If the population of elapsed time intervals until an event occurs is assumed to follow an exponential distribution, implying a constant hazard rate throughout every observation subwindow, the maximum likelihood estimate of that hazard rate is 0.2361, with a standard error of 0.013790.
The assumption of an exponential distribution with a constant hazard rate produces an EXTREMELY GOOD fit with the observed data. The analogue of an unadjusted coefficient of determination (R-squared) would be 0.9974.
An attempt was made to fit a Weibull distribution to the same data. A Weibull distribution permits either an increasing or a decreasing hazard rate over all observation subwindows. This additional flexibility failed to provide a substantially better fit. Consequently, the constant hazard rate assumed by the
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Notice that an exponential function fit the Kaplan-Meier survival estimates for the 325 SR patients extremely closely (R-squared = 0.9974). An exponential survival function implies a constant hazard rate of further disease progression over time. No Weibull function with either an increasing or a decreasing hazard rate could provide a better fit with the same SR patient survival data.
The maximum likelihood estimate of the constant (exponential) hazard rate was
0.2361 focal events per year. Reading from figure 8, the "typical" or "average"
SR patient could therefore expect to experience with 50 percent probability some event evidencing further disease progression within approximately 2.91 years following diagnosis and treatment. In stark contrast MR patients could expect never to experience further disease progression, at least never again from this particular bout with their breast cancer. They were presumed to