Given a set of PSA values, we answer the question: &#x201c;Is its information content typical for the existence of a prostate cancer, or not?&#x201d; Our findings support PSA screening

Hans-Heinrich Gl&#xe4

Hans-J&#xfc

Juergen Durner

English

Nature Precedings

 1
Brief Communication to Nat. Med  21. 6. 2010. 
Is it Prostate Cancer ?      
 
Hans-Heinrich Glättli1, Jürgen Durner2, Hans-Jürg Gerber3 
 
Given a set of PSA values, we answer the question: “Is its information content typical 
for the existence of a prostate cancer, or not ?” Our findings support PSA screening. 
 
Prostate cells, benign or malignant or both together, cause the blood to contain the Prostate-
Specific Antigen (PSA), whose concentration may be regularly measured. We describe how 
to extract parameter values which are characteristic for specific properties of the producing 
cells, but otherwise independent of environmental influences, as long as these are 
approximatlely constant in time. 
It is important to note that the Least Squares analysis we are using, does not only allow for the 
determination of the cell-parameter values of interest, but also for a quantitative appreciation 
(“goodness of fit”) of the empirical validity of the assumptions made. Inadequate conjectures 
are likely to be unveiled. 
Our basic assumption is that the measured PSA concentration is caused by one or two 
growing cell populations which develop, at least for some initial time span, uninfluenced and 
independently from each other with characteristic, constant cell reproduction times, the 
doubling times,  DT1 and DT2. Since such populations grow, each, according to an 
exponential law, our measured PSA concentration, PSA(t), is thus a superposition of two 
exponentials 
 
PSA(t)  =  a ·2 t / DT1 +  b · 2 t / DT2  .    (1) 
 
The task is two-fold. First: Given a set of measured PSA(t) values. Find the constants DT1 
and DT2 without any (previous) knowledge of the values of a and b, and give a quantitative 
estimate (standard deviation, std) of the reliability of the results. This is a purely mathematical 
application, independent of any medical considerations, see 1, 2. 
Second: Show that formula (1) represents real patient data, calibrate DT2 versus diagnostic 
findings, and apply the method to early diagnosis of prostate cancer. 
 
Figure 1 (top) shows the agreement of 10 measured PSA data points with the curve calculated 
from the formula (1). It establishes the action of a second, faster growth mechanism, and 
demonstrates, that the method is capable to predict this mechanism already 20 months earlier, 
on the basis of the first 7 data points, as represented in the bottom of Fig. 1. 
 
Out of a random collection3 of measured PSA data, 36 sets have been chosen, and analyzed 
with formula (1). 
The reader is invited to consult the corresponding graphs which show the reductions of the 
various PSA time-evolutions to their exponential components. They are available from 
www.psadynamics.com (→ “Wissenschaftliche Grundlagen”, in english) 
 
The resulting frequencies of the components’ doubling times are displayed in Fig. 2; 
DT1 in green, DT2 in red. 
____________________________________ 
1Seestrasse 252, CH-8700 Küsnacht, 2 Universitätsklinikum, IPT, D-80336 München,  
3Swiss Federal Institute of Technology, IPP, ETHZ, CH-8093 Zürich. 
Correspondence should be addressed to J. Durner,  juergen.durner@med.uni-muenchen.de 
 
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For the data of a single person, it is natural (and true) that  0 < DT2 < DT1 for DT1 > 0.  
However, for a collection of doubling times from different persons, this is no more applicable. 
It is thus a non-trivial finding, that there is a region of short doubling times, as displayed in 
the bottom part of Fig. 2, where the red and green events (the DT2 and DT1 values) are 
entirely separated. This is the first and main message of this paper. 
 
 
 
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Fig. 1. Agreement and prediction. 
Top:  Measured PSA values show good statistical agreement with the blue curve, calculated 
from formula (1). (Points ± 9 % std assumed, resulting χ2 /d = 2.6). 
In the (semi-log) plot, the exponential components are represented by the straight, dashed 
lines. Evidence for the existence of a second growth processs comes from the value found for 
DT2 = 10 ± 4 months, which is incompatible with the value found for DT1 = 430 months. 
Bottom:  This conclusion could have been reached 20 months earlier !  The analysis, based on 
the first 7 PSA values, would have predicted DT2 = 6 ± 5 months (in perfect statistical 
agreement), and would have led to the same conclusion. 
The patient is 49 years old. Note that all of the PSA values, in this part of the figure, are 
below  (the widely used reference value of)  4 ng/ml.   (Figure: χ2 /d = 0.95). 
 
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We note in passing, that only an adequate mathematical procedure is able to produce this 
clean separation. 
 
In order to arm this formal result with diagnostic power, we have calibrated DT  against a new 
and independent  PSA data set3 with a total of 411 patients, having a diagnosis of a Benign 
Prostatic Hyperplasia (BPH), and no prostate cancer. None of the doubling times was shorter 
than 27 months. The second main result of this paper thus is, that the “DT1-free” region of  
Fig. 2 is also “BPH free”. 
 
To conclude, we answer the question, posed in the abstract, with reference to the set of PSA 
values in Fig. 1: Its information content, expressed by the value of DT2 = 10 ± 4 months, 
which falls well into the “DT1-free region”, is typical for a cell-reproduction process other 
than BPH, even though the PSA values are low. 
 
Early PSA screening helps by providing early data points as needed by the algorithm to 
disentangle the processes. 
 
 
 
COMPETING INTERESTS STATEMENT 
The authors D.D and H.-J.G  are consultants of Praxis für Prävention, D-Freising. 
Besides this, the authors declare to have no competing final interests. 
 
 
  
1. Hans-Heinrich Glättli, Der PSA-Wert im Laufe der Zeit,  www.psadynamics.com , 2008. 
2. Hans-Jürg Gerber, http://precedings.nature.com/documents/3930/version/1 , 2009. 
3. Collection H.H. Glättli. 
 
 
 
 
 
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Fig. 2. The first main finding of this work. Separation of the cell population’s properties. 
Top:  Measured PSA doubling times DT1 due to the first cell population are distributed over a 
wide range (34 cases of 36 reach from -500 to +500 months), whereas those from the unveiled 
second population (DT2) cluster around small values. 
Bottom: Zoom of the top subpicture. Clustering of the DT2 values. 
In the range from 0 to 13 months, 30 (of 36) values of DT2 are located, in contrast to none (of 
36) of DT1. With high probability, they are not BPH events. 
 
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Is it Prostate Cancer ?

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Is it Prostate Cancer ?

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