Using splines to detect changes in PSA doubling times.

Abstract

PSA doubling time (PSADT) can predict the likelihood of clinical progression in patients with biochemical relapse after surgery or radiation for prostate cancer. Changes in PSA doubling time in response to therapy may be of clinical or investigational significance. How does one estimate PSADT before and after the initiation of therapy and determine if any change is statistically significant or simply the result of random variation? These are the type of questions addressed. Our technique uses a best-fitting spline (i.e., a broken-line approximation) to a graph of log PSA on time to estimate PSADTs before and after treatment initiation. A linear regression program is used to produce the fit and to evaluate the statistical significance of any change in PSADT. This method differs from previous methods in that it uses all the data, exploits the continuity of PSA at the time of treatment initiation, and allows one to make statistical significance statements about specific individuals. Our technique is illustrated with data from a pilot clinical trial using a nutritional supplement in 12 men with prostate cancer. A detailed analysis of the first patient shows how the data are handled, how two lines of computer code are sufficient to fit the spline model, and how the doubling times and statistical significance of a change are read from the computer output. In the study, 9 of 12 patients had a statistically significant increase in doubling time. Because the study is preliminary and used only to illustrate our method, no medical discussion of the study is included. The last section of the study, in part expository, is devoted to explaining the underlying principles for those who may want to know not only what to do, but why it works. The method presented here for determining changes in PSADT is both simple and broadly applicable. It allows the evaluation of the size and statistical significance of an observed change or increase in PSADT in response to therapy for prostate cancer. It can be done using essentially any statistical software and widely accepted statistical methods.