7 case-control_analysis_Chihaya_hundout.ppt

7/23/2019 7 case-control_analysis_Chihaya_hundout.ppt

1/47

Analysis and presentation of

Case-control study data

Chihaya Koriyama

February 14 (Lecture 1)


2/47

Study design in

epidemiology


3/47

Why case-control study?

In a cohort study you need a lar!e number

of the sub"ects to obtain a sufficient number

of case especially if you are interested in a

rare disease#$ %astric cancer incidence in &apanese male'

1#* + 1,,,,, person year

A case-control study is more efficient in

terms of study operation time and cost#


4/47

Comparison of the study design

Case-control Cohort

are diseases suitable not suitable

.umber of disease 1 1/0ample sie relati2ely small need to be lar!e

Control selection difficult easier

0tudy period relati2ely short lon!

ecall bias yes nois3 difference no a2ailable a2ailable


5/47

Case-control study- 0euence of determinin! e5posure and outcome status

0tep1' Determine and select cases of

your research interest

0tep' Selection of appropriate controls

0tep6' Determine exposure status in

both cases and controls


6/47

Case ascertainment

7hat is the definitionof the case8

$ Cancer (clinically8 9atholo!ically8)

$ :irus carriers (Asymptomatic patients)

;


7/47

Who will be controls?

Control ? non-case

$ Controls are also at ris3 of the disease

in his(her) future#

$ @Controls are e5pected to be arepresentati2e sample of the catchment

population from =hich the case arise#

$ In a case-control study of !astriccancer a person =ho has recei2ed the

!astrectomy cannot be a control since

he ne2er de2elop !astric cancer #


8/47

a population-basedcase-control study

Both cases and controls are recruited from the

population#

a case-control study nested in a cohort

Both case and controls are members of the cohort#

a hospital-basedcase-control studyBoth case and controls are patients =ho are

hospitalied or outpatients#

Controls =ith diseases associated =ith the e5posure

of interest should be a2oided#

:arious types of case-control studies


9/47

he follo=in! points should be

recorded (described in your paper) he list (number) of eli!ible cases

=hose medical records una2ailable

he list (number) of refused sub"ects ifpossible =ith descriptions of the

reasons of refusal

he len!th of inter2ie=

he list (number) of sub"ects lac3in!

the measurement data =ith

descriptions of the reasons


10/47

Exploratory or Analytic

D5ploratorycase-control studies

$ here is no specific a priori

hypothesis about the relationship

bet=een e5posure and outcome#

Analyticcase-control studies

$Analytic studies are desi!ned to test

specific a priori hypotheses aboute5posure and outcome#


11/47

Case-control study - information

0ources of the information of e5posure and

potential confoundin! factors

$ D5istin! records

$ Euestionnaires

$ Face-to-face + telephone inter2ie=s

$ Biolo!ical specimens

$ issue ban3s$ atabases on biochemical and

en2ironmental measurements


12/47

emporality is essential in GillHs criteria

he study e5posure

is unli3ely to bealtered at this sta!e

because of the

disease#

he study e5posure

is more li3ely to bealtered at this sta!e

because of the

symptoms#

Dssential Dpidemiolo!y (7A lec3no)


13/47

Bias should be minimied

Bias > Confoundin!

$ 0election bias

$ etection bias

$ Information bias (recall bias)

$ Confoundin!

Confoundin! can be controlledby statistical analyses but =e

can do nothin! about bias after

data collection#


14/47

Case-control studies

are potential

sources of many

biasesshould be carefully

desi!ned analyed

and interpreted#


15/47

!ow can we sol"e the problem of

confounding in a case-control study?

Prevention at study design

Limitation

Matchingin a cohortstudy But not in a case-control study


16/47

#atching in a case-control study

Jatched by confoundin!

factor(s) to increase the

efficiency of statistical analysis

Cannotcontrol confoundin!

$A conditional lo!istic analysis is

reuired#


17/47

$"er matching

Jatched by factor(s) stron!ly

related to the e5posure =hich is

your main interest

$ CA.. see the difference in

the e5posure status bet=een

cases and controls


18/47

!ow can we sol"e the problem of

confounding?

Treatment at statistical analysis

Stratifcationby a conounder

Multivariateanalysis


19/47

7hat you should describe in the

materials and methods1# 0tudy desi!n

# efinition of eli!ible cases and

controls

$ Inclusion + e5clusion criteria of

cases and controls

6# .umber of the respondents

and response rate4# Jain e5posure and other

factors includin! potential

confoundin! factors


20/47

*# 0ources of the information of

e5posure and other factors

# Jatched factors if any# he number of sub"ects used

in statistical analyses

# 0tatistical test(s) and model(s)

M# .ame and 2ersion of the

statistical soft=are

7hat you should describe in the

materials and methods


21/47

Assurin! adeuate study po=er

Follo=in! information is necessary

$ he confidence le2el desired (usually M*N

correspondin! to a p-2alue of ,#,*)

