(31), and 18.4% (range, 18.1%–18.6%) for months monitoring (23)(28). In addition, the CVb ranges from different subpopulations overlapped within the monitoring periods, e.g., for days monitoring the mean CVb was 11.9% (range, 2.1%–19.6%) for prostate cancer patients (22)(25)(26) and 9% (range, 8.6%–10.5%) for healthy persons (32) (1 study, 2 populations; Table 1
). More likely, the increasing CVb results are explained by the length of the monitoring period and the sampling interval. This relationship between CVb and monitoring interval is a general characteristic of biochemical compounds controlled by homeostatic regulation. If tests are performed frequently, serial results will not be random but will be auto-correlated (7). Accordingly, 2 sets of measurements, each consisting of (for example) 3 consecutive results obtained from the same individual, may show relatively little variation within each set but quite a large variation between the 2 sets. Auto-correlation is considered eliminated and the CVb unfolded when CVb remains constant at increasing monitoring period or increasing sampling intervals (48)(49). However, this may be impossible to achieve for tPSA because the concentration increases with age as a result of the physiologically increased volume of the prostate (50). Additionally, CVb data derived from patients with prostate cancer may not represent steady-state estimates if the monitoring period or sampling interval is unduly long.
The CVb estimates in Table 1
derived from days monitoring are too inconsistent to be of real value. The biological variation estimates derived from weeks monitoring are consistent but based on a relatively small population (n = 131). The CVb estimates derived from monitoring for 2–32 months and a sampling interval of weeks to months are consistent and based on (a) a large population (n = 890), (b) healthy individuals as well as prostate cancer patients managed conservatively with watchful observation, (c) various study designs, and (d) different assay methods. The weighted average CVb is 19.6%, compared with the arithmetic mean CVb of 19.9%. Both estimates provide a rounded up CVb of 20%. Although a CVb estimate based on previous measurements for the patient in question is theoretically superior to a population-based average, the number of specimens needed to determine a reliable subject-specific CVb may not be available.
The following EGTM conclusions concerning the biological variation of tPSA apply to men above 50 years with a tPSA within the range 0.1–20 µg/L and are based on the data provided in Table 1
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1 month may be necessary when estimating biological variation. |
Consequences for Clinical Practice |
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It is appropriate to estimate the dispersion of tPSA measurements expressed as the confidence interval (CI) in more detail. Three questions should be addressed: What is the CI of the tPSA result? Does the CI include the cutoff concentration? Is the reliability of the tPSA determination improved by replicate sampling? The 1-sided CI for a single sample analyzed once is calculated as:
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The CI is calculated as 1-sided because it is compared only with the cutoff concentration, 4 µg/L. Consequently, + is used for below cutoff and – for above cutoff concentrations. Z is the number of standard deviations appropriate to the chosen probability. The 1-sided Z values in the examples below are 0.52 (probability, 70%), 1.64 (probability, 95%), and 2.33 (probability, 99%) (51). The assumed corresponding values for tPSA concentration and CVa in the examples are for illustrative purposes only and should be adjusted to local laboratory standards. The CVb was set to 20% as defined in the section on biological variation. The tPSA concentration lies within the CI limit with a probability specified by the Z value. The 1-sided CI for the mean of replicate samples each analyzed once is calculated as:
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where n is the number of measurements used (7).
Interpretation of 1-sided CI limits for tPSA results below the cutoff concentration 4 µg/L are illustrated in the examples provided in Fig. 1
, A and B. For tPSA results above the cutoff, results interpretation is illustrated in Fig. 1
, C and D. In Fig. 1A
, the single result is 3.3 µg/L (CVa = 5%). According to the 70% CI limit (3.7 µg/L), >70% of the possible tPSA concentrations are below the cutoff. However, the 95% and 99% CI limits (4.4 and 4.9 µg/L, respectively) include the cutoff, and the probability of an above cutoff tPSA concentration exceeds 5% (P >0.05). In Fig. 1B
, the mean concentration (3.3 µg/L) is based on 3 samples. The 70%, 95%, and 99% CI are moved to the left with limits of 3.5, 3.9, and 4.2 µg/L, respectively, and >95% of the possible tPSA concentrations are below the cutoff (P <0.05). In Fig. 1C
, the single result is 5.1 µg/L (CVa = 4%). According to the 70% CI limit (4.6 µg/L), >70% of the possible tPSA concentrations are above the cutoff. However, the 95% and 99% CI limits (3.4 and 2.7 µg/L, respectively) include the cutoff, and the probability of a below-cutoff tPSA concentration exceeds 5% (P >0.05). In Fig. 1D
, the mean concentration (5.1 µg/L) is based on 3 samples. The 70%, 95%, and 99% CIs are moved to the right with limits of 4.8, 4.1, and 3.7, respectively, and <5% of the possible tPSA concentrations are below the cutoff (P <0.05). Figs. 1
demonstrates that (a) the higher the percentage CI, the wider the limits for tPSA concentrations attributable to random variation, (b) the probability that the cutoff concentration will be included in the CI is increased by a higher CI, and (c) the precision of the tPSA concentration estimate is improved by replicate measurements because the dispersion is reduced.
