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Censoring is common in survival analysis. If only the lower limit l for the true event time T is known such that T > l, this is called right censoring. Right censoring will occur, for example, for those subjects whose birth date is known but who are still alive when they are lost to follow-up or when the study ends. We generally encounter right ...
Special techniques may be used to handle censored data. Tests with specific failure times are coded as actual failures; censored data are coded for the type of censoring and the known interval or limit. Special software programs (often reliability oriented) can conduct a maximum likelihood estimation for summary statistics, confidence intervals ...
Censored regression models are used for data where only the value for the dependent variable is unknown while the values of the independent variables are still available. Censored dependent variables frequently arise in econometrics. A common example is labor supply. Data are frequently available on the hours worked by employees, and a labor ...
The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. [1] It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events. An "event" can be the failure of a non-repairable component, the death ...
The logrank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of the groups at each observed event time and then adding these to obtain an overall summary across all-time points where there is an event.
This approach to survival data is called application of the Cox proportional hazards model, [2] sometimes abbreviated to Cox model or to proportional hazards model. [3] However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky. [4] [5]
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way. [1] The term was coined by Arthur Goldberger in reference to James Tobin, [2] [a] who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods.