On 2015 Aug 23, David Keller commented:

Information theory contradicts Guideline Statement 4: more frequent PSA testing should benefit patients, not harm them

Information theory describes the reconstruction of continuous signals from discrete samples, and the extraction of signals from noise. Screening for prostate cancer involves scrutiny of a man's serial PSA measurements, with the goal of determining the likelihood that his prostate has developed a malignancy which could affect his longevity or quality of life (ie: his mortality or morbidity). Statement 4 from the 2013 Early Detection of Prostate Cancer: AUA Guideline [1] is as follows:

"Guideline Statement 4: To reduce the harms of screening, a routine screening interval of two years or more may be preferred over annual screening in those men who have participated in shared decision-making and decided on screening. As compared to annual screening, it is expected that screening intervals of two years preserve the majority of the benefits and reduce over diagnosis and false positives. (Option; Evidence Strength Grade C)"

Guideline Statement 4 can be proved false using the principles of information theory as follows. Individual PSA blood test results constitute discrete samples of the continuous signal which would result from continuous monitoring of the patient's PSA. The Nyquist-Shannon Sampling theorem states that the minimum sampling rate for perfect reconstruction of a signal is equal to twice the bandwidth of the signal [1]. Expressed another way, the maximum bandwidth of a signal to be perfectly reconstructed from samples taken at a sampling frequency f is f/2.

The crucial signal we wish to detect is a rising PSA consistent with a dangerous prostate cancer. Empirically, the faster a prostate cancer grows, the more rapid the rise in PSA and therefore the higher the bandwidth of the PSA signal. We would like to detect PSA signals which rise rapidly (have high bandwidth) in order to treat the patient while his cancer is confined to his prostate. The more frequently we sample the PSA, the higher the bandwidth of the PSA signal we can detect, meaning the more rapid rises in PSA will not escape detection. So, increasing the PSA sampling rate from once every 2 years to once every year can only improve the detection of the high-bandwidth signal caused by a rapidly growing prostate cancer. In fact, increasing the PSA sampling rate to twice per year, 4 times per year or even higher will only increase the maximum detectable bandwidth of the PSA signal.

Harms associated with PSA screening are generally associated with the prostate biopsy procedure and downstream diagnostic and therapeutic intervetions. The purpose of PSA sampling is to inform us when a prostate biopsy is likely to be more beneficial than harmful. The cumulative harm of multiple biopsies is proportional to the number of biopsies done, so we want to minimize the number of biopsies without missing a dangerous cancer. However, if the PSA signal includes useful information about the presence of cancer, the best way to reduce the number of biopsies is to improve the quality (bandwidth) of the detected PSA signal, which requires increasing the PSA sampling rate.

Reducing the PSA sampling rate in an attempt to reduce the harms caused by prostate biopsy is akin to hiding one's head in the sand. Continuous monitoring of the PSA signal would be ideal, but the maximum practical PSA sampling frequency should be employed to maximize the quality of the reconstructed PSA signal, and thereby increase the likelihood of detecting a fast-growing tumor while it is confined to the prostate. Application of a low-pass filter to the PSA signal should reduce the number of biopsies triggered by noise.

Lastly, the prostate biopsy rate need not be correlated with the PSA sampling rate, and indeed should be inversely correlated with it if the PSA signal has useful information about the presence of dangerous cancer in the prostate.

Reference

1: Shannon CE, Communication in the presence of noise, Proc. Institute of Radio Engineers, vol. 37, no. 1, pp. 10–21, Jan. 1949

On 2015 Aug 23, David Keller commented:

Information theory contradicts Guideline Statement 4: more frequent PSA testing should benefit patients, not harm them

Information theory describes the reconstruction of continuous signals from discrete samples, and the extraction of signals from noise. Screening for prostate cancer involves scrutiny of a man's serial PSA measurements, with the goal of determining the likelihood that his prostate has developed a malignancy which could affect his longevity or quality of life (ie: his mortality or morbidity). Statement 4 from the 2013 Early Detection of Prostate Cancer: AUA Guideline [1] is as follows:

"Guideline Statement 4: To reduce the harms of screening, a routine screening interval of two years or more may be preferred over annual screening in those men who have participated in shared decision-making and decided on screening. As compared to annual screening, it is expected that screening intervals of two years preserve the majority of the benefits and reduce over diagnosis and false positives. (Option; Evidence Strength Grade C)"

Guideline Statement 4 can be proved false using the principles of information theory as follows. Individual PSA blood test results constitute discrete samples of the continuous signal which would result from continuous monitoring of the patient's PSA. The Nyquist-Shannon Sampling theorem states that the minimum sampling rate for perfect reconstruction of a signal is equal to twice the bandwidth of the signal [1]. Expressed another way, the maximum bandwidth of a signal to be perfectly reconstructed from samples taken at a sampling frequency f is f/2.

The crucial signal we wish to detect is a rising PSA consistent with a dangerous prostate cancer. Empirically, the faster a prostate cancer grows, the more rapid the rise in PSA and therefore the higher the bandwidth of the PSA signal. We would like to detect PSA signals which rise rapidly (have high bandwidth) in order to treat the patient while his cancer is confined to his prostate. The more frequently we sample the PSA, the higher the bandwidth of the PSA signal we can detect, meaning the more rapid rises in PSA will not escape detection. So, increasing the PSA sampling rate from once every 2 years to once every year can only improve the detection of the high-bandwidth signal caused by a rapidly growing prostate cancer. In fact, increasing the PSA sampling rate to twice per year, 4 times per year or even higher will only increase the maximum detectable bandwidth of the PSA signal.

Harms associated with PSA screening are generally associated with the prostate biopsy procedure and downstream diagnostic and therapeutic intervetions. The purpose of PSA sampling is to inform us when a prostate biopsy is likely to be more beneficial than harmful. The cumulative harm of multiple biopsies is proportional to the number of biopsies done, so we want to minimize the number of biopsies without missing a dangerous cancer. However, if the PSA signal includes useful information about the presence of cancer, the best way to reduce the number of biopsies is to improve the quality (bandwidth) of the detected PSA signal, which requires increasing the PSA sampling rate.

Reducing the PSA sampling rate in an attempt to reduce the harms caused by prostate biopsy is akin to hiding one's head in the sand. Continuous monitoring of the PSA signal would be ideal, but the maximum practical PSA sampling frequency should be employed to maximize the quality of the reconstructed PSA signal, and thereby increase the likelihood of detecting a fast-growing tumor while it is confined to the prostate. Application of a low-pass filter to the PSA signal should reduce the number of biopsies triggered by noise.

Lastly, the prostate biopsy rate need not be correlated with the PSA sampling rate, and indeed should be inversely correlated with it if the PSA signal has useful information about the presence of dangerous cancer in the prostate.

Reference

1: Shannon CE, Communication in the presence of noise, Proc. Institute of Radio Engineers, vol. 37, no. 1, pp. 10–21, Jan. 1949