Commentary: On measurement error, PSA doubling time, and prostate cancer

Abstract

Exposure measurement error is a pervasive problem for epidemiology research projects designed to provide valid and precise statistical evidence supporting postulated exposure-disease relationships of interest. The purpose of this commentary is to highlight an important real-life example of this exposure measurement error problem and to provide a simple and useful diagnostic tool for physicians and their patients that corrects for the exposure measurement error. More specifically, prostate-specific antigen doubling time (PSADT) is a widely used measure for guiding future treatment options for patients with biochemically recurrent prostate cancer. Numerous papers have been published claiming that a low calculated PSADT value (denoted $\widehat{\text{PSADT}}$) is predictive of metastasis and premature death from prostate cancer. Unfortunately, none of these papers have adjusted for the measurement error in $\widehat{\text{PSADT}}$, an estimator that is typically computed using the popular Memorial Sloan Kettering website very often visited by both physicians and their patients. For this website, the estimator $\widehat{\text{PSADT}}$ of the true (but unknown) PSADT for a patient (denoted PSADT^∗) is computed as the natural log of 2 (i.e., 0.6931) divided by the estimated slope of the straight-line regression of the natural log of PSA (in ng/mL) on time. We utilize $\widehat{\text{PSADT}}$ to derive an expression for the probability that the unknown PSADT^∗ for a patient is below a specified value C ($>0$) of concern to both the physician and the patient. This probability is easy to interpret and takes into account the fact that $\widehat{\text{PSADT}}$ is a statistical estimator with variability. This variability introduces measurement error, namely, the difference between a computed value $\widehat{\text{PSADT}}$ and the true, but unknown, value PSADT^∗. We have developed an Excel calculator that, once the [time, ln(PSA)] values are entered, outputs both the value of $\widehat{\text{PSADT}}$ and the desired probability. In addition, we discuss problematic statistical issues attendant with PSADT^∗ estimation typically based on at most three or four PSA values. We strongly recommend the use of this probability when physicians are discussing $\widehat{\text{PSADT}}$ values and associated treatment options with their patients. And, we stress that future epidemiology research projects involving PSA doubling time should take into account the measurement error problem highlighted in this Commentary.

Keywords: Measurement error; Probability; Prostate-specific antigen doubling time; Simple linear regression; T-distribution.