Data For Research
beta

Regression Models and Life-Tables

  • D. R. Cox
  • Journal of the Royal Statistical Society. Series B (Methodological), Vol. 34, No. 2 (1972), pp. 187-220

  • Published by: Blackwell Publishing;Royal Statistical Society
  • Stable URL: http://www.jstor.org/stable/2985181
  • Abstract: The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
  • Subjects: statistics
  • Keyterms: sample, failure, hazard, likelihood, censor, survivor, regression, function, model, table, censoring, mantel, distribution, maximum, gehan, asymptotic, statist, estimation, conditional, estimate, variable, analysis
  • CiteRank: 3
  • Times cited by articles in JSTOR: 1856

Top Words
Word Count
the1088
of695
is355
and330
to330
a304
in301
for217
that185
be181
are132
this124
on110
with108
by104
Top Bigrams
Bigram Count
### ###1036
### #268
# ###213
of the162
## ##123
### ##109
# the103
### and100
### is82
## ###80
in the77
of ###75
and ###72
### the72
the ###66
Top Trigrams
Trigram Count
### ### ###557
### ### #98
## ## ##80
# ### ###54
### ### ##43
### and ###36
### ## ###33
### ### where31
exp ### ###30
## ### ##29
## ### ###27
### ## ##26
## ## ###25
professor ### paper22
### where ###22
Top Quadgrams
Quadgram Count
### ### ### ###319
### ### ### #63
## ## ## ##47
# ### ### ###37
### ### ### where23
### ## ## ##22
## ## ## ###22
on professor ### paper20
## ## ### ##20
discussion on professor ###19
## ### ## ##19
### ### ### ##19
### ### where ###18
### exp ### ###17
## ### ### ###17
Top Keyterms
Keyterm Weight
sample1.0
failure0.929
hazard0.92
likelihood0.861
censor0.702
survivor0.694
regression0.672
function0.617
model0.58
table0.529
censoring0.516
mantel0.505
distribution0.439
maximum0.418
gehan0.403

References

BRESLOW, N. (1970). A generalized Kruskal-Wallis test for comparing samples subject to unequal patterns of censoring. Biometrika, 57, 579-594.

CHERNOFF, H. (1962). Optimal accelerated life designs for estimation. Technometrics, 4, 381-408.

CHIANG, C. L. (1968). Introduction to Stochastic Processes in Biostatistics. New York: Wiley.

COCHRAN, W. G. (1954). Some methods for strengthening the common x2 tests. Biometrics, 10, 417-451.

COX, D. R. (1959). The analysis of exponentially distributed life-times with two types of failure. J. R. Statist. Soc. B, 21, 411-421.

(1964). Some applications of exponential ordered scores. J. R. Statist. Soc. B, 26, 103-110.

(1972).The statistical analysis of dependencies in point processes. In Symposium on Point Processes (P. A. W. Lewis, ed.). New York: Wiley (to appear).

COX, D. R. and LEWIS, P. A. W. (1972). Multivariate point processes. Proc. 6th Berkeley Symp. (to appear).

EFRON, B. (1967). The two sample problem with censored data. Proc. 5th Berkeley Symp., 4, 831-853.

GEHAN, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily single-censored samples. Biometrika, 52, 203-224.

GRENANDER, U. (1956). On the theory of mortality measurement, I and II. Skand. Akt., 39, 90-96, 125-153.

KAPLAN, E. L. and METER, P. (1958). Nonparametric estimation from incomplete observations. J. Am. Statist. Assoc., 53, 457-481.

LEHMANN, E. L. (1953). The power of rank tests. Ann. Math. Statist., 24, 23-43.

MANTEL, N. (1963). Chi-square tests with one degree of freedom: extensions of the Mantel- Haenzel procedure. J. Am. Statist. Assoc., 58, 690-700.

(1966). Evaluation of survival data and two new rank order statistics arising in its con- sideration. Cancer Chemotherapy Reports, 50, 163-170.

MANTEL, N. and HAENZEL, W. (1959). Statistical aspects of the analysis of data from retro- spective studies of disease. J. Nat. Cancer Inst., 22, 719-748.

PETO, R. and PETO, J. (1972). Asymptotically efficient rank invariant test procedures. J. R. Statist. Soc. A135, 185-206.

PRATT, J. W. (1962). Contribution to discussion of paper by A. Birnbaum. J. Am. Statist. Assoc., 57, 314-316.

SAMPFORD, M. R. (1952). The estimation of response-time distributions, II: Multi-stimulus distributions. Biometrics, 8, 307-369.

- (1954). The estimation of response-time distribution, III: Truncation and survival. Biometrics, 10, 531-561.

