A Vitamin and Mineral Mega-dose Treatnient for Non-metastatic Breast Cancer Patients: A Historical Comparison Study
Angelia Selena May Vanderlaan B.Sc., Dalhousie University, 2000
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
in the Department of Mathematics and Statistics
@ Angelia S.M. Vanderlaan, 2004 University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author.
Supervisors: Dr. M. Lesperance
(Department of Mathematics and Statistics)
Abstract
With alternative therapies for cancer becoming more commonly used by women with breast cancer and a paucity of studies evaluating their effectiveness, this study's objective was to assess the usefulness of mega-doses of vitamins and minerals as supplementary alterative treatment for breast cancer. The prescribed regimen of mega-doses of vita- mins and minerals used to treat cancer patients consisted of various doses of p-carotene, vitamin C, niacin, selenium, coenzyme Q10 and zinc. The case patients were cancer patients with unilateral non-metastatic breast cancer diagnosed between 1989 and 1998. The control patients were matched (2:l) to the vitamin and mineral patients for di- agnostic and prognostic variables. Three endpoints were considered and survival was measured as disease-free survival, breast cancer-specific survival, and overall survival. Cox proportional hazards models were used to analyse the data. The survival times were not enhanced for the vitamin and mineral treated group compared to the controls.
Contents
Abstract ii
Table of Contents iv
List of Figures ix
List of Tables xix
Acknowledgements xxii
1 Introduction 1
. . .
1.1 Breast Cancer 1
. . .
1.2 Vitamins and Minerals 3
. . . 1.2.1 $-carotene 3 . . . 1.2.2 Vitamin C 3
. . .
1.2.3 Niacin B3 4. . .
1.2.4 Seleniun 5. . .
1.2.5 Coenzyme Q10 5. . .
1.2.6 Zinc 6. . .
1.2.7 Vitamins arid Minerals Taken in Condhation 6. . .
1.3 Surnniary of the Breast Ca.ncer Study 7
2 Survival Analysis 8
2.1 Product-Limit Estimators . Nonparametric Estirnatiou of Basic Quantities 8
. . .
2.2 Censorii~g of Su1)jects 10
. . .
2.3 Cox Proportional IIazards Model 10
. . . .
2.4 Tirne-Dependent Covariates and Cox Proportional IIazarcls XIodel 12
. . .
2.5 Timc-Dependent Covariates and Breast Cancer 13. . . 2.6 Residual Analysis 14
. . .
2.6.1 Martingale Resicluds 14. . .
2.6.2 Deviame Residuals 14. . .
2.63 Schoenfeld Residuals 15 . . . 2.6.4 Influential Observations 15. . .
2.7 Proportional Hazard Tests 16
3 Description of Data 17
. . .
3.1 Subjects 17
. . .
3.2 Descript. ion of Variables 18
. . .
3.3 Measuring Survival 21
. . .
3.4 Vit-arnin and Mineral Treatment Regimen 22
. . .
3.5 Cases a. nd Controls and the Quality of Ma. tching 31
. . .
3.6 The Data Sets: Full and Subset 35
. . .
3.6.1 The Full Da~ta Set 35
. . .
3.6.2 The Subset Data Set 35
4 Preliminary Analysis of the Full Data Set 39
. . .
4.1 DiseascFree Survival 39
. . .
4.2 Breast Cancer-Spccific Survival 53
. . .
4.3 Overall Snrvisml 66
. . .
4.4 Kaplan-kieier Curves for the Subset Data Set 77
5 Cox Proportional Hazards Models with All Patients 78 . . .
5.1 Diseax-Free Survival 78
. . .
5.11 Cox Regression: The Full Model 78
. . .
5.l.2 Cox Regression: The Reduced Model 80
. . .
5.1.3 Cox Regression Models: Double Indica. tors for Treatment 89. . .
5.1.4 Cox Regression Models: Influential Data Points 95. . .
5.1.5 Cox Itegression Models: Time Dependent; Covariates 106 5.1.6 Cox Regression Models: Interactions with the Vitamin ad Min-. . .
era1 Regimen 110
. . .
5.2 Breast Cancer-Specific Survival 112
. . .
5.2.1 Cox R. cgrcssion. The Full Model 112
. . .
5.2.2 Cox
R.
egression. The Rectuccd Model 113. . .
5.2.3 Cox Regressiori Models: Double Indicators for Treatment 119. . .
5.2.4 Chx Regression Models: Time Depenc-fent Covariates 122
. . .
5.2.5 Cox Regression Models: Interactions with Treat. ment 1285.3 Overa.11 Survival
. . .
1335.3.1 Cox Regression: The Full Model . . . 133
. . . 5.3.2 Cox Regression: The Rectuced Model 135
. . .
5.3.3 Cox Regression Models: Double Indimtors for Trestrneri t. 137. . .
5.3.4 Cox Regressioll Models: Time Dependent C:ovariates 141 . . . 5.3.5 Cox Regression Models: Irit. eractioris with Treatment 144 6 Cox Proportional Hazards Models with Subset Data Set 147 6.1 Disease-Free Survival . . . 1476.1.1. Cox Regression: The Full Model
. . .
1486.2.2 Cox Regression: The Reduced Model . . . 151
6.1.3 Cox Regression Models: Time Dependellt Covariates . . . 152
6.1.4 Cox R. egression hifodels: Interactions with Tst~tmeni; . . . 156
. . . 6.2 Breast Cancer-Specific Survival 157 6.2.1 Cox Regression: The Full Model . . . 157
6.2.2 Cox Regression: The Reduced Model
. . .
1616.2.3 Cox Regression Models: Time Dependent Comriates . . . 164
6.2.4 Cox
H.
egression Models: Interactions with Eea;tment; . . . 167. . .
6.3 (:>~w-all Si.uviva1 174 . . . 6.3.1. Cox Regression: The Full Model 174. . .
6.3.2 Cox Regression: The Reduced Model 174 6.3.3 Cox Regression Models: Time Dependent Covariates. . .
1806.3.4 Cox R~gressio~l Models: Interactions with 'I'rcatmcnt;
. . .
183 7 Survival within the Vitamin and Mineral Regimen 191. . .
7.1 Vitamin and Mineral Doses 191
. . .
7.2 Survival for Each Vitamin or Mineral 191
. . .
7.2.1 j3-carotene 191. . .
7.2.2 Vitarnirl C 193. . .
7.2.3 Niacin 193. . .
7.2.4 Selenium 197. . .
7.2.5 Cocnzyrrlc 6210 197. . .
7.2.6 Zinc 197. . .
vii 7.3.1 Disease-Free Survival . . . 200 7.3.2 Breast Cancer-Specific Survival
. . .
206 7.3.3 Overall Survival . . . 2068 Summary and Conclusions 209
References 212
A Kaplan-Meier Curves for the Subset Data Set 217
A.l Disease-Free Survival . . . 218 A.2 Breast Cancer-Specific Survival
. . .
227 A.3 Overall Survival. . . 236
B Residual Analysis for Models using the Full Data Set 245 B.l Disease-Free Survival. . .
245 B.l.l DFS Model 6. . .
246. . .
B . 1.2 DFS Motlel 7 250. . .
B.1.3 DFS Model 9 257. . .
B.l.4 DFS Model 10 262. . .
B.1.5 DFS Model 11 267 . . . B . 1.6 DFS Model 12 274B.2 Breast Cancer-Specific Surviva. 1
. . . 278
. . .
B.2.1 RCSS Model 1 278. . .
B.2.2 BCSS Model 2 285 . . . B.2.3 BCSS Model 3 289. . .
B.2.4 BCSS Y1ot:kl 4 292. . .
B.2.5 BCSS Model 5 299. . .
B.2.6 BCSS Model 6 305. . .
13.2.7 BCSS Model 7 309. . .
B.2.8 BCSS Model 8 316. . .
B.2.9 BCSS Model 10 320. . .
B.3 Overall Survival 324. . .
13.3.1 OS Model 1 324. . .
B.3.2 OS Model 2 331. . .
B.3.3 OS Model 3 336. . .
B.3.40s
Model 4 342. . .
B.3.5 OS Model 5 347...
Vlll
. . .
B.3.6 CIS Model 6 354
B.3.7 OS Model 7
. . .
