A generalized and efficient robust algorithm for handling censored values in one parameter exponential distribution.

Abstract

Often in survival analysis, response that is measured over time is not a continuous measure but is the occurrence of a particular event or the number of such event occurring in a particular interval. Events such as exacerbation or epileptic seizures during each month of follow-up are examples. In this situation it is very difficult to specify specific distribution for the data, but when distribution is not specified, maximum likelihood estimate cannot be used. To specify a functional form for the expectation and the marginal variance, generalized estimation model are  used assuming that there is no repeated measurement. Asymptotically, censored distributions are not normal but to achieve consistency and sufficiency in estimate, the derivative of their distributions should be normal, chi-square, follow t-statistics or other well known functions. This is because the derivatives of these distributions are easier to understand and maximum likelihood estimates have minimum variance even if percentage of censored values increases.

Keywords: hazard, censoring, generalize, normalize, Jacobian.