Breast cancer is the most common cause of mortality due to cancer for women both in Lithuania and worldwide. Chances of survival after diagnosis differ significantly depending on the stage of disease at the time of diagnosis. Extended term periods are required to estimate survival of, e.g., 15–20 years. Moreover, since mortality of the average population changes with time, estimates of survival of cancer patients derived after a long period of observation can become outdated and can be no longer used to estimate survival of patients who were diagnosed later. Therefore, it can be useful to construct analytic functions that describe survival probabilities. Shorter periods of observation can be enough for such construction. We used the data collected by the Lithuanian Cancer Registry for our analysis. We estimated the chances of survival for up to 5 years after patients were diagnosed with breast cancer in Lithuania. Then we found analytic survival functions which best fit the observed data. At the end of this paper, we provided some examples for applications and directions for further research. We used mainly the Kaplan–Meier method for our study.
The article focuses on mortality models with a random effect applied in order to evaluate human mortality more precisely. Such models are called frailty or Cox models. The main assertion of the paper shows that each positive random effect transforms the initial hazard rate (or density function) to a new absolutely continuous survival function. In particular, well-known Weibull and Gompertz hazard rates and corresponding survival functions are analyzed with different random effects. These specific models are presented with detailed calculations of hazard rates and corresponding survival functions. Six specific models with a random effect are applied to the same data set. The results indicate that the accuracy of the model depends on the data under consideration.
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