358 C Residual Analysis for Models using the Subset Data Set 362. . . C . 1 Disease Free-Survival 362
. . .
1 1 DFS180 Model 1 363. . .
C . 1.2 DFS180 Model 2 368 . . . C.1.3 DFS180 Model 3 371 . . . C . 1.4 DFS18O Model 4 376 . . .(2.2 Breast Cancer-Specific Survivid 379
. . . C.2.1 BCSS180 Model 1 379
. . .
C.2.2 BCSS1.80 Moclel 2 385. . .
C.2.3 BCSS1.80 Model 3 389 . . . (2.2.4 BCSS180 Model 4 394 . . . C.2.5 BCSS180 Model 5 398 . . . C.2.6 BCSS180 Model 6 402. . .
C.2.7 BCSS180 Model 7 405 . . . C.3 Overall Survival 409 . . . C.3.1 OS180 Model 1 409. . .
(2.3.2 OS180 Model 2 415. . .
C.3.3 (IS180 Model 3 418. . .
(2.3.4 OS180 Model 4 423. . .
(2.3.5 OS180 Model 5 427. . .
C.3.6 OS180 %lode1 6 431. . .
C.3.7 OS180Model7 435. . .
(2.3.8 OS180 Model 8 438List
of Figures
Figure Page
3.4.1 The number of different agents each of Dr . Hoffer's patients tvcre prescribed
. . .
24 3.4.2 The daily niacin doses (grams) for Dr . Hoffer's 153 patients . . . 25 3.4.3 The beta-carotene doses (1000 iu) per day for Dr . TIoffer's 1.53 patients . 26 3.4.4 The usage of coenzyme Q10 by Dr . Hoffer's 153 patients . . . 27 3.4.5 The daily selenium doses (mcg) for Dr.
Hoffds 153 patients . . . 28 3.4.6 The da. ily vitamin C (loses (grams) for Dr.
Hoffer's 153 patients . . . . 29 3.4.7 The daily zinc: doses (rrig) for Dr . Hoffer's 153 patients. . .
30 3.5.1. Histogram of the age at dia.gnosis. . .
32. . .
3.5.2 Histogram of t. he diagnosis year 33
3.6.1.1 Histogram of the days from diagnosis to ciatc of first consultation with Dr . Hoffer (days2hofr) . . . 36 4.1.1 KM survival functions (DFS)for the vitainin/minc?ral treated a.nd con-
. . .
trol patients 44
4.1.2 KM survival functions for disea.se-free survival for pathological N-stage pztients (stngepn.)
. . .
45 4.1.3 KM survival functions for disease-free survival for patients with thecat. egorical number of positive nodes ( p o m o d c n )
. . .
46 4.1.4 KM survival functions for disease-free sr.lrvi.c.al for patients with thefive categories of T-stage (staget)
. . .
47 4.1.5KM
survival functions for disease-free survival for pa.tients wit. h lym-pha.tic, vanscular or neural invasion ( d x h )
. . .
48 4.1.6 KM survival functions for disease-free survival for patients wit. h vario1.1~4.1.7 KM survival functions for disease-free survival for pstients with various estrogen receptor status ( d z e r ) . . . . . . . . . . . . . . . . . .
.
. ..
..
4.1.8 KM survival furictioris for disease-free survival for pat,ients either re- ceiving systemic therapy or receiving no systemic treatment (s:ystemca). .
4.1.9 KM survival funct,ions for disease-fme survival for patSients receiving local treatment (localnm).
. . . . . . . . . . . . . . . . . . . . . .
. ..
.4.2.1 KM survival functiorls for breast ca11c;er-specific survival for the vita- miri/rnirieral treated and control patients
.
. . . . . . . . . . . . . . . . .4.2.2 KM survival functions for breast cancer-specific survival for patholog- ical K-stage patients (stagepn.) . . . . . .
.
. . . . . . . . . . . .4.2.3 KM srirvival functions for breast cancer-specific survival for pat3ients with the categorical number of posit,ive nodes (posnodca).
. . . . . . .
..
4.2.4 KM surviva.1 functiorls for breast cmcer-specific survival for pa.tier1t.swith the five categories of T-stage (staget). . . . . . . . . . . . . . . .
4.2.5 KM survival functions for breast cancer-spccific survival for patients with lymphatic; vascular or neural invasion (cI:xkm j. . . . .
.
. . ..
.4.2.6 KM survival functions for breast cancer-specific survival for patients with various tumour grades (dxgrade) . . . . . . . . . . . . . . . .
.
..
.4.2.7 KM survival funct~ions for breast cancer-specific survival for patients with various estrogen receptor status ( h e r ) . . . .
. . .
. . . . . . . . . .4.2.8 KM surviva.1 functions for breast cancer-specific survival for patients either receiving systemic therapy or receiving no systemic t,reatment. ( s y s -
temca). . . . . . . .
.
. .. . . . . . . . . . . . . . .
. .. .
. . . . .4.2.9 KM survival functions for breast cancer-specific survival for patients receiving local treatment (localnm).
. . . . .
..
. . . . . . . . . . . . . .4.3.1 KM survival fuiictions for overall survival for tho vitamin/mineral treaied a.nd control patients.
. .
. . . .. . . . . . . . . .
. .. .
. . . . .4.3.2 KM survival functions for overall survival for pat,hological N-sttage patients (stagepn). . . . . . . . . .
. .
.. . . . . . . . . .
. . . . . . . .4.3.3 KM survival functions for overall survival for patients with the cate- gorical number of positive nodes (posnodca).
.
..
. . . . . . . . . . . . .4.3.4 KM survival furict.ioris for overall survival for pa,tierits with the five categories of T-stage (staget).
. . . . . . . . .
.. .
. . . . . . . ..
..
.4.3.5
ICM
survival functions for overall survival for patients with ly rnphatic, vascular or neural invasion (dzlvrr,)..
. .. . . . . . .
. . . . . .. . . . .
4.3.6 KM survival functions for overall survivd for patients wit. h various turnour grades (dxgrade) . . . 73 4.3.7 KM survival functions for overall survival for patients wi.th mrious
estrogen receptor status (dxer) . . . 74 4.3.8 KM survival functions for overall survival for paticnts eithcr receiving
systemic therapy or receiving no systernic treatment (systerrm) . . . 75 4.3.9 KM survival fuiictions for overall survival for patients re( . !eiving l o ~ d
treatment (1occr.lnm).
. . .
76. . .
5.1.2.1 A plot of t. he devia.rice residuals for DFS Model 3 85
. . .
5.1.2.2 Plots of t. he influence by observation number for DFS Model 3 86
. . .
5.1.2.3 Plots of the influence by observation number for DFS Model 3 87
. . .
5.1.2.4 Plots of the influerice by observation number for DFS Model 3 88
. . .
5.1.4.1 Plots of the influence by obsermtion riurriher for DFS Model L 96
. . .
5.1.4.2 Plots of the influence by observation nurnber for DFS Model 2 97. . .
5.2.2.1 The rescaled Schoenfeld residuals for BCSS Model 3 118 6.2.1.1 Plot of the log transformed resealed Schoenfeld residuals for BCSS180Model1
. . .
160 6.2.2.1 Plot of the log transformed rescaled Schoe~~fcld residuals for BCSS180Model 2
. . .
163 6.31 1 . Plot of the log transforrried rescalecl Sclioenfeld resi.dua1s for OSlrjOModel 1 . . . 177 6.3.2.1 Plot of the log transformed rcscded Schoenfeld residuals for OS180
Model 2
. . .
179 7.2.1.1 KM suruivd curves for the patierits prescribed various doses of 3-carotene arid the control patier1t.s
. . .
194 7.2.2.1 KM survival curves for t. he patients prescribed vitamin (1 and thecontrol pa.tient.s
. . .
195 7.2.3.1 KM survival curves for the patients prescribed various doses of niacinand the c(:)ntrol patients
. . .
196 7.2.4.1 KM survival curves for t. he patients prescrik)ed twions doses of sele-nium arid the cont*rol patients
. . .
