Epidemiologic Methods - Fall 2010

Where we have been:

Designing studies, measuring disease occurrence, andestimating associations

Lecture Title

1 Study Design

2 Measures of Disease Occurrence I

3 Measures of Disease Occurrence II

4 Measures of Disease Association I

5 Measures of Disease Association II

Unifying theme of design

Design begets measures

Where we are going:

Threats to validity in clinical research studies and how can they be prevented

6 Selection Bias

7 Understanding Measurement: Reproducibility & Validity Journal Club

8 Measurement Bias

9 Confounding and Interaction I: General Principles

Journal Club

10 Confounding and Interaction II: Assessing Interaction

11 Confounding and Interaction III: Stratified Analysis Journal Club

12 Journal Club

Bias in Clinical Research: General Aspects and Focus on Selection Bias

• Framework for understanding error in clinical research

– systematic error, aka threats to internal validity or bias

– random error, aka sampling error or chance

• Selection bias (a type of systematic error)

– by study design:• descriptive • cross-sectional• case-control• longitudinal studies (cohort: observational or experimental)

WARNING: SHIFTING GEARS

• Today: A lot of theory– Rare equations or cook-book algorithms

• Why?– Identifying (or preventing) bias not a plug & play process– Requires human intelligence

• sound knowledge of theory

A Framework for Classifying Error

Clinical Research:SampleMeasure

(Intervene)Analyze

Infer• Inference

– Websters: act of passing from sample data to generalizations, with unknown degree of certainty

– All we can do is make educated guesses about the soundness of our inferences

– Those who are more educated will make better guesses

• Anyone can get a numeric answer

• The challenge is to tell if it is correct

Disease

Exposure

+ -

+

-

REFERENCE/TARGET/SOURCE POPULATIONaka STUDY BASE STUDY SAMPLE

OTHER POPULATIONS

Two types of inferences

Disease

Exposure

+ -

+

-

San Franciscans, 20 to 65 years old

SAMPLE of San Franciscans, 20 to 65 yrs old

>65 years old in U.S.

20 to 65 year olds, in U.S., outside of San Francisco

20 to 65 year olds, in Europe

Disease

Exposure

+ -

+

-

REFERENCE/TARGET/SOURCE POPULATIONaka STUDY BASE STUDY SAMPLE

Most important inference is the

first one

Without an accurate first

inference, there is little point

considering the second

inference

Attempts in study design to enhance the second inference are

often in conflict with goal of making a sound first inference

• The goal of any study is make an accurate (true) inference, i.e.:

– measure of disease occurrence in a descriptive study

– measure of association between exposure and disease in an analytic study

• Ways of getting the wrong answer:

– systematic error; aka “threat to validity” or bias

• any systematic process in the conduct of a study that causes a distortion from the truth in a predictable direction

• captured in the validity of the inference

– random error; aka chance or sampling error

• occurs because we cannot study everyone (we must sample)

• direction is random and not predictable

• captured in the precision of the inference (e.g., SE and CI)

Error in Clinical Research

Good Validity

Good Precision

Poor Validity

Poor Precision

Validity and Precision: Each Shot at Target Represents a Study Sample of the

Same Sample Size of a Given Study Design

Validity and Precision

Poor Validity

Good Precision

Good Validity

Poor Precision

Validity and Precision

Poor Validity

Good Precision

Good Validity

Poor Precision

Systematic error (bias)

Random error

(chance)

Random error

(chance)

No

Systematic error

Performing an Actual Study: You Only Have One Shot

Field of “statistics” can tell you the random

error (precision)

with formulae for

confidence intervals

Only judgment can tell you about

systematic error

(validity)

Judgment requires

substantive and

methodologic knowledge

Disease

Exposure

+ -

+

-

REFERENCE/TARGET/SOURCE POPULATION

? INTERNAL VALIDITY

OTHER POPULATIONS

? EXTERNAL VALIDITY (generalizability)

STUDY SAMPLE

Two Types of Inferences

Correspond to Two Types of Validity

Two Types of InferencesCorrespond to Two Types of Validity

1. Internal validity– Do the results obtained from the actual subjects accurately

represent the target/reference/source population?– Theory guides assessment

2. External validity (generalizability)– Do the results obtained from the actual subjects pertain to persons

outside of the source population?– Internal validity is a prerequisite for external validity– Always just a guess

• “Validity” to us will mean internal validity– “Threat to validity” = threat to internal validity– Identifying threats to validity is a critical aspect of research

Why Do We Need Valid Studies?

