Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 45,181

The DOI matches its Crossref record.

Nonparametric Estimation from Incomplete Observations

Kaplan, E. L., Meier, Paul·1992·Springer Series in Statistics
DOI 10.1007/978-1-4612-4380-9_25
Open this paper in CoChat — free account

Abstract

Abstract In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t). The observation for each item of a suitable initial event, marking the beginning of its lifetime, is presupposed. For random samples of size N the product-limit (PL) estimate can be defined as follows: L...

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/978-1-4612-4380-9_25

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 23

  1. Bailey. W.G.. and Haycocks, H.W, “A synthesis of methods of deriving measures of decrement from observed data.” Journal of the Institute of Actuaries, 73 (1947). 179–212. · DOI
  2. Bartlelt, M.S.. “On the statistical estimation of mean lifetime,” Philosophical Magazine (Series 7 ), 44 (1953), 249–62. · DOI
  3. Berkson, J., and Gage, R.P. “Calculation of survival rates for cancer,” Proceedings of the Staff Meetings of the Mayo Clinic. 25 (1950), 270–86.
  4. Berkson, J, and Gage, R.P., “Survival curve for cancer patients following treatment.” Journal of the American Statistical Association. 47 (1952), 501–15. · DOI
  5. Berkson. J., “Estimation of the interval rate in actuarial calculations: a critique of the person-years concept.” (Summary) Journal of the American Statistical Association 49 (1954). 363.
  6. Böhmer, P.E., “Theorie der unabhängigen Wahrscheinlichkeiten,” Rapports. Mémoires et Prooès-verbaux de Septième Congrès International d’Actuaires, Amsterdam. 2 (1912), 327–43.
  7. Brown, G.W. and Flood, M.M.. “Tumbler mortality,” Journal of the American Statistical Association. 42 (1947). 562–74. · DOI
  8. Davis, D.J., “An analysis of some failure data,” Journal of the American Statistical Association 47 (1952), 113–150. · DOI
  9. Epstein, Benjamin, and Sobel, Milton, “Lifetesting,” Journal of the American Statistical Association. 48 (1953). 486–502. · DOI
  10. Epstein, Benjamin, and Sobel, Milton, “Some theorems relevant to lifetesting from an exponential distribution,” Annals of Mathematical Statistics. 25 (1954), 373–81. · DOI · Paper page
  11. Fix. Evelyn, and Neyman, J., “A simple stochastic model of recovery, relapse, death and loss of patients.” Human Biology, 23 (1951), 205–41.
  12. Goodman, L.A., “Methods of measuring useful life of equipment under operational conditions.” Journal of the American Statistical Association. 48 (1953) 503–30. · DOI
  13. Greville, T.N.E., “Mortality tables analyzed by cause of death.” The Record, American Institute of Actuaries, 37 (1948). 283–94.
  14. Hald, A., “Maximum likelihood estimation of the parameters of a normal distri¬bution which is truncated at a known point.” Skandinavisk Aktuarietidskrift, 32 (1949) 119–34.
  15. Harris, T.E., Meier, P.. and Tukey, J.W., “Timing of the distribution of events between observations,” Human Biology, 22 (1950), 249–70.
  16. Irwin. J.O., “The standard error of an estimate of expcctational life.” Journal of Hygiene, 47 (1949), 188–9. · DOI
  17. Littell, A.S., “Estimation of the T-year survival rate from follow-up studies over a limited period of time,” Human Biology, 24 (1952), 87–116.
  18. Merrell, Margaret, “Time-specific life tables contrasted with observed survivorship,” Biometrics. 3 (1947), 129 - 36. · DOI
  19. Sartwell, P.E., and Merrell. M. “Influence of the dynamic character of chronic disease on the interpretation of morbidity rates,” American Journal of Public Health, 42 (1952), 579–84. · DOI
  20. Savage. I.R., “Bibliography of nonparametric statistics and related topics.” Journal of the American Statistical Association, 48 (1953), 844–906. · DOI
  21. Seal, H.L., “The estimation of mortality and other decremental probabilities,” Skamlinavisk Aktuarletidskrift, 37 (1954), 137–62.
  22. Stephan. F.F., “The expected value and variance of the reciprocal and other negative powers of a positive Bernoullian variate,” Annals of Mathematical Statistics, 16 (1945), 50–61. · DOI
  23. Wolfowitz. J., “Additive partition functions and a class of statistical hypotheses.” Annals of Mathematical Statistics, 13 (1942), 247–79. · DOI

Cited by

Items 401–500 of 573

Metadata

Authors
Kaplan, E. L., & Meier, P.
Venue
Springer Series in Statistics
Publisher
Springer New York
Published
1992
Pages
319-337
ISSN
0172-7397 (ISSN-L)
DOI
10.1007/978-1-4612-4380-9_25
OpenAlex
W1979300931
Cited by
45,181
References
0
FWCI
732.91
Type
book chapter
Language
en
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.