198 7.2.5.1 KM survival curves for control patients and H o a r pa. tients (HP) ca.t,-xii
7.2.6.1 KM survival ccurves for control patients a,nd Hoffer patients (HP) cat-
. . .
egorised by whether t,hey were presc:riE:)ed zinc supplements 201 7.3.1.1 KM surviva.1 curves for DFS for breast-cancer patients a.ccording to the
nunher of different vitanlin and nlineral mega-dosing they were prescribed. 203 7.3.2.1 KM survival curves for BCSS for breast-cancer patients according to
the number of different vitamin a i d mineral mega-dosing they were pre-
. . .
scribed. 207
7.3.3.1. KM survival curves for OS for breast,-cancer patients a.ccording to t h e number of different vitamin and mineral mega-dosing they were prescribed. 208 A. 1.0.1 ICM ssurvivaJ for disease-free survival for t,he vitamin/mineral t,reilted
. . .
and control patients. 218
4.1.0.2 KM survival for disease-free survivd for pathological n'-stage ptients. 219 A.1.0.3 KRiI survival for disease-free surviva,l for patients with the categorical
. . .
number of posit,ive lyrnpll nodes (yosnodcu). 220
A.1.0.4 KM survival for disease-free surviva.1 for pat,ients with the five cate-
. . .
gories of TI'-stagc (stuget). 221
A. 1.0.5 KM survival for disease-free survival for patients with lymphatic, vas-
. . .
culaa or neura.1 invasion (dxlvn). 222
A.1.O.G KYI survival for disease-free survival for patierits with wsious tumour
. . .
grades ( dxgrude) 223
A. 1.0.7 KM survival for disease-free survival for patients with -va.rious estrogcn
. . .
receptor statas (d:xw). 224
A.1..0.8 KM survival for disease-free survivarad for patients either receiving sys- t,ernic therapy or receiving no syst,ernic treatment (syste,mcu).
. . .
225 A.1.0.9 KM survival for disease-free survival for patients receiving local t,reat,-. . .
ment (localnm). 226
A.2.0.1 KM survival for breast cancer-specific survival for the vitarniri/rnineral
. . .
treated and control paftients. 227
A.2.0.2 KM survival for breast cancer-specific survival for pathological N-stage
. . .
pa,t,ient,s. 228
A.2.0.3 KM survival for breast cancer-specific survival for patients with the
. . .
categorical number of positive lymph nodes (po.modca). 229 A.2.0.4 KM survival for breast cancer-specific sur~iva~l for pa.tiexits with the. . .
xiii
A.2.0.5 KM survival for breast cancer-specific si~rvival for patients with lyrn-
p h t i c , vascular or neural i~lvibsion (dx11:n) . . . 231
A.2.0.6 KM survival for breast cancer-specific survival for pa.tient. s with various tumour grades ( d q r a d e )
. . .
232A.2.0.7 KM survival for breast cancer-specific survival for paticnts with mrious estrogerl receptor status (dxer)
. . .
2334.2.0.8 KM survival for breast cancer-specific: survival for patients either re- ceiving systerriic therapy or receiving no systemic treatment (systemcaj . . 234
A.2.0.9 KM survival for breast cancer-specific survival for patients receiving local treatment (locnlnrrr)
. . .
235A.3.0.1 I<M survival for overall survival for the vitarnin/rnineral treated and control patients
. . .
236. . . A.3.0.2 KM survival for overall survival for pathological IT-stage patients. 237 A.3.0.3 KM survival for osrerall surviva.1 for patients with the categorical num- ber of positive lymph nodes (posnodca)
. . .
238A.3.0.4 KM sr~rvival for overall survival for patients with the five categories of T-stage (sta.get)
. . .
239A.3.0.5 KM survival for overall survival for patients witsh lymphatic, va.scular or neural invasion (dxlvn)
. . .
240A.3.0.6 KM survit-a1 for overall survival for patients with various t:wmour grades (dxgrude) . . . 241
8.3.0.7 KM survival for overall surviva.1 for patients with various estrogen recept.or status ( d x e r ) . . . 242
A.3.0.8 KM survival for overall survival for paticnts either recciving systemic therapy or receiving no syst.emic treatment (systemcu); a cross represents
. . .
a censored ol-,servation 243 A.3.0.9 KM surviva. 1 for overall survival for pat.ient.s receiving local treatment. . .
(loculnm) 244 13.1.1.1 The rescaled Schoenfelcl residuals for DFS Model G. . .
246B
.
1.1.2 The deviance residuals for DFS Model 6. . .
247. . .
B.1.1.3 Plots of the influence by observation number for DFS Model 6 248 B.1.1.4 Plots of the influenc:e by observation ri~mlber for DFS Model 6. . .
249B.1.2.1 The deviance residuads for DFS Model 7
. . .
250B.1.2.2 Plots of the influence by observation number for DFS Model 7
. . .
251xiv
B.1.2.4 Plots of the influence by observation number for DFS Model 7
. . .
253B.1.2.5 Plots of the influence by observation nuni1:)er for DFS hlodel 7
. . .
254R.1.2.6 Plots of the influence by obserw. tion xiumber for DFS Model 7 . . . 255
13.1.3.1 The rescaled Schoenfeld residuals for DFS Model 9 . . . 257
B.1.3.2 Plots of the influence by observat.ion number for DFS Model 9 . . . 258
. . . B.1.3.3 Plots of the influence by oltservat.ion number for DFS Model 9 259 B.1.3.4 Plots of the influence by observation riunll-xr for DFS k c - i e l 9 . . . 260
B.1.3.5 The deviance residua.1~ for DFS Model 9 . . . 261
B.1.4.1 The cleviance residuals for DFS Model 10
. . .
262. . .
B.1.4.2 The rescaled Schoenfeld residuals for DFS Model 10 263. . . .
B.1.4.3 Plots of the influence by observattion nunher for DFS Model 10 264 B.1.4.4 Plots of the influence by observation riurnber for DFS Model 10 . . . . 265I3.1.4.5 P1ot.s of the influence by- ol-, servation nurnber for DFS Model 10 . . . . 266
13.1.5.1 The deviance residuals for DFS Model 11
. . .
267B
.
1.5.2 Plots of the influence by observation nrmlber for DFS Model 11 . . . . 268. . . . B.1.5.3 Plots of the influence 1.1y observation nurriber for DFS Mo/Iodel 11 269 B.l.5.4 Plots of the influence by observation riumber for DFS Model IS . . . 270
B.1.5.5 Plots of the influence by observat. ion number for DFS Model 11 . . . . 271
B.1.5.6 Plots of the influence by observ~~tion number for DFS Model 11
. . . .
272B.1.6.1 The devizmce residuals for DFS Model 12 . . . 274
B.1.6.2 Plots of the influerice hy observat. ion numt>er for DFS Model 12 . . . . 275
B.1.6.3 Plots of the influence by observation number for DFS blodel 12
. . . .
276B.1.6.4 Plots of the influence by observation number for DFS Model 12 . . . . 277
B.2.1.1 Plot of the deviance residuals for BCSS Moclcl
L
. . . 278. . . . B.2.1.2 Plots of the influence by observation nuniber for BCSS Model 1 279 B.2.1.3 Plots of the influence by ohserva~tiori nurrher for BCSS Model 1
. . . .
280. . . B.2.l.4 Plots of the irlfl~~ence by observation mrmber for RCSS Model 1 281
. . . .
B.2.1.5 Plots of the influence by observat.ion number for BCSS Model 1 282. . .
13.2.1.6 Plot of the influence by observation iiuniber for BCSS Model 1 284 B.2.2.1 Plot . of the deviance residuals for BCSS Model 2. . .
285B.2.2.2 Plot. s of the iufluence by observaation nurnber for BCSS Model 2 . . . . 286
. . . . B.2.2.3 Plots of the influence by observation rwnber for BCSS Model 2 287 B.2.2.4 Plots of the influence by observation number for BCSS Model 2 . . . . 288
B.2.3.1 The deviance residuals for BCSS Model 3
. . .
289. . . .
B.2.3.2 Plots of the influence by observation numl>er for BCSS Model 3 290B.2.3.3 Plots of t>he influence by obserwition number for BCSS Moc-lel 3 . . . . 291 B.2.4.1 The tleviance residuals for BCSS Model 4
. . .
