7 Case-control Analysis Chihaya Hundout

7/28/2019 7 Case-control Analysis Chihaya Hundout

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Analysis and presentation of

Case-control study data

Chihaya Koriyama

February 14 (Lecture 1)


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Study design in epidemiology

Observationalstudy

individual

Case-control

study

Cohortstudy

population

Ecological

study

intervention


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Why case-control study?

In a cohort study, you need a large number

of the subjects to obtain a sufficient number

of case, especially if you are interested in a

rare disease. Gastric cancer incidence in Japanese male:

128.5 / 100,000 person year

A case-control study is more efficient in

terms of study operation, time, and cost.


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Comparison of the study design

Case-control Cohort

Rare diseases suitable not suitable

Number of disease 1 1


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Case-control study- Sequence of determining exposure and outcome status

Step1: Determine and select cases of

your research interest

Step2: Selection of appropriate controls

Step3: Determine exposure status in

both cases and controls


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Case ascertainment

What is the definition of the case?

Cancer (clinically? Pathologically?)

Virus carriers (Asymptomatic patients)

You need to screen the antibody

Including deceased cases?

You have to describe the following points,

the definition

when, where & how to select


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Who will be controls?

Control non-case

Controls are also at risk of the disease

in his(her) future.

Controls are expected to be arepresentative sample of the

catchment population from which the

case arise.

In a case-control study of gastric

cancer, a person who has received the

gastrectomy cannot be a control since

he never develop gastric cancer .


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a population-based case-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-based case-control studyBoth case and controls are patients who are

hospitalized or outpatients.

Controls with diseases associated with the exposure

of interest should be avoided.

Various types of case-control studies


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The following points should be

recorded (described in your paper) The list (number) of eligible cases

whose medical records unavailable

The list (number) of refused subjects,if possible, with descriptions of the

reasons of refusal

The length of interview The list (number) of subjects lacking

the measurement data, with

descriptions of the reasons


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Exploratory or Analytic

Exploratory case-control studies

There is no specific a priori

hypothesis about the relationship

between exposure and outcome.

Analytic case-control studies

Analytic studies are designed to test

specific a priori hypotheses aboutexposure and outcome.


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Case-control study - information

Sources of the information of exposure and

potential confounding factors

Existing records

Questionnaires

Face-to-face / telephone interviews

Biological specimens

Tissue banks Databases on biochemical and

environmental measurements


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Temporality is essential in Hills criteria

Disease

onset

Initial

Symptoms

Clinical

Diagnosis

The study exposure

is unlikely to bealtered at this stage

because of the

disease.

The study exposure

is more likely to bealtered at this stage

because of the

symptoms.

Essential Epidemiology (WA Oleckno)


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Bias should be minimized

Bias & Confounding

Selection bias

Detection bias

Information bias (recall bias)

Confounding

Confounding can be controlledby statistical analyses but we

can do nothing about bias after

data collection.


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Case-control studies

are potential sources

of many biases

should be carefully

designed, analyzed,

and interpreted.


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How can we solve the problem of

confounding in a case-control study?

Prevention at study design

Limitation

Matching in a cohort study But

not in a case-control study


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Matching in a case-control study

Matched by confounding

factor(s) to increase the

efficiency of statistical analysis

Cannot control confounding

A conditional logistic analysis is

required.


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Over matching

Matched by factor(s) strongly

related to the exposure which is

your main interest

CANNOT see the difference in

the exposure status between

cases and controls


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How can we solve the problem of

confounding?

Treatment at statistical analysis

Stratification by a confounder

Multivariate analysis


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What you should describe in the

materials and methods,

1. Study design

2. Definition of eligible cases

and controls

Inclusion / exclusion criteria of

cases and controls

3. Number of the respondents

and response rate4. Main exposure and other

factors including potential

confounding factors


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5. Sources of the information of

exposure and other factors

6. Matched factors, if any7. The number of subjects used

in statistical analyses

8. Statistical test(s) and model(s)

9. Name and version of the

statistical software

What you should describe in the

materials and methods,


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Assuring adequate study power

Following information is necessary

The confidence level desired (usually 95%

corresponding to a p-value of 0.05)

The level of power desired (80-95%) The ratio of controls to cases

The expected frequency of the exposure in

the control group

The smallest odds ratio one would like to beable to detect (based on practical

significance)


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Statistical analysis

Matched vs. Unmatched studiesThe procedures for analyzing the

results of case-control studies

differ depending on whether the

cases and controls are matched orunmatched.

