ADf19 8 A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT / ESTIMATOR AND GEHAN'S TEST(U) WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES A

ADf19 8 A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT / ESTIMATOR AND GEHAN'S TEST(U) WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES A P SOMS NOV 87 UNCLASSIFIED CHS-TSR-88-i5 F/G 12/5 NL

*LAS I 11 1.4111

I LL U&*. CMS Technical Summary Report #88-15 O A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT ESTIMATOR AND GEHAN'S TEST Andrew P. Soms fn Center for the Mathematical Sciences University of Wisconsin-Madison 61 Walnut Street Madison, Wisconsin 5375 November 1987 (Received November 2, 1987) Approved for public release Distribution unlimited T lc 88 3E 88 323 46

Accession For UNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES A MINITAB MACRO FOR THE KAPLAN-MEIER PRODUCT LIMIT ESTIMATOR AND GEHANS TEST Andrew P. Sores NTIS GRA&I DTIC TAB runannounced Justification_ By Distribution/ 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 test are given. The shorter, km.geh, prints the K-M ple for both groups, gives Oii Ccopy ;INSPECTED simultaneous plots of the survival curves and calculates the one and twosided 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: 62-4 a Key Words: Gehan's test; Kaplan-Meier; Macro; Minitab; Product-limit estimator Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 5321.

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. not change the K-M ple or Gehan's test. Then, using an extension of This does 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, WI 5321.

An example from Miller (1981, pp. 49-5, pp. 23-25) 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. 347-35, 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 78 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. 49-5, pp. 23-25). -3-

AA c :1.1 - - c c!.c= a C a V v 6.. ( - c do c - 1.6 c ;. QC O -DCo ' *SC 4 *C O.'-. 6>z - E- Q~ 1,- ON 1 -! - 6 C *,M.- _-. -; > C *C ~4 O O al *. r... ztf 'a"! %). * it'dc c. l 'a CL ~' -' C). I. -'->a Z.. A at - > -2 L- - '. - c6o. >- - ai- -'a OO. I - o I - ''- -9 -.!I ~ : - OC) 7; 6a o3 C%E. = - - > CL I) --a'c c C - 2 - C-a - O= * c.-. - ' - 3. f- C O X a-, I >. 1 -qt *( O - -.OeW (4 C 1.~ 'D-5 -o 1-4 -,- 3 Z-.Me.- C O.E u 4D- a--) -n'. ".- U ---- 1a- CO- 31 - C-- *=. V 3 6* C-W) e6uaa- I> - V -D -..- v ~ 1 C 1*1 ' - - a) * ". - -. * o. -. Ct 3 X2 - *- a E.- I l~ a. - ma ' -L2 6.O -'- - C1 - CO- C'. - W V, CSg* M. - - = CC CE 1. 6.% In 91 1 V... UID - 1 Z C' C "1, 1 b.-6 CO.. 1 - U a.- Cr' U. In' I 6 ( N 'X. E CM>..- ' 4-~ ~~@ ID- - -E COW~ -Il o-c (a '. -- 4 4 CL xi E E- '-c-c.7-1 6-C Q..m. 3. -1 -C*- U C a U- in.3 C 4 a(. - a.. Cc Cc --.-Q- U... OA amq 2v a - v - Qum.+C+ In.N4*-e cc a - - 6- ; C- 91 -. 1-1 CL - 6 L- a---- ISUcCI go 6. - - - 6 ft'"ft4ftof, a -- a 1

I6 C4 6 o o S S S III In- C.- L.. -3e C. A*i. f CID Q. 9C v Za AA on A -s w X W - x '.. C-,o - - --- ) ',.* -- 5 U-8,zC ' CO u. -.. Cm a %X 4 UV C --- (.. A ~- 1 A U l. u *C4C '-U-'- - * *.~ ~-5-) *t) 5 4 -S A Q I A A O U C - '~- -

