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Log-normal regression modeling through recursive partitioning. (English) Zbl 0875.62338
Summary: This article discusses a method for fitting log-normal regression models to censored survival data through binary decision trees. Recursive partitioning is performed by analysis of the distributions of residuals and cross-validation estimates of the average squared error. Several forms of strata selection and bootstrapping are examined to study their relative effectiveness. If the Newton - Raphson method for determining the maximum likelihood estimates fails because of heavy censoring, a method relying only on the first derivatives of the log likelihood function is used. The proposed method helps to identify the local effect of the covariates. The methods are illustrated with real and simulated data. Especially, a data set having categorical variables and missing values is used for modeling the tree-structured log-normal regression.

MSC:
62J12 Generalized linear models (logistic models)
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
AS 118; AS 138
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[1] Ahn, H.: Survival modeling through regression trees. Unpublished ph.d. Thesis (1992)
[2] Ahn, H.: Tree-structured extreme value model regression. Comm. statist. Theory methods 23, 153-174 (1994) · Zbl 0825.62084
[3] Ahn, H.; Loh, W. -Y.: Tree-structured proportional hazards regression modeling. Biometrics 50, 471-485 (1994) · Zbl 0825.62772
[4] Andrews, D. F.; Herzberg, A. M.: Data. 45-50 (1985)
[5] Bloch, D. A.; Segal, M. R.: Empirical comparison of approaches to forming strata. J. amer. Statist. assoc. 84, 897-905 (1989)
[6] Boag, J. W.: Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J. roy. Statist. soc. Ser. B 11, 15-53 (1949) · Zbl 0034.08001
[7] Breiman, L.; Friedman, J. H.; Olshen, R. A.; Stone, C. J.: Classification and regression trees. (1984) · Zbl 0541.62042
[8] Buckley, J.; James, I.: Linear regression with censored data. Biometrika 66, 429-436 (1979) · Zbl 0425.62051
[9] Chaudhuri, P.; Huang, M. -C.; Loh, W. -Y.; Yao, R.: Piecewise-polynomial regression trees. Statistica sinica 4, 143-167 (1994) · Zbl 0824.62032
[10] Ciampi, A.: Generalized regression trees. Comput. statist. And data anal. 12, 57-78 (1991) · Zbl 0825.62610
[11] Ciampi, A.; Thiffault, J.: Pruning regression trees for censored survival data: the RECPAM approach. Comm. statist. Theory methods 18, 3378-3388 (1989) · Zbl 0696.62368
[12] Cox, D. R.: Regression models and life-tables. J. roy. Statist. soc. Ser. B 34, 187-202 (1972) · Zbl 0243.62041
[13] Davis, R. B.; Anderson, J. R.: Exponential survival trees. Statist. med. 8, 947-961 (1989)
[14] Feinleib, M.: A method of analyzing lognormally distributed survival data with incomplete follow-up. J. amer. Statist. assoc. 55, 534-545 (1960) · Zbl 0093.16104
[15] Gart, J. J.; Krewski, D.; Lee, P. N.; Tarone, R. E.; Wahrendorf, J.: Statistical methods in cancer research, vol. 3: the design and analysis of long-term animal experiments. (1986)
[16] Glasser, M.: Regression analysis with dependent variable censored. Biometrics 21, 300-307 (1965)
[17] Kalbfleisch, J. D.; Prentice, R. L.: The statistical analysis of failure time data. 225-229 (1980) · Zbl 0504.62096
[18] Koul, H.; Susarla, V.; Van Ryzin, J.: Regression analysis with randomly right-censored data. Ann. statist. 9, 1276-1288 (1981) · Zbl 0477.62046
[19] Lawless, J. F.: Statistical models and methods for lifetime data. (1981) · Zbl 0541.62081
[20] Leblanc, M.; Crowley, J.: Relative risk trees for censored survival data. Biometrics 48, 411-426 (1992)
[21] Levene, H.: Robust tests for equality of variances. Contributions to probability and statistics, 278-292 (1960) · Zbl 0094.13901
[22] Loh, W. -Y.: Survival modeling through recursive stratification. Comput. statist. Data anal. 12, 295-313 (1991) · Zbl 0825.62855
[23] Miller, R. G.: Least squares regression with censored data. Biometrika 63, 449-464 (1976) · Zbl 0344.62058
[24] Miller, R. G.; Halpern, J.: Regression with censored data. Biometrika 69, 521-531 (1982) · Zbl 0503.62091
[25] Morgan, J. N.; Sonquist, J. A.: Problems in the analysis of survey data, and a proposal. J. amer. Statist. asso. 58, 415-434 (1963) · Zbl 0114.10103
[26] Nelson, W. B.; Hahn, G. J.: Linear estimation of a regression relationship from censored data. Part I – simple methods and their applications. Technometrics 14, 247-269 (1972) · Zbl 0249.62072
[27] Nelson, W. B.; Hahn, G. J.: Linear estimation of a regression relationship from censored data. Part II – best linear unbiased estimation and theory. Technometrics 15, 133-150 (1973) · Zbl 0276.62065
[28] Sampford, M. R.; Taylor, J.: Censored observations in randomized block experiments. J. rog. Statist. soc. Ser. B 21, 214-237 (1959) · Zbl 0117.14304
[29] Segal, M. R.: Regression trees for censored data. Biometrics 44, 35-47 (1988) · Zbl 0707.62224
[30] Schmoor, C.; Ulm, K.; Schumacher, M.: Comparison of the Cox model and the regression tree procedure in analysing a randomized clinical trial. Statist. med. 12, 2351-2366 (1993)
[31] Wei, L. J.; Ying, Z.; Lin, D. Y.: Linear regression analysis of censored survival data based on rank tests. Biometrika 77, 845-851 (1990)
[32] Wolynetz, M. S.: Analysis of type I censored normally distributed data. Unpublished ph.d. Thesis (1974)
[33] Wolynetz, M. S.: Statistical algorithms AS 138 and AS 139. Appl. statist. 28, 185-206 (1979) · Zbl 0447.62035
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