Statistical Analysis and Modeling of 
Factors Influencing 
Lung Cancer 
l^smv of mmrwum^ ]?\ 
Final Report 
The Dissertation submitted for the 
Degree of - O S " 
MASTER OF SCIENCE 
Department of Mathematics 
Faculty of Engineering 
Sri Lanka 
February, 2005 
University of Moratuwa dz^r' 
University of Moratuwa 
02/8029 
A. N. Ekanayake 
Master of Science (Full Time) 
83467 The 
8J4G7 
DECLARATION 
I certify that the d issertat ion entit led "STATISTICAL ANALYSIS AND 
M O D E L I N G O F F A C T O R S INFLUENCING LUNfir C A N C E R S IN S R I LANKA" 
i s entirely m y o w n work. It h a s not b e e n accepted for any degree a n d it i s 
not be ing s u b m i t t e d for a n y other degree. 
C a n d i d a t e 
A.N. E k a n a y a k e Signature":.. .S^Z^gLrr. 
Date :..Q).MM... 
S u p e r v i s o r 
Dr. M. Indral ingam Signature : 
Date 
ABSTRACT 
Stat i s t ics s h o w that l u n g cancer o c c u p i e s the third pos i t ion a m o n g the 
inc idence ra tes of c a n c e r s in Sri Lankan m a l e s a n d th i s rate i s increas ing 
yearly. Thi s research i s f ocused on two m a i n areas . T h e s e are to find factors 
a s s o c i a t e d wi th l u n g c a n c e r s a n d s t u d y o n t ime to dea th after detect ion of a 
l u n g cancer , k n o w n a s the survival t ime. 
i. 
D a t a col lect ion w a s d o n e at Cancer Inst i tute , *Maharagama (CIM) w h i c h is 
the largest hospi ta l for treatment for the d i s e a s e in Sri Lanka. Three s o u r c e s 
of d a t a have he lped in th i s research s tudy . First one w a s d a t a in s u m m a r y 
format at the CIM. S e c o n d w a s file be longs to e a c h of the pat i ents . Third w a s 
the pat ient 's detail form, w h i c h i s filled by a pat ient . All together two 
h u n d r e d a n d s ixty two l u n g cancer pat i ents have c o m e to CIM, in the s t u d y 
period from 1 s t J a n u a r y to 3 1 s t D e c e m b e r 2 0 0 2 . 
F indings of th i s research are a s follows. S m o k i n g i s the m a i n risk factor for 
l u n g cancers . People w h o do o c c u p a t i o n s in areas uncovered for pol luted air 
have h igh risk for l u n g cancer . There i s a genet ic effect for l u n g cancer . 
C o n s u m i n g alcohol a n d c h e w i n g betel are a l so cons iderable factors for l u n g 
cancer . Having Tubercu los i s i s a l so risk factor for l u n g cancer . A m o n g four 
t y p e s of l u n g cancer viz.; Adenocarc inoma, S q u a m o u s cell carc inoma, Smal l 
cell carc inoma a n d Large cell carc inoma, the m o s t c o m m o n types in Sri 
Lanka are Adenocarc inoma a n d S q u a m o u s cell carc inoma. Age, sex , religion 
a n d s m o k i n g habi t of the pat ient have h igh re lat ionship with t h o s e two types 
of l u n g cancer . A male p e r s o n wi th age greater t h a n 4 8 years h a v i n g 
s m o k i n g habi t i s more suscept ib le to S q u a m o u s cell carc inoma t h a n for 
Adenocarc inoma. 
This research s h o w s that the m e a n survival t ime of Tung cancer pat ient i s 
approximate ly 6 m o n t h s . Treatment given at Cancer Inst i tute , Stage of 
d iagnos i s a n d s e x of the pat ient affect survival t ime. Treatment mixture 
r e d u c e s risk of dea th by half compared to s ingle treatment . Our research 
s h o w s that of a pat ient i s d iagnosed for a l u n g cancer in ex tended s tage , 
h e / s h e h a s e leven t i m e s more in risk of death t h a n a pat ient wi th local ized 
s tage . Risk of dea th for m a l e s i s three t i m e s more t h a n females . 
ii 
ACKNOWLEDGEMENT 
It i s wi th greatest respect a n d venerat ion thajt I e x p r e s s m y s incere t h a n k s to 
x 
m y m a i n supervisor Dr. M Indralingarrf.'ihe Coordinator-of the pos tgraduate 
s t u d e n t s of D e p a r t m e n t of Mathemat ic s , 'University of Moratuwa. Also m y 
s incere t h a n k s to Proff. G.T.F. De Silva, Dr. R. b»kupit iya a n d Mr. T.M.J.A. 