292 B.2.4.2 Plots of t.he isifluerlce by observation rlumber for BCSS Model 4. . . 293 13.2.4.3 Plots of the influence by observation number for BCSS Model 4 . . . . 294 B.2.4.4 Plots of the influence by observation number for BCSS Model 4 . . . . 295 B.2.4.5 Plots of the influence by observation number for BCSS Model 4 . . . . 296 B.2.4.6 Plots of the infhxence by observation nuxnber for BCSS Model 4 . . . . 297 B.2.5.1 Plot of the deviance residua.1~ for BCSS Model 5 . . . 300 13.2.5.2 Plots of the influence by observation number for BCSS Model 5 . . . . 301 B.2.5.3 Plots of the influence by observation number for BCSS Model 5. . . .
302 B.2.5.4 Plots of the influence by ol-tservatic.)n number for BCSS Model .5 . . . . 303 13.2.6.1 The rescaled Schoenfelcl residua.1~ for BCSS Model 6 . . . 305 B.2.6.2 The deviar~ce residuals for BCSS Model 6. . .
306 B.2.6.3 Plots of the influence by observaRtion number for BCSS Model 6 . . . . 307 B.2.6.4 Plots of the influence by observation auml~er for BCSS Model 6. . . .
308 B.2.7.1 The deviarice residuals for BClSS Model 7. . .
309 B.2.7.2 Plots of the influence by observation number for BCSS Model 7 . . . . 310 B.2.7.3 Plots of the influence by observation number for BCSS Model 7 . . . . 311 B.2.7.4 Plots of the influence by observation number for BCSS Model 7. . . .
312 B.2.7.5 Plots of the influence by observation number for BCSS Model 7. . . .
313 B.2.7.6 Plots of the influence by observation number for BCSS Model 7 . . . . 314 I3.2.8.l The deviance residuals for BCSS Model 8 . . . 316 13.2.8.2 Plots of the influence by observation number for BCSS Model 8. . . .
317 B.2.8.3 Plots of t. he influence by obscrva. tion number for BCSS Model 8. . . .
318 B.2.8.4 Plots of the influence by observation num'ber for BCSS Model 8 . . . . 319 B.2.9.1 The resca. led Schoenfeld residuals for BCSS Model 10. . .
320 B.2.9.2 Plots of the influence by observation number for BCSS Model 1.0. . 321 B.2.9.3 Plots of the influence by observation number for BCSS Model 10.
.
322 B.2.9.4 Plots of the influence by obsermtion number for BCSS Modcl 10. . . .
323. . .
B.3.1.1 Plot of the deviance residuals for OS Model 1 324 B.3.1.2 Plots of the influence by observation number for CIS Model 1. . .
325 B.3.1.3 Plots of the influence by observation number for OS Model 1. . .
326 B.3.1.4 Plots of t. he influence by observation number for OS Model 1. . .
327. . .
B.3.1.5 Plots of the influence by observation number for OS Modcl 1 328. . .
B.3.1.6 Plots of the influence by observation ri11n11)er for OS Model 1 330xvi
. . .
B.3.2.1 The rescaled Schoenfeld resit-luals for CIS Model 2 331 B.3.2.2 The devia.nce residuals for OS Model 2
. . .
332. . .
B.3.2.3 Plots of the irifluence by observa. tion nurnber for OS Model 2 333. . .
13.3.2.4 Plots of the influence by observa. tion number for OS Model 2 334. . .
B.3.2.5 Plots of the influence by observation number for OS Model 2 335 B.3.3.1 Plot of the devianw residuals for OS Motfel 3
. . .
336. . .
B.3.3.2 Plots of the influence by observation nrmlbes for OS Model 3 337
. . .
B.3.3.3 Plots of t. he isifluerice by- obserw. tion nurr~ber for OS Model 3 338
. . .
B.3.3.4 Plots of the influence by observation number for OS Model 3 339
. . .
B.3.3.5 Plots of the influence by observation number for OS Model 3 340
. . .
B.3.3.6 Plots of the influence by observation number for OS Model 3 341. . .
B.3.4.1 The rescaled Schoenfelcl residua.1~ for OS Model 4 342
. . .
B.3.4.2 The deviance resicluaJs for OS hloclel 4 343
. . .
13.3.4.3 Plots of the influence by observation number for OS Model 4 344. . .
B.3.4.4 Plots of the influence by observation number for OS Model 4 345 B.3.4.5 Plots of the influence by observation number for C>S Model 4. . .
346 B.3.5.1 The deviance residuals for OS Model 5. . .
347. . .
B.3.5.2 Plots of the influence by observation number for OS Model 5 348
. . .
13.3.5.3 Plots of t. he influence by observation number for OS Model 5 349
. . .
B.3.5.4 Plots of the influence by observation number for OS Model 5 350
. . .
B.3.5.5 Plots of the influence by observation numt>er for CIS Model 5 351. . .
13.3.5.6 Plots of the influence by observation number for OS Model 5 352
. . .
B.3.6.1 Plots of the influence by- observat~ion number for OS Model 6 354
. . .
B.3.6.2 Plots of the influence by observation number for OS Model 6 355. . .
B.3.6.3 Plots of the influence by observation nunlber for OS Model 6 356
. . .
B.3.6.4 Plots of the influence hy 01-)servaattion nurnber for CIS Model 6 357 B.3.7.1 The deviance residuals for OS Model 7. . .
358. . .
13.3.7.2 P1ot.s of the influence by observation number for OS Model 7 359
. . .
B.3.7.3 Plots of the influence by o't~servation number for OS Model 7 360. . .
B.3.7.4 Plots of thc influence by observation number for OS Model 7 361 C . l . l . l Plot of the deviance residuals for DFS180 Model 1. . .
363 C.1.1.2 Plots of the influence by observation nurnber for DFS180 Model 1. .
364 C.1.1.3 Plots of t. he influence by obsers7a.t. ion nurnber for DFS180 Moclel 1 ..
365 C.1.1.4 Plots of the influence by observation number for DFS180 Model 1. .
366 C.1.1.5 Plots of the influence by observation number for DFS180 Model 1 . . 367xvii
C.1.2.1 Plot of the deviance resid~ials for DFS180 Model 2 . . . . . . . . . . . 368 C.1.2.2 Plots of the influence by observation nunher for DFS180 Moclel 2 . . 369 C.1.2.3 Plots of the influence by observation nurriber for DFS180 Moclel 2 . . 370 C.1.3.1 Plot of t,he deviance residuals for DFS180 Model 3 . . . . . . . . . . . 371 (2.1.3.2 Plots of the influence by observation nunlbcr for DFS180 Model 3 .
.
372 C.1.3.3 Plots of the influence by observation number for DFS180 Model 3 ..
373 C.1.3.4 Plots of the influence by observation nunher for DFSlKO h4octel 3 . . 374 C. 1.3.5 Plots of the influence by observa,t.ion nurr~.ber for DFS18C) Model 3 . . 375 (2.1.4.1 Plot of the deviance residuals for DFS180 Model 4 . . ..
. . . ..
. . 376 C. 1.4.2 Plots of the influence by observation number for DFSl80 Model 4 . . 377 C.1.4.3 Plots of the influence by o1:)servatictn nurriber for DFS180 Model 4 . . 378 C.2.1.1 Plot of the devia.nce residuals for BCSS180 Model 1. . . . . . . . . . . 379 C.2.1.2 Plots of the influence ?)y observakion nurnber for BCSSlSO Model 1..
380 C.2.1.3 Plots of the influence by observation number for BCSS180 Model 1. . 381 (3.2.1.4 Plots of t,he influence t)y observation number for BCSS180 Model 1. . 382 C.2.1.5 Plots of the influence by olr:)servat~ictn number for BCSS180 Model 1. . 384 C.2.2.1 Plot of the deviance residuals for BCSS180 Model 2.. .
. . ..
. . ..
385 C.2.2.2 Plots of the influence by observat,ion number for BCSS180 Model 2. . 386 (3.2.2.3 Plots of the influence by observa,tion number for BCSS180 Model 2. . 387 C.2.2.4 Plot of t>he influence by observation number for BCSS180 Modcl 2. . . 388 (2.2.3.1 Plot of the deviance residuals for BCSS180 Moclel 3..
. . .. .
. . ..
