Unification of three-type likelihood-inferences and its application development in Cox-type counting processes model under incomplete data

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In this research, we studied the statistical inference theory and statistical methods outstanding in several situations accompanied with incomplete data, in order to create further useful applications and developments of the Cox regression models, which are often used as a tool for data analysis to evaluate the effect of patient's treatment or prognosis factors statistically in the area of clinical medicine, and so on. We investigated the properties and roles on the three types of partial likelihoods, and their relationships to elucidate them in terms of theory and applications.