Cooray, Senior Lectureres of Depar tment of Mathemat ic s , Universi ty of 
Moratuwa a n d Mrs. C.P.N. Attygalle, Inst i tute of Technology, University of 
Moratuwa. I have to appreciate the a s s i s t a n c e of Dr. Roshini Sooriarachchi , 
Senior Lecturer of D e p a r t m e n t of Stat i s t ics , University of Colombo. My 
special t h a n k s for Dr. Murali Val l ipuranathan, Ministry of Health a n d 
Dr.R.V.Rabel, Medical Officer, University of Moratuwa w h o give m e k ind 
support in Medical field. Without the knowledge , advice a n d vas t experience , 
w h i c h w a s imparted to m e by m y superv isors I m a y not have b e e n able to 
comple te the project success fu l ly . 
I w o u l d like to take th i s opportunity to t h a n k special ly for Proff (Mrs) N. 
Rathnayake , Director of Post Graduate un i t of University of Moratuwa a n d 
ADB for grant ing m e th i s s cho larsh ip to c o n d u c t th i s research a n d the h e a d 
of the D e p a r t m e n t a n d all the staff m e m b e r s a n d n o n academic staff of the 
D e p a r t m e n t of Mathemat i c s , University of Moratuwa. It i s m y obl igation to 
t h a n k all m y fr iends for their support . * 
I w o u l d a l so like to t h a n k Dr. Yasantha- Ariyarathna, Director, Cancer 
Inst i tute , Dr.(Mrs) Nirmala Gammanpi la , a n d the staff of the record room 
a n d director's office of the Cancer Inst i tute , M a h a r a g a m a for providing m e 
relevant information a n d d a t a to carry ou t th i s research . 
The a s s i s t a n c e given by Dr. T h u s h a r a Fernando a n d the staff m e m b e r s of 
P lanning divis ion, Ministry of Health i s gratefully acknowledged . Also a 
special t h a n k s h a s to be given for the Medical Stat i s t ics Unit of C e n s u s a n d 
Stat i s t i cs Department . 
i. • ' . . . ' 
I gratefully acknowledge the support a n d e n c o u r a g e m e n t given by m y loving 
p a r e n t s a n d m y sister . 
Finally spec ia l t h a n k are d u e to m y loving h u s b a n d for h i s va luable advice, 
e n c o u r a g e m e n t in all m y endeavors in th i s research. 
iii 
CONTENTS
 % 
Page no. 
DECLARATION V- ' i 
ABSTRACT ii 
ACKNOWLEDGEMENT iii 
CONTENTS iv 
LIST OF TABLES - « vii 
LIST OF FIGURE ix 
DEDICATION xi 
1. INTRODUCTION 
1.1 B a c k g r o u n d v 1 
1.2 What i s a l u n g cancer? 1 
1.2.1 Introduct ion . ± 
1.2.2 U n d e r s t a n d i n g the cancer p r o c e s s 1 
1.2.3 Risk factors of l u n g cancer 2 
1.2.4 Types of l u n g cancer 4 
1.2.5 S y m p t o m s a n d s i g n s of l u n g cancer 4 
1.2.6 D iagnos ing l u n g cancer 5 
1.2.7 Stage explanat ion '] 5 
1.2.8 Treatment for l u n g cancer • 6 
1.3 Objectives of the s t u d y 9 
2 . LITERATURE REVIEW 
2.1 S t u d i e s carried ou t in Sri Lanka 10 
2 .2 S t u d i e s carried out in other countr ies 14 
3 . METHODOLOGY AND TECHNIQUES" U S E D 
3 .1 Methodology 2 7 
3 . 1 . 1 Literature survey v ' . 2 7 
3 . 1 . 2 S t u d y area a n d s t u d y populat ion 2 8 
