E. L. Kaplan, P. Meier, Nonparametric estimation from incomplete observations, Journal of the American Statistical Association 53 (1958) 437-- 481.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....7.2. Prognostic analysis We analyzed performance on this data set by looking for clinical relevance in the resulting clusters. Specifically, we observe the actual outcome (time to recurrence, or known disease free time) of the cases in the three clusters. Figure 12 shows Kaplan Meier estimates [32] of the true disease free survival times for patients in the clusters found by ELSA K means. Figure 12 displays well separated survival characteristics of three prognostic groups: good (88 patients) intermediate (83 patients) and poor (27 patients) The good prognostic group was significantly ....

E.L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53 (1958), 457--481.

....function over future states. Assumptions about the form of this utility function are necessary to faciliate its assessment and computation; for example, in the case of a critically ill ICU patient, a time separable utility model that aggregates instantaneous risks over time may be appropriate [23, 43]. Third, one must develop models that can predict the temporal effects of candidate interventions. Several methodologies have been proposed to address this modeling challenge mathematical models, Markov decision processes [11, 40] and forecasting methods [7, 52] to name a few. Related to the ....

E. L. Kaplan and P. Meir. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457--481, 1958.

....least up to a certain time. The hazard function represents the probability that an individual will die at a certain time, conditioned on his survival up to that time, and denotes the instantaneous death rate [1] Survival analysis models, such as actuarial life tables [2] product limit estimators [3], proportional hazards [4] and fully parametric models [5] produce estimates for both the survivor function and the hazard function. Parametric methods of survival analysis require specification of a probability density function for estimating these functions. Nonparametric models do not require ....

Kaplan EL; Meier P. Nonparametric estimation from incomplete observations. American Statistical Association Journal, 1958 June, 457--81.

....reduces the space requirement from O#jSp#X#j # to O#kjSp#X#j#. Time separated sample value functions have diverse applications. For example, in the case of a critically ill ICU patient, the sample values represent the well known, independent instantaneous risks of death at various time points [40], which can then be aggregated over a time interval into a cumulative risk of death for the trajectory of physiologic states [53] For some problems, however, the time separability assumption may be overly restrictive. For example, the prognosis of an ICU patient who remains stable over an ....

E. L. Kaplan and P. Meir. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457--481, 1958.

....the medical literature. A survival curve plots the probability of survival against time, as time increases from zero. Since these probabilities are not directly available due to the right censoring of the samples, a standard approximation known as the Kaplan Meier or product limit plot can be used [42]. Product limit curves can be seen as a special case of the traditional life table estimate [11] in which a large number of samples are grouped into bins based on survival time. The survival probabilities s(t i ) in the Kaplan Meier curve are computed as follows: For the time of first recurrence, ....

E. L. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457--481, 1958.

....the cluster center to the points. It is precisely the mean that is used in the k Mean algorithm subproblem. We focus on evaluating the k Median Algorithm 3.1.3 and the k Mean Algorithm 3.1.4 in three clustering tasks. 3.1. 3 Data Mining Survival Curves In many medical domains, survival curves [84] are important prognostic tools. Our goal was use the k Median Algorithm 3.1.3 and the k Mean Algorithm 3.1.4 as data mining tools in a KDD process over two medical datasets to identify groups with distinct survival characteristics. We used an altered version of the WPBC dataset [119] For a ....

....time of surgery. Nodes positive = 8 corresponds to 8 or more positive nodes. When referring to the SEER dataset, we are referring to this set of 21,960 points in R 2 . We applied the k Median and k Mean algorithms with k = 3, as data mining tools, to the WPBC and SEER datasets. Survival curves [84] were then constructed for each cluster, representing expected percent of surviving patients as a function of time, for patients in that cluster. The value of k = 3 was chosen in the hope of determining clusters that represented patients with good , average and poor prognosis, as depicted by ....

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E. L. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457--481, 1958.

....does to summation. The mathematical theory of product integration is not terribly di#cult and not terribly deep, which is perhaps one of the reasons it was out of fashion again by the time survival analysis came into being in the fifties. However it is terribly useful and it is a pity that Kaplan and Meier (1958), the inventors of the product limit or Kaplan Meier estimator (the nonparametric maximum likelihood estimator of an unknown distribution function based on a sample of censored survival times) did not make the connection, as neither did the authors of the classic and papers on this estimator, ....

....to survival analysis, using some product limit theory from Aalen and Johansen (1978) but not highlighting this part of the theory. Gill (1994) is perhaps cryptically brief in parts, but a yet more polished treatment of product integration and its applications in survival analysis. The classic Kaplan and Meier (1958) is actually number 2 in the list of most cited ever papers in mathematics, statistics and computer science (fourth place is held by Cox, 1972; first place by Duncan, 1955, on multiple range tests) The authors never met but submitted simultaneously their independent inventions of the ....

Kaplan, E. and P. Meier (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457--481, 562--563.

....the use of a particular distribution for the lives of business firms. In the absence of a direct theoretical basis for the durations distribution, we used the nonparametric method of the Kaplan Meier product limit estimator (see Appendix 1) to find the survivor function, which is defined as: E.L. Kaplan and P. Meier 1958) where n j is the number operators alive (with no censoring withdrawals) and therefore, at risk, at time t j , and d j is the number of completed durations at each value of t j . The survivor function is the probability of surviving until (at least) the determined time and is the upper tail ....

Kaplan, E.L., and P. Meier. 1958. Nonparametric Estimation from Incomplete Observations.