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As the decision for prostate biopsy frequently depends on whether the tPSA result is below or above the cutoff concentration, 4 µg/L, the probability for the cutoff being within the CI is addressed in Table 2
. The corresponding values for tPSA concentration and analytical variation are as follows: 2.9 µg/L (CVa = 5.3%), 6.1 µg/L (CVa = 3.9%), 3.3 µg/L (CVa = 5%), and 5.1 µg/L (CVa = 4%). In examples 1–4, the cutoff concentration, 4 µg/L, lies within the 1-sided 70% CI limits of the assumed concentrations with a probability <30% (P <0.3) and within the 1-sided 95% CI limits with a probability <5% (P <0.05), whereas the cutoff concentration lies within the 1-sided 99% CI limit with a probability >1% (P >0.01). Adopting a probability of <5% (P <0.05) for the cutoff lying within in the 1-sided 95% CI, the highest below-cutoff single concentration justifying biopsy is 2.9 µg/L and the lowest above cutoff concentration justifying omission is 6.1 µg/L (examples 1 and 2 in Table 2
). Between 3 and 6 µg/L, a single tPSA result is too uncertain as a basis for biopsy decision because the cutoff concentration, 4 µg/L, will lie within the 1-sided 95% CI with a probability exceeding 5% (P>0.05).
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The utility of replicate sampling before deciding on prostate biopsy is shown in examples 3 and 4 of Table 2
. Between 3.0 and 3.3 µg/L, up to 3 measurements may be necessary to obtain a probability <5% for the cutoff being within the 1-sided 95% CI limit and thus justifying omission of biopsy. Between 3.4 and 5.0 µg/L, 3 measurements are not enough to decide on biopsy because the cutoff will lie within the 1-sided 95% CI limit. Between 5.1 and 6.0 µg/L, up to 3 measurements may be necessary to obtain a probability <5% for the cutoff being within the 1-sided 95% CI limit and thus justifying biopsy.
The intention of the examples in Table 2
is not to suggest a new cutoff value for tPSA but to illustrate that CIs can be helpful for decisions on prostate biopsy. For single measurements, the 1-sided 95% CI limit is 33%, and for the mean of 3 measurements, the 1-sided 95% CI limit is 20% of the result (Table 2
). Consequently, replicate measurements allow biopsy decisions based on concentrations closer to the cutoff compared with a single result. Below cutoff, the decision limit is 3.3 µg/L for the mean of 3 measurements and 2.9 µg/L for a single result. Above cutoff the values are 5.1 and 6.1 µg/L, respectively. Helpful calculators to determine the CI limit of a single result, the CI limit of the mean of replicate measurements as well as the number of samples needed to obtain an estimate of and individual’s tPSA concentration at a predetermined probability are available on the internet (52). The sampling interval, however, is important because, if short, replicate measurements may be auto-correlated, influencing their mean value and the range of the CI. To reduce the influence of auto-correlation, the interval between replicate samples should be 1 month (Table 1
). Application of CI limits may also be useful to consider in studies involving age-dependent cutoff concentrations as well as fixed cutoffs lower or higher than 4 µg/L (50)(53).
The following EGTM recommendations for screening and diagnosis of prostate cancer apply to men above 50 years with a tPSA within the concentration range 0.1–20 µg/L:
1 month.
interpretation of serial measurements during monitoring
tPSA monitoring may provide early information about recurrent, responsive, and progressive prostate cancer, influencing treatment decisions. It is frequently asked how much a concentration should change to exceed the random variation—or to put it in other words, what is the reference change value (RCV)? The formula to use is (7):
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The number 2 in the formula is a constant for 2 measurements. The assumed corresponding values for tPSA concentration and CVa in the examples are for illustrative purposes only and should be adjusted to local laboratory standards. The CVb was set to 20% as defined in the section on biological variation. The RCV provides the limit for a change attributable to random variation with a probability specified by the Z value (54)(55).
