{'fraction_non_alphanumeric': 0.019427402862985686, 'fraction_numerical': 0.00408997955010225, 'mean_word_length': 5.398692810457517, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Optimal Estimation for Regression Models on τ-Year Survival Probability

A logistic regression method can be applied to regressing the -year survival probability to covariates, if there are no censored observations before time . But if some observations are incomplete due to censoring before time , then the logistic regression cannot be applied. Jung (1996) proposed to modify the score function for logistic regression to accommodate the right-censored observations. His modified score function, motivated for a consistent estimation of regression parameters, becomes a regular logistic score function if no observations are censored before time . In this article, we propose a modification of Jung’s estimating function for an optimal estimation for the regression parameters in addition to consistency. We prove that the optimal estimator is more efficient than Jung’s estimator. This theoretical comparison is illustrated with a real example data analysis and simulations.