$ he le2el of po=er desired (,-M*N)$ he ratio of controls to cases

$ he e5pected freuency of the e5posure in

the control !roup

$ he smallest odds ratio one =ould li3e to beable to detect (based on practical

si!nificance)


22/47

0tatistical analysis

@Jatched 2s# @Onmatched studieshe procedures for analyin! the

results of case-control studies

differ dependin! on =hether the

cases and controls are matched orunmatched#

#atched %nmatched

Jc.emarHs test

Chi-suare test Conditional lo!istic Onconditional

lo!istic

re!ression analysis re!ression analysis


23/47

Ad2anta!esof pair matchin! in case-

control studies Assures comparability bet=een cases andcontrols on the selected 2ariables

Jay simplify the selection of controls by

eliminatin! the need to identify a randomsample

Oseful in small studies =here obtainin! cases

and controls that are similar on potentially

confoundin! factors may other=ise be difficult

Can assure adeuate numbers of sub"ects =ith

specified characteristics so as to permit

statistical comparisons Dssential Dpidemiolo!y (7A lec3no)


24/47

isd2anta!esof pair matchin! in case-

control studies Jay be difficult or costly to find a sufficient

number of controls

Dliminates the possibility of e5aminin! the effects

of the matched 2ariables on the outcome Can increase the difficulty or comple5ity of

controllin! for confoundin! by the remainin!

unmatched 2ariables

2ermatchin!

Can result in a !reater loss of data since a pair

of sub"ects has to be eliminated e2en if ne

sub"ect is not responsi2e Dssential Dpidemiolo!y (7A lec3no)


25/47

Lun! cancer Controlscases

.P1,, .P1,,

0mo3ers (. recently started) Q Q

, 4,

An e5ample of unmatched case-control study

Cases Controls

smoker ! "!

#on-smoker $! %!

dds ratioP


26/47

&is' measure in a case-control study

$dds( pre"alence ) *+ pre"alence,

$dds ratio( odds in cases ) odds in controls

Disease

case control a c

Exposure b d

Exposure odds in cases a ) b

Exposure odds in controlsc ) d

$dds ratio*a ) b, ) *c ) d, a . d ) b . c


27/47

Lun! cancer Jatched controlsCases by se5 > a!e

.P1,, .P1,,

0mo3ers (. recently started)

Q Q

, 4,

An e5ample of matched case-control study

Case

Smoker #on-

smoker

Controlsmoker $! &!

#on-smoker "! '!.otice that this is the distribution of 1,, matched

pairs#


28/47

Jc.emarHs test

Case

Smoker #on-smoker

Control

smoker $! &!

#on-smoker "! '!

Chi-suare (test) statistic

P (4, $ 1,)+ (4,R1,)

P 1

=here de!ree of freedom is @1#

dds ratio P 4, + 1, P 4


29/47

Lo!istic re!ression analysis

Lo!istic re!ression is used to

model the probability of a

binary response as a function

of a set of 2ariables thou!ht topossibly affect the response

(called co2ariates)#

1' case (=ith the disease)

< P

,' control (no disease)


30/47

ne could ima!ine tryin! to fit a linear model

(since this is the simplest model S) for the

probabilities but often this leads to problems'

In a linear model fitted probabilities can fall

outside of , to 1# Because of this linear models

are seldom used to fit probabilities#

9robability


31/47

In a lo!istic re!ression analysis the

logitof the probability is modelled

rather than the probability itself#

9 P probability of !ettin! disease

plo!it (p) P lo!

1-p

As al=ays =e use the natural lo!# he lo!it

is therefore the log odds

since odds P p + (1-p)


32/47

Simple logistic regression *with a continuousco"ariate,

0uppose =e !i2e each of se2eral beetles some

dose of a potential to5ic a!ent (x

Pdose) and =eobser2e =hether the beetle dies (


33/47

he 2alues of and =ill determine =hether or

not and ho= steeply the dose-response cur2e

rises (or falls) and =here it is centered#

If P , p5is constant o2er 5

T , p5increases =ith 5 / , p5decreases =ith 5

G,' P , is the null hypothesis in a @test of trend=hen 5 is a continuous 2ariable# Kno=led!e of =ould !i2e us insi!ht to the direction and de!ree

of association outcome and e5posure#

e (R5)

95 P

1 R e(R5)


34/47


35/47

In case of e5posure (VP1)' lo!it(9D1)Pintercept R

In case of non-e5posure (VP,)' lo!it (9D,) Pintercept

If you =ant to obtain odds ratio of e5posure !roup

9D1+ (1-9D1)+ (9D,+ (1-9D,))

lo!() P lo! W9D1+ (1-9D1)+ (9D,+ (1-9D,))X

P lo! (9D1+ (1-9D1)) $ lo!(9D,+ (1-9D,))

P lo!it (9 for e5posure) $ lo!it (9 for non-e5posure)

P (intercept R ) $ intercept

P $& ( e

efinition of odds

ratio


36/47

Simple logistic regression

*with a co"ariate ha"ing more than two categories,

0uppose =e are considerin! a case-control study =here

the predictor 2ariable is current smo3er + e5-smo3er +non-smo3er =hich =e @code as a dummy 2ariable#

Case Smokingstatus

SMK1(X1)

SMK2(X2)

& (urrent & !