SAMPFORD, M. R. and TAYLOR, J. (1959). Censored observations in randomized block experi- ments. J. R. Statist. Soc. B, 21, 214-237.

SAVAGE, I. R. (1956). Contributions to the theory of rank order statistics-the two-sample case. Ann. Math. Statist., 27, 590-615.

SHOOMAN, M. L. (1968). Reliability physics models. IEEE Trans. on Reliability, 17, 14-20.

WATSON, G. S. and LEADBETTER, M. R. (1964a). Hazard analysis, I. Biometrika, 51, 175-184.

WATSON, G. S. and LEADBETTER, M. R. (1964b). Hazard analysis, II. Sankhyā, A, 26, 101-116.

ARMITAGE, P. (1959). The comparison of survival curves. J. R. Statist. Soc. A, 122, 279-300.

(1966). The chi-squared test for heterogeneity of proportions after adjustment for stratifi- cation. J. R. Statist. Soc. B, 28, 150-163

Addendum: 1967, 29, 197.

BARLOW, R. E., BARTHOLOMEW, D. J., BREMNER, J. M. and BRUNK, H. D. (1972). Statistical Inference under Order Restrictions. Chichester: Wiley.

BARLOW, R. E. and DOKSUM, K. (1972). Isotonic tests for convex orderings. In Proc. 6th Berkeley Symp. on Math. Statist. Prob., pp. 293-323. Berkeley: University of California Press.

BARLOW, R. E. and VAN ZWET, W. (1970). Asymptotic properties of isotonic estimators for the generalised failure rate function. In Proc. 1st Int. Symp. on Non-parametric Techniques in Statistical Inference, pp. 159-174. Cambridge: University Press.

BARTLETT, M. S. (1937). Properties of sufficiency and statistical tests. Proc. Roy. Soc. A, 160, 268-282.

BARTON, D. E. (1968). The solution of stochastic integral relations for strongly-consistent estimators of an unknown distribution function from a sample subject to variable censoring and truncation. Trab. Estadist., 19, 51-73.

BENJAMIN, B. (1972). Stochastic aspects of life tables. I.M.A. Bull., 8, 12-16.

BENJAMIN, B. and HAYCOCKS, H. W. (1971). The Analysis of Mortality and other Actuarial Statistics. Cambridge: University Press.

BIRCH, M. W. (1965). The detection of partial association, II. The general case. J. R. Statist. Soc. B, 27, 111-124.

BRADLEY, J. V. (1968). Distribution-free Statistical Tests. Englewood Cliffs, N.J.: Prentice Hall.

COCHRAN, W. G. (1954). Some methods for strengthening the common x2 tests. Biometrics, 10, 417-451.

COX, D. R. (1958). The regression analysis of binary sequences (with Discussion). J. R. Statist. Soc. B, 20, 215-242.

DAVID, H. A. (1963). The Method of Paired Comparisons. London: Griffin.

DE HASS, J. H. (1964). Changing Mortality Patterns and Cardiovascular Diseases. N. V. Haarlem: De Erven F. Bohn.

DOKSUM, K. (1967). Asymptotically optimal statistics in some models with increasing failure rate averages. Ann. Math. Statist., 38, 1731-1739.

ESARY, J. D., MARSHALL, A. W. and PROSCHAN, F. (1972). Shock models. Ann. Math. Statist., in the press.

FORBES, A. F. (1971). Non-parametric methods of estimating the survivor function. The Statistician, 20, 27-52.

FRASER, D. A. S. (1968). The Structure of Inference. New York: Wiley.

GART, J. J. (1970). Point and interval estimation of the common odds ratio in the combination of 2 x 2 tables with fixed marginals. Biometrika, 57, 471-475.

GRENANDER, U. (1956). On the theory of mortality measurement, Part II. Skan. Aktuarietidskr., 39, 125-153.

HARRIS, T. E., MEIER, P. and TUKEY, J. W. (1950). Timing of the distribution of events between observations. Hum. Biol., 22, 249-270.

KALBFLEISCH, J. D. and SPROTT, D. A. (1970). Application of likelihood methods to models involving large numbers of parameters (with Discussion). J. R. Statist. Soc. B, 32, 175-208.

MANTEL, N. and HAENZEL, W. (1959). Statistical aspects of the analysis of data from retro- spective studies of disease. J. Nat. Cancer Inst., 22, 719-748.

NELSON, W. (1969). Hazard plotting for incomplete failure data. J. Qual. Tech., 1, 27-52.

ZELEN, M. (1971). The analysis of several 2 x 2 contingency tables. Biometrika, 58, 129-137.

Selected: 6,428,186

JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways.
©2000-2010 ITHAKA. All Rights Reserved. JSTOR®, the JSTOR logo, and ITHAKA® are registered trademarks of ITHAKA.