389 (3.2.3.2 Plots of the influence by observation number for RCSS180 Model 3. . 390 (3.2.3.3 Plots of the influence by observation number for BCSS180 %ode1 3. . 391 C.2.3.4 Plots of the influence by observittion number for BCSSl80 Model 3 . . 392 C.2.3.5 Plots of the influence by observation nurnber for BCSS180 Model 3. . 393 C.2.4.1 Plot of the devirzrrce resictuals for BCSS180 Model 4. .. .
. .. .
. ..
394 C.2.4.2 Plots of the influence by observation number for DCSS180 Model 4..
395 C.2.4.3 Plots of the influence by ob~ervat~ion number for BCSS180 Model 4..
396 (2.2.4.4 Plots of the influence by observation number for BCSS180 Mocfel 4. . 397 C.Z.5.l Plot of the deviance residuals for BCSS180 Modcl 5. ..
. . ..
. . . . 398 C.2.5.2 Plots of the influence by observation for BCSS180 Model 5 .. .
. .. .
399 C.2.5.3 Plots of the influence by observation for BCSS180 Model 5.. .
. .. .
400 C.2.5.4 Plots of the influence by observation for BCSS180 Model 5.. . . . . .
401 C.2.6.1 Plot of the deviance residuals for BCSS180 Moclel 6. .. .
. .. .
. ..
402 (3.2.6.2 Plots of the influence by observation for BCSS180 Model 6. ..
. . ..
403xviii
C.2.6.3 Plots of the influence hy observation for BCSS180 Model 6 . . . 404
C.2.7.1 Plot of t. he deviance residuals for reduced rnotlel for BCSS180 Model 7 . 405 (2.2.7.2 Plots of the influence by observation for BCSSlSO Model 7 . . . 406
(2.2.7.3 Plots of the influence by observation for BCSS180 Model 7 . . . 407
(3.2.7.4 Plots of the influence by observation for BC3S180 Model 7
. . .
408C.3.1.1 Plot of the deviance residuals for OS180 Model 1
. . .
409C.3.1.2 Plots of the infli.lexe 197 observation n ~ m b e r for OS180 Model 1 . . . . 410
C.3.1.3 Plots of the influence by observation number for OS180 Model 1 . . . . 411
(2.3.1.4 Plots of the influence by observation number for OS180 Model 1 . . . . 412
C.3.1.5 Plots of the influence by observation nun~ber for OS180 Model 1 . . . . 413
C.3.2.1 Plot of the cleviance residual for OS180 Model 2
. . .
415C.3.2.2 Plots of the influence by observation riuxnber for OSl80 Model 2
. . . .
416C.3.2.3 Plots of the irifluerlce by observation nurnber for OS180 Model 2 . . . . 417
C.3.3.1 Plot of the deviance residuals for OS180 Model 3
. . .
418C.3.3.2 Plots of the influence by observation number for OS180 Model 3 . . . . 419
C.3.3.3 Plots of the influence 1:)y observation nurnber for OS180 Model 3 . . . . 420
. . . .
C.3.3.4 Plots of the influence by observation r~umber for US180 Model 3 421
. . . .
(2.3.3.5 P1ot.s of the influence by observation number for OS180 Model 3 422. . .
C.3.4.1 Plot of the deviance residuals for OS180 Model 4 423. . . .
C.3.4.2 Plots of the influence by observation number for OS180 Model 4 424
. . . .
C.3.4.3 Plots of the illflrlence by observation number for OS180 Model 4 425
. . . .
C.3.4.4 Plots of the influence by observation number for OS180 Moclel 4 426
. . .
C.3.5.1 Plot of the deviance residuals for OS180 Model 5 427. . .
(2.3.5.2 Plots of the influence 13~7 observation for OS180 Model 5 428. . .
C.3.5.3 Plots of the influence by observation for OS180 Model 5 429. . .
(3.3.5.4 Plots of the influence by observation for C)S180 Model 5 430. . .
C.3.6.1 Plot of t. he deviance residuals for OS180 Model 6 431. . .
C.3.6.2 Plots oft. he influence by observation for OS180 Model 6 432. . .
C.3.6.3 Plots of the influcncc by observation for OS180 Model 6 433. . .
C.3.6.4 Plots of the influence by observation for OS180 Model 6 434. . .
C.3.7.1 Plot of the deviance resitfuals for OS180 Model 7 435. . .
C.3.7.2 Plots of the influence by observation for US180 Model 7 436. . .
C.3.7.3 Plots of the influence by observation for OS180 Model 7 437. . .
C.3.8.1 Plot of thc devimce residuals for OS180 Model 8 438. . .
(2.3.8.2 Plots of the infhence by observation for OS180 Model 8 439xix
List of Tables
Table Page
3.5.1 Comparison of cases and controk for pathologic and treatment vari-
ables at diagnosis for the f ~ d l data set . . . 34
3.6.2.1 Comparison of cases and controls for patllologic arid treatment vari- ables at diagnosis for the subset data set
. . .
384 . 1. 1 he rneari survival times for disease-free survival of each of the clitignostic and treatment variables
. . .
404.2.1 The mean survival times for breast cancer-specific survival of each of tmhe diagnostic and treatment variables
. . .
544.3.1 The rneari survival tirnes for overall survival of each of the diagnostic and treatment variables
. . .
675.1 ..I.. 1 Parameter estimates for for DFS Model 1
. . .
795.1.1.2 Tests of the proportional hazards assumption for DFS Model 1
. . .
815.1.2.1 Parameter estimates for DFS Model 2 . . . 82
5.1.2.2 'I'ests of the proportional hxzards assumption for DFS Model 2 . . . 83
5.1.2.3 Parameter estimates for DFS Model 3 . . . 84
5.1.2.4 Tests of the proportiorla1 hazascls a~surnpt~iori for DFS Model 3
. . .
895.1.3.1 Parameter estimates for DFS Model 4
. . .
905.1.3.2 Tests of the proportional hazards assumption for DFS Model 4
. . .
915.1.3.3 Parameter estinmtes for DFS Model 5
. . .
925.1.3.4 Tests of the proportional hazards assumption for
DFS
Model 5 . . . 935.1.3.5 Para.rneter esti~riates for DFS Model 6
. . .
945.1.3.6 Tests of the proportional haza.rds assumption for DFS Model 6 . . . 95
5.1.4.1 Parameter estimakes for DFS Model 7
. . .
99. . .
5.1.4.2 Tests of the proportional hazards assumption for DFS Model 7 100 5.1.4.3 Parameter estimates for DFS Model 8. . .
101xxi
5.1.4.4 Tests of the proportional hazards assurngtion for DFS Model 8 . . . 102
5.1.4.5 Parameter estimates for DFS Model 9
. . .
1035.1.4.6 Test. s of the proportional ha. mrcls assumption for DFS Model 9
. . .
1045.1.4.7 Parameter estimates for DFS Model 10
. . .
1055.1.4.8 'I'ests of the proportional hazards assumption for DFS Model 10
. . . .
1065.1.5.1 Parameter estimates for DFS Model 11 . . . 108
5.1.5.2 Tests of the proportional hazards ass~xrnptiori for DFS Model 11
. . . .
1095.1.5.3 Para. meter estimates for DFS >lode1 12
. . .
1105.1.5.4 Tests of the proportional hazards assumption for DFS Model 11 . . . . 111
5.2.1.1 Parameter estimates for BCSS Model 1
. . .
1145.2.1.2 .Tests of the proy~rt~ional hazards assumption for BCSS Model 1 . . . . 115
5.2.2.1 Parameter est. imates for BCSS Model 2
. . .
1165.2.2.2 Tests of the proportional hazarcls assurnpt. ion for BCSS Model 2 . . . . 116
5.2.2.3 Parameter estimates for BCSS Model 3
. . .
1175.2.2.4 Tests of the proportional hazards assumption for BCSS Model 3
. . . .
1175.2.3.1 Parameter estimates for BCSS Model 4
. . .
1205.2.3.2 Tests of t. he proportional hazards assumption for BCSS Model 4 . . . . 121
5.2.3.3 Pa. rameter estimates for BCSS Model 6
. . .
123. . . .
5.2.3.4 Tests of the proportional hazards assumption for BCSS Model 6 124 5.2.4.1 Parameter estimates for breast BCSS Model 7 . . . 1255.2.4.2 .Tests of the progortkmal hazards assumption for BCSS Model 7
. . . .
