Prostate cancer is a condition of public health significance in the United States. A new method for predicting survival is derived for the domain around the change point from a semiparametric ratio estimator (SPRE) to predict survival in response to treatment for prostate cancer. Using an extended maximum spacing estimator, the geometric mean of sample spacings from a uniform distribution is derived with known endpoints given at 0 and at the value of the change point from an ordinary least squares (OLS) regression for SPRE. To determine the maximum interval on the ‘x’ axis between point estimates, the maximum spacing estimation method is derived from a continuous univariate distribution where spacing will be defined as gaps between ordered values of the distribution function. The maximum is defined as a single value in the neighborhood of the change point and spacing defined as a function of time. This maximum spacing defines the gaps between point estimates at each time-dependent predicted outcome from the change point and results in a semiparametric ratio estimator that is reliable and repeatable. Performance is discussed through a simulation of change point values for a real application in clinical medicine and, using SPRE, in personalized medicine for a single prostate cancer patient.