iv 
% 
3 . 1 . 3 D a t a col lect ion 
3 . 2 T e c h n i q u e s u s e d 
3 . 2 . 1 Descript ive m e t h o d s 
3 . 2 . 2 Univariate m e t h o d s 
3 . 2 . 3 Model fitting 
3 . 2 . 4 Survival data ana lys i s 
3 . 2 . 5 Special software u s e d in analyz ing 
4 . DESCRIPTIVE STUDY ON LUNG CANCER.PATIENTS 
4 .1 Personal deta i l s of l u n g cancer pat i ent s in Sri Lanka 4 7 
4 .2 General information o n Lung cancer pat i ents 5 4 
4 . 3 Habi t s of Lung Cancer Pat ients 5 8 
4 . 4 Clinical Fea tures of Lung Cancer Pat ients 6 0 
4 . 5 Identify the c o m m o n l u n g c a n c e r s in Sri Lanka according 
to cell t ypes 6 2 
4 . 6 S u m m a r y ' 6 7 
5. LOGISTIC REGRESSION ANALYSIS TO LUNG CANCER PATIENTS 
5.1 Univariate ana lys i s for determining variables affecting two 
c o m m o n types of l u n g cancer in Sri T*anka 6 8 
5 .1 .1 Test ing the re lat ionship be tween two types of l u n g 
cancer wi th personal infofination 6 9 
5 .1 .2 Tes t ing the re lat ionship b e t w e e n two t y p e s of l u n g 
cancer with personal h a b i t s 7 2 
5 .2 Fitt ing logistic mode l for two types of l u n g cancer; 
Adenocarc inoma a n d S q u a m o u s cell carc inoma 7 3 
%f 5 .2 .1 Model fitting procedure 7 3 
5 .2 .2 Parameter e s t i m a t e s of the fitted mode l 7 5 
5 . 2 . 3 G o o d n e s s of fit of the model 7 6 
5 .3 Further areas of s t u d y 7 6 
5 .4 S u m m a r y 7 7 
6. SURVIVAL DATA ANALYSIS FOR LUNG CANCER PATIENTS 
6 .1 S o m e Definit ions 7 8 
6 .2 Descriptive Methods of Comparing Survival Time for Different 
Groups of Individuals 8 1 
2 8 
3 5 
3 5 
3 6 
3 7 
4 4 
4 5 
6 . 3 Log-Rank te s t to compare survival t i m e s for different g r o u p s of 
indiv iduals ^ 1 0 0 
6 .4 Model ing survival data 102 
6 .4 .1 The se lect ion of the variables to be ' inc luded in 
the mode l 1 0 3 
6 . 4 . 2 Parameter e s t i m a t e s of the se lec ted mode l 106 
6 . 5 Model D iagnos t i c s 107 
6 .5 .1 Plots of the Cox-Snel l r e s idua l s 107 
6 . 5 . 2 Plots of Martingale res idua l s 1 0 8 
6 . 5 . 3 Plot of Dev iance re s idua l s 1 1 0 
6 .6 S u m m e r y 110 
7. CONCLUSIONS AND DISCUSSION 
7.1 D i s c u s s i o n 112 
7 .1 .1 Descript ive S t u d y on l u n g cancer 112 
7 . 1 . 2 Assoc ia t ion be tween c o m m o n types of l u n g cancer viz. 
Adenocarc inoma a n d S q u a m o u s cell carc inoma a n d 
s o m e variables 1 1 3 
7 . 1 . 3 Stat ist ical ana lys i s of t ime to death after detect ing l u n g 
cancer • - 114 
7 .2 C o n c l u s i o n s of the s t u d y 1 1 5 
7 .2 .1 C o n c l u s i o n s of the general f indings 115 
7 . 2 . 2 C o n c l u s i o n s of analyz ing t ime to death after detect ing 
(survival time) a l u n g cancer 1 1 6 
7 .3 R e c o m m e n d a t i o n s 117 
7 .4 Problems of the s t u d y V 1 1 ? 
7 .5 Limitat ions of the s t u d y - 118 
7 .6 Further s t u d i e s 1 1 8 
APPENDIX I - . i 
APPENDIX II ""• xxii 
REFERENCES A N D BIBLIOGRAPHY xxvii 
LIST OF TABLES 
Page no. 