....see Kooperberg and Stone (1991, 1992) and Kooperberg, Stone and Truong (1995a) for discussion of log spline methods. These ideas have been used to construct unconstrained log hazard rate estimates; see Kooperberg, Stone and Truong (1995b,c) 2 In the spirit of Grenander (1956) and also of the Kaplan Meier (1958) estimator, Mukerjee and Wang (1993) took a nonparametric maximum likelihood approach to this constrained estimation problem. The resulting monotone hazard rate estimator is relatively rough, however, and requires smoothing if it is to be easily interpreted. From this viewpoint, hazard rate ....

KAPLAN, E.L. AND MEIER, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 33, 457--481.

....models. Both parametric and nonparametric estimators under various censoring models have been studied extensively in the literature. The most common case of censoring is right censoring. For this case the nonparametric maximum likelihood estimator is the well known Kaplan Meier estimator (Kaplan and Meier 1958). Turnbull (1974, 1976) gives a way of obtaining a nonparametric maximum likelihood estimator of a distribution function F for the general case of interval censoring. Susarla and van Ryzin (1976) and Hjort (1990) and later Damien et al. 1996) and Laud et al. 1996) used a Bayesian approach ....

....Y (k) L(Y j (k) G (k) X (k 1) B; L(Y j G (k) X (k 1) c) Draw X (k) L(X j (k) Y (k) B; L(X j Y (k) B) where as before, G is only generated implicitly. To illustrate a situation with incomplete data, we have chosen to use the data given in Kaplan and Meier (1958). We analyzed these data using a prior on F given by the model (5) 7) and (16) So in our notation (B 1 ; 1 ) f0:8g; 1) B 2 ; 2 ) f3:1g; 1) B 3 ; 3 ) f5:4g; 1) 13 months of survival 0 2 4 6 8 10 14 (a) months of survival 0 2 4 6 8 10 14 KM samples post. mean prior mean ....

Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-81.

....by either estimating the baseline nonparametrically, or alternatively assuming a priori distribution. 8 Two specifications of the baseline hazard, 0 h , were employed: the log logistic and lognormal. The justification for employing these parametric functions is based on the nonparametric Kaplan Meir (1958) estimate of the baseline hazard for ATM diffusion as shown in Figure 1 below. 9 This suggests that the conditional probability of adoption increased up until 13 years postcommercialisation of ATMs and then decreased. For appropriate parameter values, both the log logistic and lognormal ....

Kaplan, E. L. and Meier, P. (1958). `Nonparametric estimation from incomplete observations', Journal of American Statistical Association, Vol. 53, pp. 457-481.

....between the two survival functions along with a con#dence band for the di#erence. Visually examining these 1 plots and comparing the con#dence bands with the zero line summarizes how the di#erence betwen the two survival functions change with time. Recently, Parzen et al. #1997# used the Kaplan Meier #1958# estimators of the two survival functions, F 1 ### and F 2 ###, to estimate the di#erence between the survival functions and they proposed a simulation method to construct a con#dence band for this di#erence. In many applications there is a need, when comparing two treatments, to make ....

Kaplan, E.L. and Meier, P. #1958#, #Nonparametric estimation from incomplete observations ", Journal of the American Statistical Association, 53, 457#481.

....and is independent of C 1 n ; C n n , which are i.i.d. also. The effectiveness of an anti depression drug can be statistically evaluated through F T (t) P (T k n t) We would like to estimate this quantity. This example is known as the right censoring problem. Kaplan and Meier [18] derived an estimator of F T using nonparametric maximum likelihood theory. There are also other types of situation where data are collected incompletly. These problems have been approached using nonparametric maximum likelihood theory (Kaplan and Meier [18] the self consistency idea (Efron ....

....censoring problem. Kaplan and Meier [18] derived an estimator of F T using nonparametric maximum likelihood theory. There are also other types of situation where data are collected incompletly. These problems have been approached using nonparametric maximum likelihood theory (Kaplan and Meier [18]) the self consistency idea (Efron [9] the EM algorithms (Dempster, Liard, and Rubin [8] among other methods. 1.3. Basic connections We illutrate the basic connections through heuristic arguments. Example 1 will be our cannonical model for such a purpose. Let Xn (t; k) 1(T k n t) Xn (t) ....

Kaplan, E.L. and Meier, P. (1958) Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc.66, p65-70.

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E. L. Kaplan, P. Meier, Nonparametric estimation from incomplete observations, Journal of the American Statistical Association 53 (1958) 437-- 481.

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Kaplan, E.L. and Meier, P. (1958), Nonparametric estimation from incomplete observations, Journal of the American Statistical Association 53, 457-481.

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E. L. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc., 53:457--481, 1958.

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Kaplan, E.l., Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457-481

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Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc 1958; 53:457-81.

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E. L. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457--481, 1958.

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Kaplan EL, Meier P. Non-parametric estimation from incomplete observation. J Am Stat Ass 1958; 53:457-81.

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Kaplan, E.L. and Meier, R. (1958), "Non-parametric Estimation from Incomplete Observations," Journal of the American Statistical Association, 53,457-481.

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Kaplan E. and Meier P. (1958). Non parametric estimation from incomplete observations, J.A.S.A. 53, 457-481.

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Kaplan E, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc 1958; 53:457-81.

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Kaplan EL, Meier P. Non parametric estimation from incomplete observations. J Am Stat Assoc 1958; 53: 457-81.

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Kaplan, E. L. and Meier, P. `Nonparametric estimation from incomplete observations', ####### ## ### ######## ########### ###########, ##, 457-481, 1958.

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