Matched Unmatched

McNemars test Chi-square test

Conditional logistic Unconditional logistic

regression analysis regression analysis


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Advantages of pair matching in case-

control studies

Assures comparability between cases and

controls on the selected variables

May simplify the selection of controls by

eliminating the need to identify a randomsample

Useful in small studies where obtaining cases

and controls that are similar on potentially

confounding factors may otherwise be difficult

Can assure adequate numbers of subjects with

specified characteristics so as to permit

statistical comparisons Essential Epidemiology (WA Oleckno)


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Disdvantages of pair matching in case-

control studies

May be difficult or costly to find a sufficientnumber of controls

Eliminates the possibility of examining the effects

of the matched variables on the outcome Can increase the difficulty or complexity of

controlling for confounding by the remaining

unmatched variables

Overmatching

Can result in a greater loss of data since a pair

of subjects has to be eliminated even if ne

subject is not responsive Essential Epidemiology (WA Oleckno)


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Lung cancer Controlscases

N=100 N=100

Smokers (NOT recently started)

70 40

An example of unmatched case-control study

Cases Controls

smoker 70 40

Non-smoker 30 60

Odds ratio=


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Risk measure in a case-control study

Odds = prevalence / (1 prevalence)Odds ratio = odds in cases / odds in controls

Disease

+case control+ a c

Exposure b dExposure odds in cases a / bExposure odds in controlsc / dOdds ratio(a / b) / (c / d) a * d / b * c


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Lung cancer Matched controlsCases by sex & age

N=100 N=100

Smokers (NOT recently started)

70 40

An example of matched case-control study

Case

Smoker Non-smoker

Control smoker 30 10Non-smoker 40 20

Notice that this is the distribution of 100 matched pairs.


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McNemars test

Case

Smoker Non-smoker

Controlsmoker 30 10

Non-smoker 40 20

Chi-square (test) statistic

= (40 10)2 / (40+10)

= 18

where degree of freedom is 1.

Odds ratio = 40 / 10 = 4


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Logistic regression analysis

Logistic regression is used to

model the probability of a

binary response as a function

of a set of variables thought topossibly affect the response

(called covariates).

1: case (with the disease)

Y =

0: control (no disease)


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One could imagine trying to fit a linear model

(since this is the simplest model !) for the

probabilities, but often this leads to problems:

In a linear model, fitted probabilities can fall

outside of 0 to 1. Because of this, linear models

are seldom used to fit probabilities.

Probability


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In a logistic regression analysis, the

logit of the probability is modelled,

rather than the probability itself.

P = probability of getting disease

plogit (p) = log

1-p

As always, we use the natural log. The logit

is therefore the log odds,

since odds = p / (1-p)


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The values ofa and b will determine whether or

not and how steeply the dose-response curve

rises (or falls) and where it is centered.

Ifb = 0 px is constant over x

b > 0 px increases with xb < 0 px decreases with x

H0: b= 0 is the null hypothesis in a test of trendwhen x is a continuous variable. Knowledge ofb

would give us insight to the direction and degree

of association outcome and exposure.

e (a+bx)

Px =

1 + e(a+bx)


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Simple logistic regression (with a dichotomous covariate)

Suppose we are considering a case-control study

where the response variable is disease (case) /

non-disease (control) and the predictor variable is

exposed / non-exposed, which we code as an

indicator variable, or dummy variable.

1 D1 1 E1

Y = x =

0 D0 0 E0

And px = Prob (disease given exposure x)= P (Y = 1 | x) x = 0, 1

Thus, p1 = probability of disease among exposed

p0 = probability of disease among non-exposed


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In case of exposure (X=1): logit(PE1)=intercept + b

In case of non-exposure (X=0): logit (PE0) =intercept

If you want to obtain odds ratio of exposure group,

ORPE1 / (1-PE1)/ (PE0 / (1-PE0))

log(OR) = log {PE1 / (1-PE1)/ (PE0 / (1-PE0))}

= log (PE1 / (1-PE1)) log(PE0 / (1-PE0))

= logit (P for exposure) logit (P for non-exposure)= (intercept + b)intercept

= b OR = e b

Definition of odds ratio

Si l l i ti i


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Simple logistic regression

(with a covariate having more than two categories)

Suppose we are considering a case-control study

where the predictor variable is current smoker / ex-smoker / non-smoker, which we code as a dummy

variable.

Case Smokingstatus

SMK1(X1)

SMK2(X2)

1 Current 1 0

0 Ex-smoker 0 1

1 Non-smoker 0 0

1 Ex-smoker 0 1

0 Non-smoker 0 0

0 Non-smoker 0 0

Original data Dummy variables


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Logistic regression model of the previous example

logit (P) = a + b1(X1) + b2 (X2)

In case of current smoker (X1=1, X2=0):

logit(Pcurrent)= a + b1

In case of ex-smoker (X1=0, X2=1) :

logit(Pex)= a + b2

In case of non-smoker (X1=0, X2=0) :logit(Pnon)= a

ORcurrent = e b1

ORex = e b2

ORnon = 1 (referent)


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Walds test for no association

The null hypothesis of no association betweenoutcome and exposure corresponds to

H0: OR=1 or H0: b =logOR=0

Using logistic regression results, we can testthis hypothesis using standard coefficients or

Walds test.