Table 3 . 1 : Format of d a t a s u m m a r i z i n g at d a n c e r Inst i tute 3 0 
Table 3 .2 : D a t a col lect ing format ' 3 4 
Table 3 . 3 : Cont ingency Table of Factor A by Factor B •. 3 6 
Table 4 . 1 : Frequency distr ibution of pa t i en t s district w i se 4 9 
Table 4 .2 : Frequency distribution of pa t i en t s e thn ic group w i s e 5 1 
Table 4 . 3 : Frequency distr ibution of religion 51 
Table 4 . 4 : Frequency distr ibut ion of n o . of chi ldren to the l u n g cancer 
pat ient 5 2 
Table 4 .5 : Frequency distr ibution of occupat ion of l u n g cancer pat ient 5 3 
Table 4 .6 : Frequency distr ibution of m o n t h l y i n c o m e of l u n g cancer 
p a t i e n t s 5 4 
Table 4 .7 : Frequency distr ibution of gett ing l u n g cancer previous ly 5 5 
Table 4 .8 : Frequency distribution of g e n e effect 5 6 
Table 4 .9 : Frequency distr ibut ion of type of the hospi ta l referring from 5 6 
Table 4 . 1 0 : Frequency distr ibution of hav ing or h a d TB 5 7 
Table 4 . 1 1 : Frequency distr ibution of years wi th s m o k i n g 5 8 
Table 4 . 1 2 : Frequency distr ibution of s m o k i n g quant i ty per day 5 8 
Table 4 . 1 3 : Frequency distr ibution of c o n s u m i n g alcohol 5 9 
Table 4 . 1 4 : Frequency distr ibution of pa t i ent s c h e w i n g betel 5 9 
Table 4 . 1 5 : Frequency distr ibut ion of laterality , 6 0 
Table 4 . 1 6 : Frequency distr ibution of d iagnost ic s t a t u s 6 0 
Table 4 . 1 7 : Frequency distr ibution of d iagnost ic ev idence 6 1 
Table 4 . 1 8 : Frequency distr ibut ion of s tage of d iagnos i s 6 1 
Table 4 . 1 9 : Frequency distr ibution of t rea tment given at cancer ins t i tute 6 2 
Table 4 . 2 0 : Frequency distr ibution according to cell type of l u n g cancer 6 2 
Table 5 . 1 : Assoc ia ted demographic variables wi th two types of 
l u n g cancer 6 9 
Table 5 .2 : Assoc ia ted family background variables with two types of 
l u n g cancer '* 7 1 
Table 5 .3 : Assoc ia ted personal h a b i t s wi th two types of l u n g cancer 7 2 
Table 5 .4: Factors u s e d for fitting logist ic model 7 3 
Table 5 .5: Deta i l s of adding m a i n effects to nul l mode l 7 4 
vii 
Table 5 .6: Deta i l s of add ing m a i n effects to mode l conta in ing s m o k i n g 
s t a t u s 7 5 
Table 5.7: Parameter e s t i m a t e s of the fitted mode l 7 5 
Table 6 . 1 : Median survival t i m e s for type of the l u n g cancer 8 2 
Table 6 .2: Median survival t i m e s for s tage of d iagnos i s 8 4 
Table 6 .3 : Median survival t i m e s for t rea tment given at Cancer Inst i tute 8 5 
Table 6 .4 : Median survival t imes by s e x of the pat ient 8 7 
Table 6 .5: Median survival t imes by age 8 8 
Table 6 .6: Median survival t i m e s for ethnic i ty 9 0 
Table 6 .7: Median survival t i m e s for religion 9 1 
Table 6 .8: Median survival t i m e s for s m o k i n g habit of the pat ient 9 3 
Table 6 .9: Median survival t i m e s for c h e w i n g betel habi t of the pat ient 9 4 
Table 6 .10 : Median survival t i m e s for c o n s u m i n g alcohol hab i t of 
the pat ient 9 6 
Table 6 . 1 1 : Median survival t i m e s for genet ic effect of the pat ient 9 7 
Table 6 . 1 2 : Median survival t i m e s for present ing Tubercu los i s of 
the pat ient 9 9 
Table 6 . 1 3 : Log-Rank te s t r e su l t s for variables cons ider ing in survival 
ana lys i s 1 0 0 
Table 6 .14 : Resu l t ing -21ogL a n d degrees of freedom o n fitting e a c h variable 
separate ly 1 0 3 
Table 6 .15 : Resul t ing -21ogL a n d degrees of freedom o n adding e a c h term to 
the mode l adjus ted for t rea tment given 104 
Table 6 .16 : Resul t ing -21ogL a n d degrees of freedom on add ing e a c h term to 
the mode l adjus ted for t rea tment given a n d s tage of d iagnos i s 104 
Table 6 .17: Resu l t ing -21ogL a n d degrees of freed*om o n adding e a c h term to 
the mode l adjus ted for treatment given, s tage of d iagnos i s a n d 
s e x of the pat ient 1 0 5 
Table 6 .18 : Parameter e s t i m a t e s of the selected'nuJdel 106 
viii 
LIST OF FIGURES 
Page no. 