Example 5 in Table 3
provides the 1-sided RCV for a postoperative nadir tPSA concentration of 1.5 µg/L (CVa = 8%) and demonstrates how much the nadir result should increase to exceed random variation with a specified probability. Accordingly, the probability that the increase is attributable to random variation is (a) < 30% if a following concentration exceeds 1.7 µg/L (Z = 0.52; P <0.30), (b) <5% if it exceeds 2.3 µg/L (Z = 1.64; P <0.05), and (c) < 1% if it exceeds 2.6 µg/L (Z = 2.33; P <0.01). The Z values are 1-sided because the concentration is only expected to increase. Example 6 in Table 3
provides the 2-sided RCV for a baseline tPSA concentration of 20 µg/L (CVa = 4%) and demonstrates how much the baseline result should decrease or increase after initiation of therapy to exceed random variation with a specified probability. Accordingly, the probability that the change is attributable to random variation is (a) <30% if a subsequent concentration exceeds 26 µg/L or decreases <14 µg/L (Z = 1.04; P <0.30), (b) <5% if the concentration exceeds 31 µg/L or decreases <9 µg/L (Z = 1.96; P <0.05), and (c) <1% if the concentration exceeds 35 µg/L or decreases <5 µg/L (Z = 2.58; P <0.01). The Z-values are 2-sided because the concentration may either increase or decrease. The calculation procedures in both examples provide objective limits for concentration changes. Once determined, subsequent concentrations can easily be referenced as being nonsignificantly (e.g., P <0.30), significantly (P <0.05), or highly significantly (P <0.01) increased compared with the test concentrations of, e.g., 1.5 and 20 µg/L. The importance of the procedure is that the new tPSA result is compared with a previous result instead of a traditional or age-adjusted cutoff concentration. The sampling interval in the 2 specified monitoring situations has minor importance for the RCV once the CVb is adjusted to 20%. A helpful calculator to determine the RCV is available on the internet (56).
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It has been advocated that a tPSA velocity (change in concentration per year) exceeding 0.75 µg/L may be useful to identify patients with carcinoma of the prostate (57)(58)(59). Example 7 demonstrates that it may be advantageous to estimate the significance of the change in concentrations by calculating the Z-value with the formula (7):
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where PC is the percentage change between 2 tested concentrations. During 1 year, assumed tPSA concentrations for a man are 3.8 µg/L (CVa = 4.5%), 4.1 µg/L, and 4.7 µg/L. The total increase is 24% with a tPSA velocity of 0.9 µg/L, suggesting emerging prostate cancer. However, this may be an invalid conclusion because the calculated 1-sided Z-value is 0.8, demonstrating that the change is nonsignificant (P >0.2) (51). The example supports a recent clinical study questioning the diagnostic value of a tPSA velocity of 0.75 µg/L per year (60). Example 8 suggests how to optimize the use of tPSA velocity in differentiating between random fluctuations and prostate cancer–induced increments. At the baseline concentration of 3.8 µg/L (CVa = 4.5%), the increment limits attributable to analytical and biological variation (1-sided RCV) are 15%, 47%, and 67% for the 1-sided Z-values 0.52, 1.64, and 2.33, respectively. The probability that the change in concentration per year is attributable to random variation is (a) <30% if the tPSA velocity exceeds 0.6 µg/L, (b) <5% if it exceeds 1.8 µg/L, and (c) <1% if it exceeds 2.5 µg/L. Consequently, the tPSA velocity should exceed 1.8 µg/L per year to be significant (P <0.05) and 2.5 µg/L per year to be highly significant (P <0.01).
The following EGTM recommendations for monitoring of patients with prostate cancer apply to men above 50 years with a tPSA within the concentration range 0.1–20 µg/L:
50%. |
Discussion |
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Several clinical and analytical factors may have a potential influence on tPSA concentrations. Ejaculation and exercise have been debated intensively in this context. The issues have been reviewed recently, but no clear effect on tPSA concentrations has been demonstrated (4)(5). By comparing before and after values, some studies reported a slight increase, others found no change, and some studies reported a decrease in concentrations. The changes were too small to be of clinical significance.
It may be relevant to ask why the values for analytical variation were assumed instead of obtained from a specified method? The values were used for illustrative purposes to show that analytical variation depends on concentration, a characteristic that applies to all tPSA assay systems. On a general basis, the values are representative; however, they should be adjusted to local laboratory standards.
Another important question is whether biological variation differs among healthy individuals compared with patients with prostate cancer. A systematic difference in biological variation would cause concern. The mean biological variation for prostate cancer patients and screened men are of the same order, and the ranges overlap within each of the monitoring periods days, weeks, and months (Table 1
). Accordingly, a difference in biological variation between prostate cancer and non-prostate cancer is not likely among men above 50 years with a tPSA concentration within the range 0.1–20 µg/L.