Note: STATA and SAS present two-sidedWalds test p-values.


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Likelihood Ratio Test (LRT)

An alternative way of testing hypotheses in alogistic regression model is with the use of a

likelihood ratio test. The likelihood ratio test

is specifically designed to test between

nested hypotheses.

H0: log (Px / (1-Px)) = a

HA: log (Px / (1-Px)) = a + bxand we say that H0 is nested in HA.


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Likelihood Ratio Test (LRT)

In order to test H0 vs. HA, we compute the likelihood

ratio test statistic:

G= -2log(LH0 / LHA) = 2 (log LHA log LH0)

= (-2log LH0) (-2log LHA)

Where

LHA is the maximized likelihood under the

alternative hypothesis HA and

LH0 is the maximized likelihood under the nullhypothesis H0.

If the null hypothesis H0 were true, we would expect

the likelihood ratio test statistic to be close to zero.


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Walds test vs. LRT

In general, the LRT often works a little better thanthe Wald test, in that the test statistic more closely

follows a X2 distribution under H0. But the Wald test

often works very well and usually gives similar

results.

More importantly, the LRT can more easily be

extended to multivariate hypothesis tests, e.g.,

H0: b1 = b2 = 0 vs. HA: b1 = b2 = 0


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World J. Gastroenterology 2006


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216CASES

173formalin-fixed

paraffin-embeddedblocks

We could not obtain the information

on tumor location for 23 cases, and

those cases were excluded from the

tumor location specific analysis.

81 cases were excluded

7

65

91

16

REFUSED TOPARTICIPATE

IN THE STUDY

LIVED INVALLE DEL CAUCALESS THAN 5 YEARS

RECURRENT CASES

COULD NOCONTACT

Recruitment of cases1

2

3

4

PATIENTSNEWLY

DIAGNOSEDAS G.C.

395

Sep.2000Dec.2002


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431CONTROLS

POTENTIALCONTROLS

528

67

1

29

LIVED INVALLE DEL CAUCALESS THAN 5 YEARS

REFUSED TO

PARTICIPATE

IN THE STUDY

Histry of G.C.

Recruitment of controls1

2

3

Matched by sex, age (5-year ),hospital, date of

administration

Case: control= 1 : 2

Major diseases of controls

cardiovascular diseases 208 trauma 117 infectious diseases 38 urological disorders 21)

| i


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xi:logistic casocon i.fumar

i.fumar _Ifumar_0-2 (naturally coded; _Ifumar_0 omitted)

Logistic regression Number of obs = 647

LR chi2(2) = 4.24

Prob > chi2 = 0.1198

Log likelihood = -409.93333 Pseudo R2 = 0.0051

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

casocon | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------------------------

_Ifumar_1 | 1.479399 .2817549 2.06 0.040 1.018526 2.148813

_Ifumar_2 | 1.205128 .2660901 0.85 0.398 .7817889 1.857706

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

| gastric cancer

Smoking | 0 1 | Total

-----------+----------------------+----------

Never 0 | 188 78 | 266

Ex- 1 | 145 89 | 234

Current 2 | 98 49 | 147

-----------+----------------------+----------

Total | 431 216 | 647

Walts test p values


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xi:clogit casocon i.fumar, group(identi) or

Conditional (fixed-effects) logistic regression Number of obs = 647

LR chi2(2) = 4.64

Prob > chi2 = 0.0982

Log likelihood = -234.5745 Pseudo R2 = 0.0098

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

casocon | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]

-------------+-------------------------------------------------------------------------------------

_Ifumar_1 | 1.535023 .3061998 2.15 0.032 1.038295 2.269389

_Ifumar_2 | 1.219851 .2784042 0.87 0.384 .7799 1.907985

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

Walds test p values

Fumar=0

Fumar=1

Fumar=2

Results ofconditional logistic regression analysis using the same data

Case Control OR (95%CI)

Stata command


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OR (95%CI)Lower Middle Upper(N=116)* (N=52)* (N=24)*

cigarrete smokingnever 1.0 referent 1.0 referent 1.0 referent

ex-smoker 1.9 (1.1 - 3.4) 1.2 (0.6 - 2.5) 3.7 (1.1 - 12.5)current 1.3 (0.7 - 2.3) 1.3 (0.5 - 3.4) 3.0 (0.6 - 13.9)

P for trend 0.257 0.597 0.083P forheterogeneity 0.059 0.859 0.070

GC risk by smoking in Cali, Colombia

results of tumor-location specific analysis

P= 0.51 P value by LRT

This test examines the difference in the magnitude of the

association between smoking and GC risk among 3 tumor sites.

7 Case-control Analysis Chihaya Hundout

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