'I. I.. em. a CL C - a - 9Lz a S C- CL I a a. Q CL CL MSfla (ODO *' cm- a. ac C;,- a. e- n3u a. Z,2ZC _ - m -C-C - uit Q u U.M XX 4 t jxx,- 6. a - -- - - -as IC1. o 5a CO "q. E hfq k- O- -.- -a 2 2 22..- a. C -6- C~C -

tt ( a (I - C ow "D C. a a C OD Q ; Z a -- -. Ol - a *C.C a o 6 *o e(1 - O D.S C 1- U C C~. Voa' C C4am-. S- z -~ SO ' C FSC C- a( - I a O -.. C C. E-U - a. Qs- C C U eo 3. so ac I - = a- S '-, - (L ': I - OCIC -. ow'- VLS in f -S.S 3 -. Q qo a -V.- *c :.- -.!% * ~ ~ ~ i U Q -. J e C -.. -u 2, vs S h 'U -..- Oo 3, ca - o s u 5J W. CL = C 'a U 1 CU- 44S~ C--C 1- -IX a ac *-S C. C4 1 l V a'. 55 W U -. '- a a a*sds- C S.em.S.- Q -- ;r C6- C '- -~ ac it C.- a 6 E (C I a C -u > *W- - - C- - cx at -~ Ozc ~. e C eon CSZ. *CW C4 N~ In. f C E-** - C -o'-eo~*- C~C OS I U - C CL>.au X - e C -V-- o N- -- C 6 CE a a- -UItCIt eeoul *fla GC- ~ > - e S Inm- o v Cv*.D-CC 6--. C ' I -a) (D Ob U -C~b- ON -5 (x - >. *CIE -- 4.U E- C C'.U O,O - ; a O. 6; U 5 1 4 1%- 4!,-a.--"I o o-.ce - -6 4 v-s )--o C - -Dt..- o 3-8=.I-M-C -.- a.-aw - in In.-OD u* VU ac U 66 a N. -~. - CL C" b- -- U C-OUC) 4 Q CA - 11 - - - a)om Q a CU O O C. fqu. C- C 62h. U. 1 U %C.~ E ao *sz z. zs. :U V U 7;-. zh -. *N!! U A. 2, COIN V mw.- oaao U -- UOC U 2 UC* ao-. CC C~ - -- Sa-NO'-1 -- U' :%U 6-' -. 6 O 6 L2, L -- -3 h U. C au

9c N6 *A QA N N on Z" - N * U~w 4( N No n U- c o o '- I ; 4MC " -. -- ;U U 4 a v * at I -4 Ct ~ OWC*nNW n VU)l * I O c4 - - ) D. - w w 4 U ) 1 6) 7; 1 A a- -- l **. ~ >. 9-. a 9Un o 5K CL~~~ 1 6 - U 6. - a - - W2UUCLuEo C U, *%.- -~ U U U. - i C. -- U 11 CLa a CC Q u *9 * C1 ) - u, u *L~ *--.- u*4- -, CL U u

'I'.' 4 > a. c 5 -. Q. O- U. l-. C4 -. 6 S. v u-'. - C N' - ~ a OS a V- - o-11 % 6 S 6 -u ' CN. c- * '.~ x ~ * 'D N N - -, 441cP.N -IO D.. - 4. -,. t -C 'Do-. r. C.Z %.2 l r ~Q C4 i U 5 -. -.-.- U 49 :ux i - QX UUC J X XI 5 SUSCU )k_ - -- U. OZ- 1; 6C--.! EE- 5 N O a.cq.qqq ec. oa 4 - qk.. f c. liq4q -.4 u * 9 u. u -

I~. p *1~ V A a ~ NO. CI - -.~ J. - U - I ~- N 3 - - Q *~. In U U- -- - --. -3 -. ~ - o C '-I- ~ I C.. - - ~ -1 C - - U - * I. 2.-- - S - o.o.- I-- -N o ~O I (3-1 1 - -'--32 ~* INS S ----. - N ~- -S ~- U NQN EN 11 ~ U COCO OLUC -- U -- ~C. -1-

,1': 6 -a - -C -- 4" M* 32 5 au a... u ~ V)Q~54Il- I~ ~VV~.V I

4 4c C'4 SD N *lc cqbmb A A A 4 4; AA CinC

N:D NGo,, CL In got~ (L I w a 4 - - I-. A- ID

,'I ic *11 U'U -. O~~~~~~ " C) I:,i"-- C4 W) I '- fl) it) OD "-4 Z ',ii- Ix" -14-

4 4. CD CD~ *N I N~ )S ) N -I C CD fn w 4 toit In 9 ODon a.4p' C4 " ) on * V A~~~ AI CD CDCD wcd 525 52

* Q o. *f 4 NN ------ N --- AAA AA -16-

W-w a w'' Uw v.w - A4