1265.2.4.3 Parameter estimates for BCSS Model 8
. . .
1275.2.4.4 Tests of the proport. ional hazards assun~pt~ion for BCSS Model 8 . . . . 128
5.2.5.1 Parameter estimates for BCSS Model 9
. . .
129. . . . 5.2.5.2 Tests of the proportional hazards assumption for BCSS Model 9 130 5.2.5.3 Parameter estirrlcztes for BCSS Model 10
. . .
131. . . 5.2.5.4 Tests of the proportional hazards assumption for BCSS Model 10 132 5.3.1.1 Parameter estimates for OS Model 1
. . .
134. . .
5.3.1.2 Tests of the proportional hazards assumption for OS Model 1 135 5.3.2.1 Pa.ramet.er estimates for OS Model 2. . .
136. . .
5.3.2.2 Test. s of the proportional hazards msumption for OS Model 2 137 5.3.3.1 P8ramet. er estimates for OS Model 3. . .
138. . .
5.3.3.2 Tests of the proportional hazards assumption for OS Model 3 139. . .
5.3.3.3 Parameter estimates for OS Model 4 140
. . .
5.3.3.4 Tests of the proportional hazards as~xrnption for OS Model 4 141xxii
5.3.4.1 Parameter estimates for OS Model 5 . . . 142 5.3.4.2 Tests of the proportional hazards assumption for OS Model 5
. . .
143 5.3.4.3 Parametes estimates for OS Model 6. . .
144 5.3.4.4 Tests of the proportional hazards assumption for OS Model 6 . . . 145 5.3.5.1 Parameter estima.tes for OS Model 7. . .
146. . .
5.3.5.2 Tests of the proportional ha. zards asurnption for OS Model 7 146 6.1.1.1 Pa.rainet>er estimates for DFSl80 Model 1
. . .
149 6.1.1.2 Test.s of the proportional hazartls assumption for DFS180 Model 1 . . . 150 6.1.2.1 Parameter estirrmtes for DFS180 Moclel 2. . .
151 6.1.2.2 Tests of the proportional hazards assumption for DFS180 Model 2 . . . 152 6.1.3.1 Parameter estimates for disease-free survival for DFS180 Model 3. . .
153 6.1.3.2 Tests of the proportional llazards assivnption for DFS180 Model 3 . . . 154 6.1.3.3 Pt~rarneter estimates for DFSl80 Model 4. . .
155 6.1.3.4 Tests of tfhe proportional ha.zards assurriptiori for DFS180 Moclel 4 . . . 156 6.2.1.1 Parasmeter estimates for BCSS180 Model 1. . .
158 6.2.1.2 Tests of the proportional hazards assumption for BCSS180 Model 1 . . 159 6.2.2.1 Pa.rameter estirrlates for BCSS180 Model 2. . .
161 6.2.2.2 Tests of the proportional hazarcls as~urnpt~ion for BCSSl80 Model 2. .
162 6.2.3.1 Pasameter estimates for BCSSI.80 Model 3 . . . 165 6.2.3.2 Tests of the proportional hazards assumption for BCSS180 Model 3 . . 166 6.2.3.3 Paranieter estimates for BCSS180 Moctel 4. . .
167 6.2.3.4 Tests of the proportional hazards assumption for BCSS180 Model 4 . . 168 6.2.4.1. Para. meter estimates for I3CSS1.80 Model 5. . .
169 6.2.4.2 Tests of the proportional hazards assumption for BCSS180 Model 5 . . 170 6.2.4.3 Pa. rameter estimates for BCSS180 Model G. . .
171 6.2.4.4 T'ests of tihe proportional hazards assumption for SCSS180 Modd 6 . . 172 6.2.4.5 Parameter estirnates for BCSS180 Model 7. . .
172 6.2.4.6 Tests of the proportionad hazarcls a.ssumpt,iori for BCSS180 Moclel 7. .
173 6.3.1.1 Paramet.er estimates for OS180 Model 1. . .
175 6.3.1.2 Tests of the proportional hazards assumption for OS180 Model 1. . . .
176. . .
6.3.2.1 Parameter estimates for overall survival OS180 Model 2 178. . . .
6.3.2.2 Tests of the proportional l~azards czssumption for OS180 Model 2 180. . .
6.3.3.1 Parameter estimates for OS180 Model 3 181
. . . .
6.3.3.2 Test. s of the proportional hazards a.ssumption for OS180 Model 3 182. . .
xxiii
. . . .
6.3.3.4 Tests of the proportional hazards assumption for OSl80 Model 4 184 6.3.4.1 Parameter estimates for OS18O Model 5
. . .
185. . . .
6.3.4.2 Test. s of the proportiorlad haza.rds assurnptiori for OS180 3~Ioclel 5 186 6.3.4.3 Parameter estimates for OS180 Model 6 . . . 187
. . . .
6.3.4.4 Tests of the proportional hazards assumption for OS180 Model 6 188 6.3.4.5 Paranleter estimates for OS180 Model 7
. . .
189. . . .
6.3.4.6 Tests of the proportional hazards assumption for OS180 Model 7 189 6.3.4.7 Parameter est.irnates for OS180 Model 8. . .
190. . . .
6.3.4.8 Test. s oft. he proportional hazards assumption for OS180 Model 8 190 7.1.1 The categories of dosage levels of each of the vitSanlins and minerals
prescribed as a treatment for breast cancer . . . 192 7.3.1.1 Parameter estimates for disease-free survival for DFSMT Model 1 . . . 204 7.3.1.2 Tests of the proport. itma1 hazards assumption for DFSMT Model 1 . . . 205 B.2.5.1 Parameter estimates for BCSS Model 5
. . .
299 B.2.5.2 Tests of the proportiorla1 hazards assuxnptiori for RCSS &lode1 5 . . . . 304. . .
D . 1 Indicator parameter coding used for the categorical variables 442 D.2 Secondary indicator paramcter coding used for the categorical variablcs.443 D.3 Indicator paramcter coding used for the categorical variables for the
xxiv
Acknowledgements
First and foremost, I thank my supervisor M. Lesperance, for supporting this work with ideas and criticism. She has been incredibly helpful, understanding, and patient during my partaking of this research and analyses. I also thank the members of my committee, M. Tsao,
H.
Foster, andI.
Olivotto, for their support and assistance in this endeavour.I thank Dr. A Hoffer for providing the data on the case patients and their vitamin and mineral regimens. I also thank the Breast Outcomes Unit of the B.C. Cancer Agency for providing the data on the breast-cancer patients; without these contributions this study would not have been possible.
I thank G. Salloum, S. Mosesova and A. Webber; without their help and support, I would not be here today. I especially thank A. Webber who I had numerous discussions related to statistics and this thesis; I am particularly grateful for the discussions where I was basically thinking out loud and he was listening.
In the department I was surrounded by knowledgeable and friendly people who helped me daily. Thanks to S. Finbow,
A.
Argyle,M.
Kim, T. Lee, T. Law, A. Culhaci, X. Yang, M. Charnell, J. Simmons, and B. Smith, all of whom were a great help in their own way.Endless thanks to C. Taggart for his confidence in me and encouragement in all my endeavours.
Many thanks to C. Sutton, L. Urquhart, K. Ricci, L. Pierce, and M. Dobie for providing an outlet for my pent-up energy and frustrations.
I am forever grateful to J. Steels for his understanding, endless patience and encour- agement when it was most required.
Most of all, I would like to thank my family, and especially my parents, Al and Joan, and my sister Toni, for their absolute confidence in me.
Chapter
1
Introduction
1.1
Breast Cancer
Breast cancer is the leading form of cancer diagnosed in Canadian women, with the exception of non-melanoma skin cancer (Guadette et al., 1996). In the United States, 32% of the estimated new cancer cases for women are breast cancer (Jemal et al., 2004); which is higher than any other form of cancer by 20% (Jemal, et al., 2004). Canada has one of the highest breast cancer rates in the world and is second only to the United States (Gaudette et al., 1996). Breast cancer survival rates are relatively more favourable than other forms of cancer (Guadett et al., 1996) with approximately 87 % of females (all races) with all stages of breast cancer surviving past five years (Jemal, et al. 2004).