! )*-smoker ! &

& #on-smoker ! !

& )*-smoker ! &

! #on-smoker ! !

! #on-smoker ! !

$riginal data Dummy "ariables


37/47

Lo!istic re!ression model of the pre2ious e5ample

lo!it (9) P R 1(V1) R (V)

In case of current smo3er (V1P1 VP,)'

lo!it(9current)P R 1

In case of e5-smo3er (V1P, VP1) '

lo!it(9e5)P R 2

In case of non-smo3er (V1P, VP,) 'lo!it(9non)P

$&current( e

$&ex( e

$&non( + *referent,


38/47

7aldHs test for no association

he null hypothesis of no association bet=eenoutcome and e5posure corresponds to

G,' P1 or G,' Plo!P,

Osin! lo!istic re!ression results =e can testthis hypothesis usin! standard coefficients or

7aldHs test#

.ote' 0AA and 0A0 present t=o-sided

7aldHs test p-2alues#


39/47

Li3elihood atio est (L)

An alternati2e =ay of testin! hypotheses in alo!istic re!ression model is =ith the use of a

li3elihood ratio test# he li3elihood ratio test

is specifically desi!ned to test bet=een

nested hypotheses#

G,' lo! (95+ (1-95)) P

GA' lo! (95+ (1-95)) P R 5

and =e say that G,is nested in GA#


40/47

Li3elihood atio est (L)

In order to test G,2s# GA =e compute the li3elihood

ratio test statistic'

%P -lo!(LG,+ LGA) P (lo! LGA$ lo! LG,)

P (-lo! LG,) $ (-lo! LGA)

7here

LGA is the ma5imied li3elihood under the

alternati2e hypothesis GAand

LG, is the ma5imied li3elihood under the nullhypothesis G,#

If the null hypothesis G,=ere true =e =ould e5pect

the li3elihood ratio test statistic to be close to ero#


41/47

7aldHs test 2s# L

In !eneral the L often =or3s a little better thanthe 7ald test in that the test statistic more closely

follo=s a X2distribution under G,# But the 7ald test

often =or3s 2ery =ell and usually !i2es similar

results#

Jore importantly the L can more easily be

e5tended to multi2ariate hypothesis tests e#!#

G,' 1P P , 2s# GA' 1 P P ,


42/47

7orld %astroenterolo!y ,,


43/47

216CASES

173ormalin!"#ed

para$n!em%edded%lo&ks

We could not obtain the information

on tumor location for /0 cases1 and

those cases were excluded from the

tumor location specific analysis2

1 cases were

excluded

7

6'

1

16

E*+SE, -./A-0C0/A-E

0 -E S-+,

405E, 05A44E ,E4 CA+CA

4ESS -A ' EAS

EC+E- CASES

C.+4, .C.-AC-

&ecruitment of cases

1

6

4

/A-0E-SE4

,0A.SE,AS 8C8

3'

Sep2/333

Dec2/33/


44/47

931C.-.4S

/.-E-0A4C.-.4S

'2:

67

1

2

405E, 05A44E ,E4 CA+CA

4ESS -A ' EAS

E*+SE, -.

/A-0C0/A-E

0 -E S-+,

istry o 8C8

&ecruitment of controls1

6

#atchedby sex1 age *4-year ,1hospital1 date of

administration

Case5 control( + 5 /

#a6or diseases of controls cardio"ascular diseases

/37

trauma ++8

infectious diseases 3

urological disorders 21)


45/47


46/47

xi5clogitcasocon i2fumar1 group*identi,or

Conditional *fixed-effects, logistic regression .umber of obs P 4

L chi() P 4#4

9rob T chi P ,#,M

Lo! li3elihood P -64#*4* 9seudo P ,#,,M

---------------------------------------------------------------------------------------------------

casocon U dds atio 0td# Drr# 9TUU [M*N Conf# Inter2al\

-------------R-------------------------------------------------------------------------------------

YIfumarY1 U 1#*6*,6 #6,1MM #1* ,#,6 1#,6M* #M6M

YIfumarY U 1#1M*1 #4,4 ,# ,#64 #MM 1#M,M*

---------------------------------------------------------------------------------------------------

Wald9s test p "alues

FumarP,

FumarP1

FumarP

&esults of conditionallogistic regression analysis using the same data

Case Control $& *:4;C


47/47

=C ris' by smo'ing in Cali1 Colombia

results of tumor-location specific analysis

P ( 324+ 9 2alue by L

his test e5amines the difference in the ma!nitude of the

association bet=een smo3in! and %C ris3 amon! 6 tumor

Documents

7 case-control_analysis_Chihaya_hundout.ppt