Statistical survival analysis of male larynx‐cancer patients ‐ a case study

Abstract  This paper deals with a concrete case: Of 90 male larynx-cancer patients, diagnosed and treated in the period 1970–1978, either the survival time or, if the patient was still alive at the end of the study, an appropriate lower bound on it was recorded. One factor (stage of the cancer) and one covariate (age of the patient) were a priori selected as important variables possibly influencing the survival function. After an elementary analysis of the 3 and 5 year survival fractions in section 2, a nonparametric estimation of the survival functions ignoring the effect of age is presented in section 3. In the last section COX'S (1972) proportional hazards model is used for a one dimensional regression on age which leads to the estimation of Si(tz), the survival function of patients with stage i and age z. This allows for a graphical comparison with the normal population. Finally some checks on the proportional hazard assumption are performed. The emphasis in this paper is on adequately applying and adapting (mostly existing) techniques, including the use of some generally available computer programs, to a practical case. Care has been given to model assumptions and theoretical foundations of the relevant methods.

[1]  Ron Brookmeyer,et al.  A Confidence Interval for the Median Survival Time , 1982 .

[2]  J. V. Ryzin,et al.  LARGE SAMPLE THEORY FOR AN ESTIMATOR OF THE MEAN SURVIVAL TIME FROM CENSORED SAMPLES , 1980 .

[3]  D. Cox,et al.  A General Definition of Residuals , 1968 .

[4]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[5]  A. Földes.  Strong uniform consistency of the product limit estimator under variable censoring , 1981 .

[6]  John D. Emerson,et al.  Nonparametwic Confidence Intervals for the Median in the Presence of Right CensoriIlg , 1982 .

[7]  F. W. Scholz,et al.  Towards a unified definition of maximum likelihood , 1980 .

[8]  B. Efron.  The Efficiency of Cox's Likelihood Function for Censored Data , 1977 .

[9]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[10]  A. Földes,et al.  STRONG UNIFORM CONSISTENCY FOR NONPARAMETRIC SURVIVAL CURVE ESTIMATORS FROM RANDOMLY CENSORED DATA , 1981 .

[11]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[12]  N. Breslow,et al.  Statistical methods for censored survival data. , 1979, Environmental health perspectives.

[13]  Jon A. Wellner,et al.  Confidence bands for a survival curve from censored data , 1980 .

[14]  M. Hollander,et al.  Small-Sample Results for the Kaplan-Meier Estimator , 1982 .

[15]  James A. Koziol,et al.  A Cramér-von Mises statistic for randomly censored data , 1976 .

[16]  Bradley Efron,et al.  Censored Data and the Bootstrap , 1981 .

[17]  B. Efron.  The two sample problem with censored data , 1967 .

[18]  David R. Cox.  A note on the graphical analysis of survival data , 1979 .

[19]  Nan M. Laird,et al.  Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques , 1981 .

[20]  B W Turnbull,et al.  A likelihood ratio statistic for testing goodness of fit with randomly censored data. , 1978, Biometrics.

[21]  N. Reid.  Influence functions for censored data , 1979 .

[22]  Nancy Reid,et al.  Estimating the median survival time , 1981 .

[23]  V. N. Nair.  Plots and tests for goodness of fit with randomly censored data , 1981 .

[24]  J. Kalbfleisch,et al.  Marginal likelihoods based on Cox's regression and life model , 1973 .

[25]  A. Tsiatis.  A Large Sample Study of Cox's Regression Model , 1981 .

[26]  M. Hollander,et al.  Testing to Determine the Underlying Distribution Using Randomly Censored Data. , 1979 .

[27]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[28]  N. Breslow.  A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship , 1970 .

[29]  P. Armitage.  The Chi‐Square Test for Heterogeneity of Proportions, after Adjustment for Stratification , 1966 .

[30]  M. Pike,et al.  Design and analysis of randomized clinical trials requiring prolonged observation of each patient. II. analysis and examples. , 1977, British Journal of Cancer.

[31]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

[32]  R. Morton.  Regression analysis of life tables and related nonparametric tests , 1978 .

[33]  D. Oakes,et al.  Survival Times: Aspects of Partial Likelihood , 1981 .

[34]  John D. Taulbee,et al.  A general model for the hazard rate with covariables and methods for sample size determination for cohort studies , 1979 .

[35]  Niels Keiding,et al.  Linear Nonparametric Tests for Comparison of Counting Processes, with Applications to Censored Survival Data, Correspondent Paper , 1982 .

[36]  Nancy Reid,et al.  On multiple comparisons among K samples subject to unequal patterns of censorship , 1977 .

[37]  S. Csörgo,et al.  Strong approximations of some biometric estimates under random censorship , 1981 .

[38]  Lloyd D. Fisher,et al.  CONFIDENCE BANDS FOR THE KAPLAN-MEIER SURVIVAL CURVE ESTIMATE , 1979 .

[39]  N. Mantel.  Evaluation of survival data and two new rank order statistics arising in its consideration. , 1966, Cancer chemotherapy reports.

[40]  D. Cox.  Regression Models and Life-Tables , 1972 .

[41]  Søren Johansen,et al.  The product limit estimator as maximum likelihood estimator , 1978 .

[42]  Jon E. Hyde,et al.  Testing survival under right censoring and left truncation , 1977 .

[43]  R. Kay,et al.  Proportional Hazard Regression Models and the Analysis of Censored Survival Data , 1977 .

[44]  Murray Aitkin,et al.  The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data using GLIM , 1980 .

[45]  Per Kragh Andersen,et al.  Testing Goodness of Fit of Cox's Regression and Life Model , 1982 .

[46]  R. Tarone,et al.  On the distribution of the maximum of the longrank statistic and the modified Wilcoxon statistic , 1981 .

[47]  J. Whitehead.  Fitting Cox's Regression Model to Survival Data Using Glim , 1980 .