Patients with breast cancer increasingly seek additional measures to conventional treatment, either on their own or with the assistance of their physicians, to enhance their prospects of survival. Complementary and alternative medical treatments (CAM) objectives include the reduction of toxicities of conventional therapy, improvement of cancer-related symptoms, enhancement of the immune system, and even a direct anti- cancer effect (Tagliaferri et al., 2000). CAM treatments are common among Canadian breast cancer survivors (Boon et al., 2000), however in a review on the CAM literature, none of the studies demonstrated definitively that a CAM treatment altered progression in patients with breast cancer (Jacobson et al., 2000). In Norway, Risberg and Jacob- sen (2003) found a higher occurrence of alternative medicine use among patients with mental distress, especially in cancer patients with high mental distress; however, these finding were not statistically significant.
One of the types of CAM treatments includes the supplementation of diet with various vitamins and minerals at different dosage levels. Dietary supplementation is
common in the United States; with 46% of responders reporting the use of vitamin and mineral supplementation and 24% reporting a regular use of at least one supplement in 1992 (Slesinski et al., 1995). There is evidence of dietary supplements in the general pubic and in breast cancer patients. Newman et al. (1998) reported that 80.9% (n= 435) of women at risk for breast cancer recurrence were using some form of dietary supplements.
Studies have shown that certain vitamins and minerals protect against the risk of cancer, specifically breast cancer, and diet has been associated with breast cancer risk. Several review papers on diet and breast cancer have associated diet and the risk of breast breast cancer, for example: Willett (2001) suggested that there is some evidence to suggest that a low intake of vegetables moderately increases the risk of breast cancer; Fairfeld and Fletcher (2002) state that inadequate ingestion of several vitamins have been linked to cancer; Patterson et al. (1997) listed various dietary agents as potential agents associated with breast cancer risk, such as vitamins A, C, E, folic acid and their precursors (e.g. ,&carotene) and minerals, such as calcium and selenium; Garland et al. (1993) in their review of antioxidant micronutrients and breast cancer suggest the available data supported a modest protective effect of vitamin A, although the authors concluded that more studies were needed to examine further this association and to assess the relative contributions of preformed vitamin A (retinol) and carotenoids; in the same review, the authors also concluded that there was an inconsistent relationship with breast cancer risk and vitamin C and E and existing data did not support a protective role of selenium in relation to breast cancer risk (Garland et al., 1993).
Vitamin C, vitamin E and selected carotenoids have been shown to have an in- verse relationship with breast cancer risk in a case-control study in Switzerland (Levi et al., 2001). In a case-control retrospective study, Moorman et al., (2001) provided limited support that vitamin supplementation may reduce the risk of breast cancer but concluded that reductions in risk are more likely to be achieved through dietary mod- ifications rather than through vitamin supplementation. In a large, prospective study designed to evaluate long-term intakes of vitamin A, C and E and breast cancer risk, Zhang et al. (1999) found a weak inverse relationship between @carotene and vitamin A and breast cancer risk, as well as a strong inverse relationship between increasing quantities of p-carotene and vitamin C and breast cancer risk.
The vitamins and minerals in this study include ,@carotene, vitamin
C,
niacin, sele- nium, co-enzyme Q10 and zinc; mega-doses of these vitamins and minerals are used to treat patients, as well as conventional treatments, with breast cancer.1.2
Vitamins and Minerals
@-carotene is a pro-vitamin that the body uses as a building block for vitamin A, which is essential for growth and bone development in children, for vision especially in low light, for health skin, for mucous membrane surfaces, as well as the integrity of the immune system (Garrison and Somer, 1985). Significant amounts of @-carotene can be converted to vitamin A, and this is the only carotenoid that has this property (Garrison and Somer, 1985). Excessive ingestion of p-carotene, either from dietary sources or supplementation may lead to the yellowing of the skin; however this is reversible with a reduction in the ingestion (Garrison and Somer, 1985). The body can only convert @-carotene into vitamin A if there is a deficiency of Vitamin A and will not produce excess and possibly toxic levels of Vitamin A (Garrison and Somer, 1985).
The recommended dietary allowance (RDA) for vitamin A (including provitamin A carotenoids that are dietary precursors of retinol) is 700 micrograms (pg) per day (d) for females over 30 and has a tolerable upper intake level of 3000 pg/d for females in this age category (as cited by Food and Nutrition Board (FNB), 2001).
In breast cancer patients the serum levels of @-carotene were found to be lower than half that of a healthy person (Ramaswamy and Krishnamoorthy, 1996, Busa et al. 1989). There have been mixed results in the literature on the effectiveness of p-carotene in both the treatment and the risk of developing breast cancer. For example, in a cohort study in Sweden (n=66,651), Michels et al. (2001) found no overall association between the intake of ascorbic acid, @-carotene, retinol or vitamin E and breast cancer incidence. In a cohort study (n=412) examining the association between dietary fiber, vitamins A, C, and
E
and the risk of breast cancer, retinol, ,&carotene, and vitamin C were found to have statistically nonsignificant reductions in risk with the increase intake of these vitamins (Rohan et al., 1992). Contrary to these findings are those of Rohan et al. (1993), who found an association between the upper levels of intake of @-carotene and vitamin C and breast cancer risk (n=89,835), reporting a reduction in the risk of death from breast cancer.1.2.2
Vitamin C
Vitamin C is a water-soluble compound that acts as a co-enzyme, a reducing agent and an antioxidant (Garrison and Somer, 1985). The human body cannot manufacture its own vitamin C and therefore it must be ingested. The recommended dietary allowance
(RDA) is 75 milligrams (mg) per day (d) for females over 30 and has an tolerable upper intake level of 2000 mg/d for females in this age category (as cited by FNB, 2001). Large doses of vitamin C may not be toxic, however the process of eliminating large doses of ascorbic acid may be. Theoretically, with doses greater that 1,000 to 10,000 mg/d, great quantities of urine are produced to eliminate the vitamin C not utilized and the large quantity of fluid required to eliminate the excess may not be replaced, causing vitamin C to crystallise and damage the kidneys (Garrison and Somer, 1985). Kidney stones could also occur as the body tries to eliminate the excess vitamin C by neutralizing it with calcium salts (Garrison and Somer, 1985). Excess amounts of vitamin C may also lead to dehydration and diarrhea as the body pulls water from the circulatory system into the colon (Garrison and Somer, 1985).
Plasma concentrations of vitamin C have been found to be significantly lower in breast cancer patients compared to controls (Ray and Husian, 2001) and Ramaswamy and Krishnamoorthy (1996) also found serum levels of vitamin C lower in breast and cervix cancer patients compared to a healthy control patient. Blood levels of vitamin C were found to be borderline significant (higher) for breast cancer patients compared to a control group by Gerber et al. (1991), however these results were slightly modified when supplement users were removed from the analysis.
In a prospective study of 34,387 postmenopausal women there was little evidence of an association between dietary antioxidant vitamin intake and the risk of breast cancer (Kushi et al., 1996) and the relative risk (0.73) were not statistically significant when comparing women consuming at least 500 mg/d of vitamin C to those who did not take vitamin C supplement.
1.2.3
Niacin B3
Niacin is a water-soluble member of the vitamin B-complex family. Humans can synthe- sis small quantities of niacin but these levels are inadequate for normal bodily functions (Garrison and Somer, 1985). Niacin is essential for the production of many hormones including cortisone, insulin and both male and female sex hormones estrogen, proges- terone, and testosterone (Garrison and Somer, 1985). Niacin is also necessary for the normal function on the nervous system (Garrison and Somer, 1985).
The RDA for niacin is 14 mg/d for females over 30 and has a tolerable upper intake level of 35 mg/d (as cited by FNB, 2001). Excess niacin is excreted in the urine and feces, which may account for the vitamin's low toxicity.
usefulness in treating breast cancer. Other members of the vitamin B-complex family, such as cobalamin (Biz) and folate (B6) have been linked to breast cancer risk, but niacin has not been specifically examined.
