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Yin-Deficiency (YD), representing a status of the human body under lack of nutrition and fluid in traditional Chinese medicine, is commonly seen in late stage of cancer patients. It is not known whether the severity of YD related symptoms/signs can predict the survival rate of cancer patients. This study evaluated the distribution of Yin-deficiency symptoms/signs (YDS) in cancer patients with YD, and investigated whether the severity of YDS can predict the survival rate of cancer patients with YD. From 5 January 2007 to 5 May 2007, we selected 43 cancer patients with diagnosis of YD from hospitalized patients and outpatients. The severity of YD was evaluated by a questionnaire. We further estimated the cumulative probabilities of the survival rates over 4 months since the start of study by the Kaplan-Meier product-limit method, and compared the differences among groups with various severities in each symptom/sign with the use of the log-rank test. The results revealed that, the 3 most common YDS were sleeplessness with annoyance, less or non-coated tongue with or without redness and dry mouth. In the survival rate analysis, only 2 parameters, rapidly small pulse (p = 0.002) and less-or non-coated tongue with paleness (p = 0.017), were found to be related to the decrease of cancer patients with YD. This suggests that, both rapidly small pulse and less-or non-coated tongue without redness may be used as predictors for the estimation of survival rate in cancer patients with YD.

Empirical cumulative lifetime distribution function is often required for selecting lifetime distribution. When some test items are censored from testing before failure, this function needs to be estimated, often via the approach of discrete nonparametric maximum likelihood estimation (DN-MLE). In this approach, this empirical function is expressed as a discrete set of failure-probability estimates. Kaplan and Meier used this approach and obtained a product-limit estimate for the survivor function, in terms exclusively of the hazard probabilities, and the equivalent failure-probability estimates. They cleverly expressed the likelihood function as the product of terms each of which involves only one hazard probability ease of derivation, but the estimates for failure probabilities are complex functions of hazard probabilities. Because there are no closed-form expressions for the failure probabilities, the estimates have been calculated numerically. More importantly, it has been difficult to study the behavior of the failure probability estimates, e.g., the standard errors, particularly when the sample size is not very large. This paper first derives closed-form expressions for the failure probabilities. For the special case of no censoring, the DN-MLE estimates for the failure probabilities are in closed forms and have an obvious, intuitive interpretation. However, the Kaplan–Meier failure-probability estimates for cases involving censored data defy interpretation and intuition. This paper then develops a simple algorithm that not only produces these estimates but also provides a clear, intuitive justification for the estimates. We prove that the algorithm indeed produces the DN-MLE estimates and demonstrate numerically their equivalence to the Kaplan–Meier-based estimates. We also provide an alternative algorithm.