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Abstract:
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The Kaplan Meier Estimator is the most well-known survival curve estimator in the branch of biostatistics. However, when the Kaplan Meier estimator is found for two datasets assuming a certain condition known as stochastic order, the estimator can violate the assumption, which presents some issues of bias and mean squared error. For example, we would expect a Degree 1 Carcinoma Cancer patient to have higher survival probabilities and an increased likelihood of living longer than a Degree 2 Carcinoma Cancer patient because of their slightly healthier condition. However, the survival functions we derived from Carcinoma Cancer datasets (survival package in R studio, Stanford University, 1977) cross over each other with respect to survival probability and time, which is a violation of stochastic ordering. In this poster, we will consider an estimator proposed by Rojo (2004) to force stochastic ordering as we evaluate the Carcinoma Cancer data in the two-sample case as well as look into a theoretical three-sample case using exponential data created using R studio.
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