1.2.4
Seleniun
Selenium is a trace mineral that functions either alone or as part of enzymatic systems. The co-factor role of selenium parallels the antioxidant and free radical scavenging action of vitamin E, and working together vitamin E and selenium have a stabilizing effect on lysosomal membranes (Garrison and Somer, 1985). Selenium also functions in the binding of heavy metals and possibly reducing the toxicity from mercury contamination (Garrison and Somer, 1985).
The RDA for selenium is 55 mg/d for females over 30 with a tolerable upper intake level of 400 mg/d (as cited by FNB, 2001). In greater than trace amounts, selenium may be toxic to humans, affecting the liver and the heart.
There have been mixed results concerning breast cancer and selenium. Selenium levels extracted from serum in benign and malignant tumours were lower than those in a control group (Kuo et al., 1999). Cann et al., (2000) suggests there is evidence for a preventive role for selenium in breast cancer but admits rigorous retrospective and prospective studies are needed to confirm this hypothesis. Contrary, Mannisto et al. (2000) established in a case-control study (n=289 cases and 433 controls) that selenium was not an important factor in the etiology of breast cancer in Finland where selenium supplementation had occurred for a decade.
1.2.5
Coenzyme Q l 0
Coenzyme Q10 is manufactured by the body naturally, and is not an essential nutrient. Jolleit et al. (1998) measured plasma levels of Coenzyme Q10 and found there to be a deficiency in plasma concentration for carcinomas and non-malignant lesions in breast cancer patients and concluded that supplementation in breast cancer could be relevant. More recently Portakal et al., (2000) established that Coenzyme Q10 concentrations
in tumour tissues were significantly lower then in the surrounding healthy tissue. The incidence rate for breast cancer patients with less than 0.5 yglml of Coenzyme Q10 in their blood is significantly higher when compared to a group of healthy individuals; the same is true for blood levels less than 0.6 yg/ml of Coenzyme Q10 in their blood (Folkers et al., 1997). Desirable effects on breast cancer patients have been seen when
treated with Coenzyme Q10 which include the overt complete regressions of tumours (Lockwood et al., 1993), partial tumour regression (6 out of 32 patients, Lockwood et al., 1994), and apparent increase in survival (n=8, Folkers et al., 1993). These results are unfortunately only in a select few patients as only a limited number of case histories were presented and these patients have also not been compared to a control group.
1.2.6
Zinc
Zinc has many functions in the human body and functions as a cofactor in over twenty enzymatic reactions and it acts as a binder in maintaining the structural configuration of some non-enzymatic molecules (Garrison and Somer, 1985). Zinc is also important for insulin activity, for protein and DNA synthesis, normal taste and healing, to maintain normal vitamin A levels and usage, in the structure of bonds, and in the immune system (Garrison and Somer, 1985).
The RDA for females over 30 is 8 mg/d and has a tolerable upper intake level of 40 mg/d for this same age and sex category (as cited by FNB, 2001). Toxicity related to large doses of zinc are rare, but the effects can include dizziness, drowsiness, vomiting, gastrointestinal disturbances, lethargy, renal failure and anemia; however these symptoms are only seen if more than 2 g are taken (Garrison and Somer, 1985).
Zinc concentrations, extracted from benign and malignant tumours have been found to be lower than serum levels of a healthy control group (Kuo et al., 1999) and Jin et al. (1999) noted that zinc content in breast cancer tissues was twice that of benign breast tissues.
1.2.7
Vitamins and Minerals Taken in Combination
Diet has been linked to the risk of cancer and dietary supplementation is prevalent in the general public, and among women at risk for breast cancer recurrence (Newman et al., 1998, Rock et al., 1997), but can combinations of vitamins and mineral at large doses assist in the treatment of breast cancer? In one physician's practice, survival of patients who had adhered to a regime of large doses of vitamin and minerals was longer for those patients in the practice who failed to continue with this treatment (Hoffer and Pauling, 1993); however no attempt was made to compare their survival with that for matched controls. Lockwood et aL's (1994) study included 32 breast cancer patients, who along with conventional treatment, added a combination of nutritional antioxidants (vitamin C, vitamin
E,
,&carotene, and selenium), essential fatty acids, and coenzymeQ10 supplements. The main observations from this study included: no deaths during the duration of the study; none of the patients showed signs of further distant metastases; patients reduced their use pain killers and did not lose weight; and six patients showed apparent partial remission. Similar to Hoffer and Pauling's study, Lockwood et al.'s study did not compare the breast cancer patients taking the vitamin and mineral regime to a control group of breast cancer patients that were similar in treatment and diagnostic characteristics.
More recently, Drisko et al. (2003) presented two cases of ovarian cancer that had been treated with high doses of vitamin C, vitamin E, p-carotene, coenzyme Q10 and a multivitamin/mineral complex with positive results. This pilot study resulted in a randomised controlled trial to evaluate safety and efficacy of antioxidants when added to chemotherapy in newly diagnosed ovarian cancer. Lesperance et al. (2003) estimated a decreased survival, both for breast cancer specific-survival (p-value = 0.19) and disease- free survival (p-value = 0.08), for breast cancer patients taking mega-doses of vitamins and minerals (n=90) compared to a matched control group (n=180).
1.3
Summary
of
the Breast Cancer Study
This study examines three survival outcomes of non-metastatic breast cancer patients prescribed different combinations of vitamins and minerals by Dr. Hoffer, a practising psychiatrist in Victoria, BC. Each of the treated patients (case, n=153) were matched on conventional treatment and diagnostic characteristics with two breast cancer patients from Vancouver Island (control patients, n=306) and compared in Chapter 3. The three measures of survival include: disease-free survival; breast cancer survival; and overall survival. Diagnostic and treatment characteristics for each measure of survival are com- pared in Chapter 4. To evaluate the role of mega-doses of vitamins and minerals on each measure of survival, Cox regression analyses were performed using various indica- tors for vitamin and mineral treatment including a time-dependent covariate (Chapter 5 and 6). Chapter 7 looks further into the vitamin and mineral regime and differences between survival for each of the vitamins and minerals prescribed to the case patients, as well as the number of different agents used. The final chapter provides conclusions and comments about this study and the results obtained.
Chapter
2
Survival Analysis
Survival analysis is used in the modelling of "time to event" data that arises in many applied fields, such as medicine, epidemiology, biology, public health, engineering and various other disciplines. The "time to event" can represent many different things; it could be failure time of a machine, or the life length of an experimental rat under adverse conditions. The event of interest is always well defined and can be either a failure or a success depending on the study. In survival analysis it is assumed that the subjects (whether it is people in a medical study or washing machines in an engineering study) fail independent of one another. In this study the three events of interest are: 1) a recurrence of breast cancer; 2) death from breast cancer; and 3) death due to any reason.
2.1
Product-Limit Estimators
-
Nonparametric Es-
t imat ion of Basic Quantities
Kaplan and Meier (1958) proposed, a now standard nonparametric estimate, for a sur- vival function called the Product-Limit estimator. This estimator allows inferences to be drawn about the distribution of time to event, based on a sample of right-censored survival data.
A
typical data point for survival data consists of a time on study for each of n individuals in the study and an indicator of whether this time is an event or a censoring time.Suppose that events occur at
D
distinct times, tl <t2<t3< -<tD, there are d events at each of theseD
distinct times, dl, d2, d3,-,
dD.
Let be the number of subjects a t risk a t ti, which is the number of subjects alive or uncensored at time ti or experience the event of interest at ti. Let hi(t) be the discrete hazard function at time ti, which isdefined as the conditional probability that an event will occur at time ti, given that the subject survived to time ti;
hi(t) = P(T = ti\
T>
ti)where T denotes the discrete random variable representing the failure time. The survival function can be represented in terms of h(ti) as
The nonparametric estimator, proposed by Kaplan and Meier (1958), for the survival function is
where h(ti) are the maximum likelihood estimators of h(ti) and rnaxirnise the function
where Y , is the number of subjects at risks at ti and di is the number of subjects who fail at ti. The log likelihood function is
1 =
C
{(di ln(hi)+
(Y, - di) ln(1 - hi)}.i
Solving for the maximum likelihood estimator
The resultant estimator 3(t) of the survival function becomes
which is known and the Kaplan-Meier estimator. Kaplan-Meier survival functions are presented as figures in Chapter 4 for the treatment and diagnostic variables of the breast cancer patients, with the various measures of survival.
