Basic Statistics

21 6 INTRODUCTION TO SURVIVAL ANALYSIS

places more emphasis on the results in the right tail of the survival function, where the
number at risk may be small, and the Pet0 test places more emphasis at the beginning
of the survival curve.

14.5.2 Regression Analysis of Survival Data

Regression analysis is also performed with survival data. The survival time is used

as an outcome variable that can be predicted by a predictor variable or variables.

This has become one of the major forms of survival analysis and is available in many

statistical programs. For further information on this topic, see Kleinbaum and Klein

[2005], Afifi et al. [2004], van Belle et al. [2004], Allison [1984], or Hosmer et

al. [2008]. For other general texts on survival analysis that cover both this topic and

survival analysis in general, see Lee [1992] or Parmar and David [1995].

PROBLEMS

14.1

14.2

14.3

14.4

14.5

Plot the estimated survival function from the information given in Table 14.3.

Plot the estimated survival function, hazard function, and death density function

from Table 14.2. Compare the results to those in Figures 14.5, 14.6 (number

4), and 14.3, respectively. Does it seem reasonable that the information given

in Table 14.2 could be a sample from the population depicted in these figures?

Compute the median survival time for the data in Table 14.2 using the linear

interpolation formula given in Section 6.2.2.

If we ignored the censored observations and the computed mean survival time

using the usual formula for the mean and only the observations from those who

died, would our estimate of the true mean be too large or too small?

The following data are survival times in days from a life-threatening condition:

15, 18, 18, 21, 2lC, 25', 26. Graph the estimated S(t) by the Kaplan-Meier

method using a computer program.

REFERENCES

AM, A., Clark, V. A. and May, S. [2004]. Computer-Aided Multivariate Analysis, 4th ed.,

Allison, P. D. [ 19841. Event History Analysis: Regression for Longitudinal Event Data,

Gross, A. J. and Clark, V. A. [1975]. Survival Distributions: Reliability Applications in the

Hosmer, D. W., Lemeshow, S. and May, S. [2008]. Applied Survival Analysis: Regression

Kleinbaum, D. G. and Klein, M. [2005]. Survival Analysis: A Self-Learning Text, 2nd ed.,

Boca Raton, FL: Chapman & Hall/CRC, 333-367.

Newbury Park, CA: Sage. 17-66.

Biomedical Sciences, New York: Wiley, 34-44.

Modeling of Time-to-Event Data, 2nd ed., Hoboken, NJ: Wiley, 1-66.

New York: Springer-Verlag, 4-129.