The major determinant for biological variation is the time period of the study (Table 1
). With the slow elimination rate of 0.8 µg/L per day for the major tPSA fraction, complexed PSA, it is hardly surprising that there may be auto-correlation of serial concentrations taken over short time periods (1). Similarly, auto-correlation has been reported for other tumor markers, including CA 15-3, CA 125, carcinoembryonic antigen (CEA), and tissue polypeptide antigen (TPA) (67)(68). Apparently, it is a general characteristic of several tumor markers that minimizing the effect of auto-correlation and unfolding of the biological variation may require a monitoring period longer than 1 month.
A tPSA-guided biopsy decision is preceded by informed consent addressing the pros and cons of this investigation. The decision may, however, be difficult if based on a single tPSA result and a traditional cutoff value of 4 µg/L. For a man with a single tPSA result of, e.g., 3.3 µg/L, the 1-sided 95% CI limit is up to 4.4 µg/L, and it can be argued that prostate biopsy has been avoided by chance (Fig. 1A
). Conversely, for a man with a single tPSA result of, e.g., 5.1 µg/L, the 1-sided 95% CI limit is down to 3.4 µg/L, and it can be argued that the biopsy has been performed by chance (Fig. 1B
). Compared with a single measurement, the mean of 3 replicate samples with 1 analysis on each narrows the 1-sided 95% CI limit from 33% to 20% of the result and may facilitate a decision on prostate biopsy, particularly for tPSA concentrations close to the cutoff value (Table 2
). The number of replicate samples and the probability for the chosen CI depend on the clinical need for reliability in the specified situation. Calculation of the mean concentration from replicate samples improves the reliability of the measurement, and if CVa > CVb, repeated analysis of 1 sample will reduce the variability further (52). It is a general characteristic of tPSA assay systems that the analytical variation, except for very low concentrations, is well below the biological variation of 20% (21)(22)(26)(27)(28)(29)(30)(31)(32).
The purpose of monitoring tPSA is to obtain reliable information about changes in prostate cancer activity in terms of recurrence, response, and progression. The provided assessment procedures enable calculation of the limits for a change attributable to random variation with a specified probability. Accordingly, a change should be 50% to be significant (P <0.05) and 70% to be highly significant (P <0.01; Table 3
). The procedures also enable estimation of the significance of a change as illustrated in examples 7 and 8 (see the Results section). The information may be used to decide whether to continue or end a therapy or to initiate a new treatment. Tumor marker assessment adjusted to the random analytical and biological variation has been suggested as a relevant monitoring tool for surveillance of breast and ovarian cancer (69)(70). At present, there are no reports from clinical trials on the practicability of this method in prostate cancer, probably because the procedure requires considerable effort if performed manually. Monitoring of tPSA concentrations may, however, be facilitated by use of graphical software programs designed for these specific purposes (71).
In conclusion, the typical biological variation of tPSA is 20% and is the main contributor of tPSA variability in the concentration range 0.1–20 µg/L for men over 50 years. For the decision to omit or perform tPSA-guided prostate biopsy, the probability should be <5% for an above- and a below-cutoff concentration, respectively. During monitoring, the probability should be <5% for the change being the result of random variation before it is considered as indicative of recurrent, responsive, or progressive disease, which means a change of 50%. It is the opinion of the EGTM that the process to establish a consensus on how to interpret single, replicate, and serial tPSA concentrations requires collaboration of competences among urology, laboratory medicine, and industry to a higher degree than previously recognized.
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Acknowledgments |
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ej Topol
an for their careful reading of the manuscript and most helpful comments. |
Footnotes |
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2 Nonstandard abbreviations: tPSA, total prostate-specific antigen; EGTM, European Group on Tumor Markers; DF, degrees of freedom; CI, confidence interval; and RCV, reference change value.
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The following articles in journals at HighWire Press have cited this article:
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  M. Dednam, B. C. Vorster, and J. B. Ubbink Biological Variation of Myeloperoxidase Clin. Chem., January 1, 2008; 54(1): 223 - 225. [Full Text] [PDF]
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C. Stephan, M. Klaas, C. Muller, D. Schnorr, S. A. Loening, and K. Jung Interchangeability of Measurements of Total and Free Prostate-Specific Antigen in Serum with 5 Frequently Used Assay Combinations: An Update Clin. Chem., January 1, 2006; 52(1): 59 - 64. [Abstract] [Full Text] [PDF]
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