Use of Bootstrapping to Evaluate Infrequent Genetic Abnormalities as Prognostic Factors for Survival in Human Acute Leukemias

  • David D. Lawrence
  • Peter A. Reese
  • Clara D. Bloomfield
Conference paper


The distributional properties of a summary random variable in a two-sample test involving a small group can be investigated through bootstrapping. With data from a prospective Cancer and Leukemia Group B (CALGB 8461) study of the prognostic significance of cytogenetic abnormalities on human acute leukemias, survival data involving an infrequent genetic abnormality was bootstrapped using Cox’s proportional hazards regression model. Eight of 578 cases in the survival analysis exhibited trisomy 13 as the sole cytogenetic abnormality. Although the bootstrap results agree with the classical log-rank test, the distribution of bootstrap regression coefficients deviates from normality (P< 0.01, Kolmogorov-Smirnov). This bootstrap methodology can be of value for exploratory studies of survival involving a small group to assess the reasonableness of the log-rank statistic when the asymptotic assumption is questionable.


Score Function Bootstrap Sample Partial Likelihood Regression Coefficient Estimate Bootstrap Distribution 
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  1. Altaian D, Andersen P (1987), ”Bootstrap Investigation of the Stability of a Cox Regression Model,” Statistics in Medicine 8, 771–783.CrossRefGoogle Scholar
  2. Breslow N (1974),”Covariance Analysis of Censored Survival Data,” Biometrics 30, 89–99.CrossRefGoogle Scholar
  3. Chang I, Pagano M (1980), ”An Algorithm for Maximizing Cox’s Likelihood Function for Censored Data,” Technical Report No. 562, Sidney Färber Cancer Institute, Division of Biostatistics, Boston.Google Scholar
  4. Chen C, George S (1985), ”The Bootstrap and Identification of Prognostic Factors Via Cox’s Proportional Hazards Regression Model,” Statistics in Medicine 4, 39–46.CrossRefGoogle Scholar
  5. Cox DR (1972), ”Regression Models and Life-Tables,” Journal of the Royal Statistical Society B 34, 187–200.MATHGoogle Scholar
  6. Cox DR (1975), ”Partial Likelihood,” Biometrika 26, 269–276.CrossRefGoogle Scholar
  7. Döhner H, Arthur D, Ball E, Sobol R, Davey F, Lawrence D, Gordon L, Patii S, Wurana R, Testa J, Verma R, Schiffer C, Wurster-Hill D, Bloomfield C (1990), ”Trisomy 13: A New Recurring Chromosome Abnormality in Acute Leukemias,” Blood 76, 1614–1621.Google Scholar
  8. Efron B (1979), ”Bootstrap Methods: Another Look at the Jackknife,” Annals of Statistics 7(1), 1–26.MathSciNetMATHCrossRefGoogle Scholar
  9. Efron B (1981), ”The Jackknife, the Bootstrap and Other Resampling Plans,” SIAM, Philadelphia.Google Scholar
  10. Efron B, Tibshirani R (1985), ”The Bootstrap Method for Assessing Statistical Accuracy,” Technical Report No. 101, Stanford University, Division of Biostatistics, Stanford.Google Scholar
  11. Emrich L, Reese P, Kalbfleisch J (1981), ”Cox Model: A Proportional Hazards Model Analysis Package for SPSS Users,” Proceedings of the Fifth Annual SPSS Users and Coordinators Conference, 215–237.Google Scholar
  12. Freedman D, Peters S (1984), ”Bootstrapping a Regression Equation: Some Empirical Results,” Journal of the American Statistical Association 79, 97–106.MathSciNetCrossRefGoogle Scholar
  13. Gehan E (1965), ”A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-censored Samples,” Biometrika 52, 203–223.MathSciNetMATHGoogle Scholar
  14. Gehan E, Thomas D (1969), ”The Performance of Some Two-sample Tests in Small Samples With and Without Censoring,” Biometrika 56, 127–132.CrossRefGoogle Scholar
  15. Gill R (1984), ”Understanding Cox’s Regression Model: A Martingale Approach,” Journal of the American Statistical Association 79, 441–447.MathSciNetMATHCrossRefGoogle Scholar
  16. Lawless J (1982), ”Statistical Models and Methods for Lifetime Data,” J. Wiley, New York.MATHGoogle Scholar
  17. Lee E, Desu M, Gehan E (1975), ”A Monte Carlo Study of the Power of Some Two-sample Tests,” Biometrika 62, 425–432.MATHCrossRefGoogle Scholar
  18. Noreen E (1989), ”Computer Intensive Methods for Testing Hypotheses,” J. Wiley, New York.Google Scholar
  19. Park S, Miller K (1988), ”Random Number Generators:Good Ones Are Hard to Find,” Communications of the ACM 31, 1192–1201.MathSciNetCrossRefGoogle Scholar
  20. Tibshirani R (1983), ”A Plain Man’s Guide to the Proportional Hazards Model,” Clin. Invest. Med. 5(1), 63–68.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • David D. Lawrence
    • 1
  • Peter A. Reese
    • 2
  • Clara D. Bloomfield
    • 1
  1. 1.Department of MedicineRoswell Park Cancer Institute, New York State Department of HealthBuffaloUSA
  2. 2.Department of BiomathematicsRoswell Park Cancer Institute, New York State Department of HealthBuffaloUSA

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