January 6, 1999
In an effort to estimate the end result of my chemotherapy (a weakened and lengthened version of the Logothetis protocol, I made a few assumptions and then did a fit to the PSA data points I have so far. The error bars shown on the plot are my best guess estimate of the measurement error on the PSA. They are given by the equation ERROR_PSA = 0.1 + 0.1*PSA.
Those of you who have been following this saga know that I used to have three models and a chi squared fitting procedure to predice my future PSA. The most recent PSA measurement has made it all too clear which of these three models is the best so the current plot shows only that.
The only model that still fits is the sum of two exponential curves so that there can be two components of cells producing PSA: one which falls with time and one which is not responding to chemotherapy and is growing with time. This model is represented by the equation PSA = PSA_Zero*exp(Prob*Ndays) + PSA_Zero2*exp(Prob2*Ndays), where PSA_Zero and PSA_Zero2 are represented by the fitted parameters m1 and m3 in the result box below. In the fit I have chosen to change the exponents so that instead of Prob and Prob2 I use parameters that correspond to the doubling time in days: these parameters are indicated by m3 and m4 where the negative value for m3 indicates a halving time. With four unknowns in the equation, the chisq is 0.48 (same as last month) for now three degrees of freedom, confirming the visual impression of an excellent fit to the data. The fit with this last point varies only slightly from the one obtained last month using one less data point, so unfortunately it looks like the last month of chemotherapy did not have much effect. The m4 value indicates a doubling time of about 27 days.
The last month's increase was in spite of being back on Lupron for a little more than a month. Apparently it had little effect on top of the other chemotherapy elements.
For those of you who might be wondering at the apparent consistency of these PSA scores, I can only say that all of my blood draws have been done in the early morning (about 7 AM) before ingesting any food or liquid.