A COMPARISON OF KAPLAN-MEIER AND CUMULATIVE INCIDENCE ESTIMATE IN THE PRESENCE OR ABSENCE OF COMPETING RISKS IN BREAST CANCER DATA

Statistical techniques such as Kaplan-Meier estimate is commonly used and interpreted as the probability of failure in time-to-event data. When used on biomedical survival data, patients who fail from unrelated or other causes (competing events) are often treated as censored observations. This paper reviews and compares two methods of estimating cumulative probability of cause-specific events in the present of other competing events: 1 minus Kaplan-Meier and cumulative incidence estimators. A subset of a breast cancer data with three competing events: recurrence, second primary cancers, and death, was used to illustrate the different estimates given by 1 minus Kaplan-Meier and cumulative incidence function. Recurrence of breast cancer was the event of interest and second primary cancers and deaths were competing risks.The results indicate that the cumulative incidences gives an appropriate estimates and 1 minus Kaplan-Meier overestimates the cumulative probability of cause-specific failure in the presence of competing events. In absence of competing events, the 1 minus Kaplan-Meier approach yields identical estimates as the cumulative incidence function.The public health relevance of this paper is to help researchers understand that competing events affect the cumulative probability of cause-specific events. Researchers should use methods such as the cumulative incidence function to correctly estimate and compare the cause-specific cumulative probabilities

Nonparametric Survival Estimation Using Prognostic Longitudinal Covariates

One of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right-censored data. This research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual. We begin by defining a survival estimate which uses time-dependent covariates to more precisely get at the underlying survival curves in the presence of censoring. This estimate has a smaller asymptotic variance than the usual Kaplan-Meier in the presence of censoring and reduces to the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) in situations where the covariate is not prognostic or no censoring occurs. In addition, this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information. Because the Kaplan-Meier estimate is known to be biased in this situation due to informative censoring, we recommend use of our estimate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91897/1/Murray Tsiatis 1996 Biometrics.pd

Turnbull versus Kaplan-Meier estimators of cure rate estimation using interval censored data

This study deals with the analysis of the cure rate estimation based on the Bounded Cumulative Hazard (BCH) model using interval censored data, given that the exact distribution of the data set is unknown. Thus, the non-parametric estimation methods are employed by means of the EM algorithm. The Turnbull and Kaplan Meier estimators were proposed to estimate the survival function, even though the Kaplan Meier estimator faces some restrictions in term of interval survival data. A comparison of the cure rate estimation based on the two estimators was done through a simulation study

Mean Survival Time from Right Censored Data

A nonparametric estimate of the mean survival time can be obtained as the area under the Kaplan-Meier estimate of the survival curve. A common modification is to change the largest observation to a death time if it is censored. We conducted a simulation study to assess the behavior of this estimator of the mean survival time in the presence of right censoring. We simulated data from seven distributions: exponential, normal, uniform, lognormal, gamma, log-logistic, and Weibull. This allowed us to compare the results of the estimates to the known true values and to quantify the bias and the variance. Our simulations cover proportions of random censoring from 0% to 90%. The bias of the modified Kaplan-Meier mean estimator increases with the proportion of censoring. The rate of increase varied substantially from distribution to distribution. Distributions with long right tails (log-logistic, log normal, exponential) increased the quickest (i.e., at lower censoring proportions). The other distributions are relatively unbiased until around 60% censoring. The Normal distribution remains unbiased up to 90% censoring. Thus, the behavior of the modified Kaplan-Meier mean estimator depends heavily on the nature of the distribution being estimated. Since we rarely have knowledge of the underlying true distribution, care must be taken when estimating the mean from censored data. With modest censoring, estimates are relatively unbiased, but as censoring increases so does the bias. With 30% or more censoring the bias may be too high. This is in contrast to the Kaplan-Meier estimator of the median which is relatively unbiased

The Distribution of the Bivariate Kaplan-Meier Estimate

1 online resource (PDF, 8 pages

Estimating the Survival Distribution for Right-Censored Data with Delayed Ascertainment

In many clinical trials, patients are not followed continuously. This means their vital status may not be immediately recorded. In such cases, the results from the Kaplan-Meier estimator or the log rank test, popular methods used for survival analysis, may be biased or inconsistent. Hu and Tsiatis first produced a new estimator to estimate survival distribution for right-censored data with delayed ascertainment, Van der Laan and Hubbard modified their estimator. We investigate each of these proposed estimators and their properties. Using simulations, we compare these new estimators to each other and to the Kaplan-Meier estimator using different sample sizes, different failure rates, and different maximum delay times. The public health importance of this thesis is that we can partially alleviate the problem caused by delayed ascertainment in the analysis of right-censored time to event data by choosing the most accurate and consistent estimator that accounts for the delayed ascertainment. The reduction of bias in analyses of public health data ensures that such studies are reliable so that proper inference can be made and hence, potential public health policy can be based on an accurate decision making process

Application of a simple nonparametric conditional quantile function estimator in unemployment duration analysis

We consider an extension of conventional univariate Kaplan-Meier type estimators for the hazard rate and the survivor function to multivariate censored data with a censored random regressor. It is an Akritas (1994) type estimator which adapts the nonparametric conditional hazard rate estimator of Beran (1981) to more typical data situations in applied analysis. We show with simulations that the estimator has nice finite sample properties and our implementation appears to be fast. As an application we estimate nonparametric conditional quantile functions with German administrative unemployment duration data. --nonparametric estimation,censoring,unemployment duration