Estimating PSA Growth Rates After Prostate Cancer Treatment

This essay studied methods for estimating the rate of growth of prostate-specificantigen (PSA) levels in the blood following prostate cancer treatment, particularlyin cases where only limited data are available. Monitoring the rate of PSA increaseis clinically important, as it can indicate cancer recurrence or progression and ahigh growth rate is associated with higher risk of death from prostate cancer. Thegrowth rate after surgery is particularly problematic to estimate since PSA valuesare typically below the detection limit (0.1 ng/ml) for a short or long period. To estimate the growth rate of PSA at the time when it has become measurable(two consecutive values above 0.1 ng/ml), we aimed to test and compare differentestimation techniques by simulating a dataset that imitated PSA behavior overtime in patients. The estimation methods evaluated included maximum likelihoodestimation (MLE), complete case analysis (CCA) with lookback and deterministicimputation (DI). A simulation study was conducted on the generated dataset toassess how accurately each method could estimate the growth rate under varyingchoices of parameters. These results were then compared to analyses on a real-lifedataset. In the simulated datasets, MLE performed the best in estimating the PSA growthrate, followed by CCA using all available information. DI showed somewhat loweraccuracy but still performed reasonably well, whereas CCA with limited informationgenerally produced the least accurate estimates. In the real-world dataset, the relativeperformance of the methods differed from the theoretical results; it was unclearwhich method performed best. These findings suggest that while MLE is generally the most effective for estimatingthe rate of growth of PSA, simpler methods like DI may be preferable when thenumber of available measurements is very limited.