ADf19 8 A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT /ESTIMATOR AND GEHAN'S TEST(U) WISCONSIN UNIV-MADISONCENTER FOR MATHEMATICAL SCIENCES A P SOMS NOV 87

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CMS Technical Summary Report #88-15

A MINITAB MACRO FOR THE KAPLAN-MEIER

PRODUCT LIMIT ESTIMATOR AND

GEHAN'S TEST

O Andrew P. Soms

fn

Center for the Mathematical SciencesUniversity of Wisconsin-Madison610 Walnut StreetMadison, Wisconsin 53705

November 1987

(Received November 2, 1987)

Approved for public releaseDistribution unlimited T lC

88 3E

88 323 046

Accession For

UNIVERSITY OF WISCONSIN-MADISON NTIS GRA&I

CENTER FOR THE MATHEMATICAL SCIENCES DTIC TABrUnannounced

A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT Justification_

ESTIMATOR AND GEHANS TEST ByDistribution/

Andrew P. Sores Availability Code

Technical Summary Report #88-15 Dist Special

November 1987

ABSTRACT

Two versions of a Minitab macro to compute the K-M ple and Gehan's testOii

are given. The shorter, km.geh, prints the K-M ple for both groups, gives Ccopy;INSPECTED

simultaneous plots of the survival curves and calculates the one and two-

sided P level of Gehan's test. The longer, kmt.geh, in addition to the

above, prints an ordered table of the observed values and their Gehan scores.

AMS (MOS) Subject Classification: 62-04

Key Words: Gehan's test; Kaplan-Meier; Macro; Minitab; Product-limit

estimator

a

Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee,

WI 53201.

A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT

ESTIMATOR AND GEHAN'S TEST

Andrew P. Soms

1. Introduction

Minitab is a user-friendly statistical computer package widely used in

industry and academia.- For more details, see Ryan, Joiner and Ryan (1985) or

Cobb and Gifford (1986). 'The Kaplan-Meier ple and Gehan's test are often used

in biostatistics and reliability theory to compare two survival distributions.

For definitions, assumptions and examples, see Brown, and Hollander (1977) or'

Miller (1981).

The main idea of the program is to first break ties between censored and

completed observations by adding to the censored observations one-half of the

smallest non-zero difference for the ordered combined observations. This does

not change the K-M ple or Gehan's test. Then, using an extension of Macro

for obtaining distinct values and replicate counts from a column of replicated

dataO by Gunter, Minitab Users' Group Newsletter, 5 (1984), 1, an ordered

table of distinct values, together with total replications, type of

observation (censored or completed), number in group one and number in group

two, is constructed. From this, the K-M ple and Gehan's test are then readily

computed. The second version of the program, kmt.geh, in addition to doing

everything the first, km.geh, does, also prints out the table and Gehan's

scores. -- -

Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI53201.

An example from Miller (1981, pp. 49-50, pp. 203-205) has been worked in

the Appendix and agrees with Miller's solution. We also checked the example

in BrownI and Hollander (1977), p. 345 and pp. 347-350, and found agreement.

The two macros listed in the Appendix can be modified by the user, if

desired, by his computer's editor. The data can be conveniently read in from a

file by the Minitab 'read' command, as was done for the example in the

Appendix. The macros can easily be used by scientists not familiar with

statistics and/or more complex statistical computer packages to quickly assess

the significance of their data. For University of Wisconsin-Madison users, it

may be possible to transfer the macros directly from the Center for the

Mathematical Sciences VAX 780 to the user's computer and interested persons

should contact the author.

*The author would appreciate any comments and suggestions from researchers

using the macros.

References

Brown, B. W., Jr. and M. Hollander, "Statistics a biomedical introduction",

New York, John Wiley, 1977.

Cobb, G. and J. Gifford, Review of "Minitab handbook (Second edition)",

Journal of the American Statistical Association 81 (1986), 1127-1129.

Gunter, B., "Macro for obtaining distinct values and replicate counts from

a column of replicated data", Minitab Users' Group Newsletter 5 (1984), 1.

Miller, R. G., Jr., "Survival analysis", New York, John Wiley, 1981.

Ryan, B. F., B. L. Joiner and T. A. Ryan, Jr., "Minitab handbook (Second

edition)", Boston, Duxbury Press, 1985.

-2-

Appendix

We include here the listings of the two macros and a worked example from

Miller (1981, pp. 49-50, pp. 203-205).

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