Figure 4 . 1 : 
Figure 4 . 2 
Figure 4 . 3 
Figure 4 . 4 
Figure 4 . 5 
Figure 4 .6 
Figure 4 .7 
Figure 4 . 8 
Figure 4 . 9 
Age distr ibut ion of l u n g cancer pat i ents 4 7 
Lung cancer pat i ent s by s e x . • 4 8 
Age distr ibut ion of l u n g cancer pat i ent s by s e x 4 8 
District distr ibut ion of l u n g cancer *'» 5 0 
Lung cancer pa t i en t s by their marital s ta te . 5 2 
Lung c a n c e r pat i ents by their living s t a t u s 5 5 
Lung cancer pat i ent s by transferred hospi ta l 5 7 
Lung cancer pat i ent s by s m o k i n g s t a t u s 5 8 
Lung cancer pat i ent s by cell type 6 2 
Figure 4 . 1 0 : Age distr ibut ion in two types ; Adenocarc inoma a n d S q u a m o u s 
cell carc inoma 6 4 
Figure 4 . 1 1 : Age distr ibut ion of two types of l u n g c a n c e r s by s e x 6 4 
Figure 4 . 1 2 : C o m m o n two types of l u n g cancer pat i ent s by s e x 6 5 
Figure 4 . 1 3 : Two types of l u n g cancer pat i ents by their s m o k i n g s t a t u s 6 6 
Figure 6 . 1 : Kaplan-Meier E s t i m a t e s of Survivor funct ions for type of the 
l u n g cancer 8 2 
Figure 6 .2 : Log-Cumulat ive Hazard plot for type of l u n g cancer pa t i en t s 8 3 
Figure 6 .3 : Kaplan-Meier E s t i m a t e s of Survivor func t ions for s tage of 
d iagnos i s 8 4 
Figure 6 .4 : Log-Cumulat ive Hazard plot for s tage of d iagnos i s of l u n g 
cancer pat i ent s ^ 8 5 
Figure 6 .5: Kaplan-Meier E s t i m a t e s of Survivor func t ions for treatment 
given . 8 6 
Figure 6 .6 : Log-Cumulat ive Hazard plot for treatment given at Cancer 
Inst i tute 8 6 
Figure 6.7: Kaplan-Meier E s t i m a t e s of Survivor funct ions by s e x of the 
pat ient 8 7 
Figure 6 .8: Log-Cumulat ive Hazard plot by s e x of the pat ient 8 8 
Figure 6 .9: Kaplan-Meier E s t i m a t e s of Survivor funct ions by age of the 
pat ient 8 9 
Figure 6 . 1 0 : Log-Cumulat ive Hazard plot by age of the pat ient 8 9 
Figure 6 . 1 1 : Kaplan-Meier E s t i m a t e s of Survivor func t ions for ethnic i ty 9 0 
Figure 6 . 1 2 : Log-Cumulat ive Hazard plot for ethnic i ty 9 1 
Figure 6 . 1 3 : Kaplan-Meier E s t i m a t e s of Survivor func t ions for religion 9 2 
Figure 6 . 1 4 : Log-Cumulat ive Hazard plot for religion • 9 2 
Figure 6 .15 : Kaplan-Meier E s t i m a t e s of Survivor funct ions for s m o k i n g 
s t a t u s 9 3 
Figure 6 .16 : Log-Cumulat ive Hazard plot for s m o k i n g s t a t u s 9 4 
Figure 6 .17 : Kaplan-Meier E s t i m a t e s of Survivor func t ions for 
c h e w i n g betel * V 9 5 
Figure 6 . 1 8 : Log-Cumulat ive Hazard plot for c h e w i n g betel 9 5 
Figure 6 . 1 9 : Kaplan-Meier E s t i m a t e s of Survivor funct ions for c o n s u m i n g 
alcohol 9 6 
Figure 6 .20 : Log-Cumulat ive Hazard plot for c o n s u m i n g alcohol 9 7 
Figure 6 . 2 1 : Kaplan-Meier E s t i m a t e s of Survivor funct ions for 
genet ic effect • 9 8 
Figure 6 . 2 2 : Log-Cumulat ive Hazard plot for g e n e t i c effect 9 8 
Figure 6 . 2 3 : Kaplan-Meier E s t i m a t e s of Survivor •functions for 
present ing TB , 9 9 
Figure 6 .24 : Log-Cumulat ive Hazard plot-for present ing TB 100 
Figure 6 . 2 5 : Plot of Cox-Snel l r e s idua l s 107 
Figure 6 . 2 6 : Log-Cumulat ive Hazard pfet of the Cox-Snel l r e s idua l s 108 
Figure 6 .27 : Plot of Martingale res idua l s Vs Rank of survival t ime 1 0 8 
Figure 6 . 2 9 : Plot of Martingale res idua l s Vs "treatment given 109 
Figure 6 . 2 8 : Plot of Martingale re s idua l s Vs Stage of d iagnos i s 109 
Figure 6 . 3 0 : Plot of Martingale re s idua l s Vs s e x of the pat ient 109 
Figure 6 . 3 1 : Plot of Dev iance re s idua l s Vs Rank of survival t ime 1 1 0