• The goal of any study is make an accurate (true) inference, i.e.:

– measure of disease occurrence in a descriptive study

– measure of association between exposure and disease in an analytic study

• Ways of getting the wrong answer:

– Our focus: systematic error; aka threats to validity or bias

• a systematic process in the conduct of a study that causes a distortion from the truth in a predictable direction

• captured in the validity of the inference

– random error; aka chance or sampling error

• occurs because we cannot study everyone (we must sample)

• direction is random and not predictable

• captured in the precision of the inference (e.g., SE and CI)

Error in Clinical Research

MetLife Is Settling Bias Lawsuit

BUSINESS/FINANCIAL DESK August 30, 2002, Friday

MetLife said yesterday that it had reached a preliminary settlement of a class-action lawsuit accusing it of charging blacks more than whites for life insurance from 1901 to 1972.

MetLife, based in New York, did not say how much the settlement was worth but said it should be covered by the $250 million, before tax, that it set aside for the case in February.

“Bias” in Webster’s Dictionary1 : a line diagonal to the grain of a fabric; especially : a line at a 45° angle to the selvage often utilized in the cutting of garments for smoother fit2 a : a peculiarity in the shape of a bowl that causes it to swerve when rolled on the green b : the tendency of a bowl to swerve; also : the impulse causing this tendency c : the swerve of the bowl3 a : bent or tendency b : an inclination of temperament or outlook; especially : a personal and sometimes unreasoned judgment : prejudice

c : an instance of such prejudice

d (1) : deviation of the expected value of a statistical estimate from the quantity it estimates

(2) : systematic error introduced into sampling or testing

4 a : a voltage applied to a device (as a transistor control electrode) to establish a reference level for operation b : a high-frequency voltage combined with an audio signal to reduce distortion in tape recording

Bias of Priene (600 - 540 BC)

• One of the 7 sages of classical antiquity• Consulted by Croesus, king of Lydia,

about the best way to deploy warships against the Ionians

• Bias wished to avoid bloodshed, so he misled Croesus, falsely advising him that the Ionians were buying horses

• Bias later confessed to Croesus that he had lied.

• Croesus was pleased with the way that he had been deceived by Bias and made peace with the Ionians.

• Bias = deviation from truthBMJ 2002;324:1071

Classification Schemes for Error

• Szklo and Nieto– Bias (Systematic error)

• Selection Bias• Information/Measurement Bias

– Confounding– Chance (Random error)

• Other Common Approach– Bias (Systematic error)

• Selection Bias• Information/Measurement Bias• Confounding Bias

– Chance (Random error)

Think of the “BIG 4” in all of your work

Sackett DL. Bias in analytic research. J Chron Dis 1979

selection biasmeasurement biasconfounding bias

vs.

popularity biascentripetal biasreferral filter biasdiagnostic access biasdiagnostic suspicion biasunmasking biasmimicry biasprevious opinion biasadmission biasprevalence-incidence biasdiagnostic vogue biasdiagnostic purity biasprocedure selection biasmissing clinical data biasnon-contemporaneouscontrol biasstarting time bias

volunteer biascontamination biaswithdrawal biascompliance biastherapeutic personality biasbogus control biasinsensitive measure biasunderlying cause biasend-digit preference biasapprehension biasunacceptability biasobsequiousness biasexpectation biassubstitution gamefamily information biasexposure suspicion biasrecall bias etc

Selection Bias• Technical definition

– Bias that is caused when individuals have different probabilities of being included in the study according to relevant study characteristics: namely, the exposure and the outcome of interest

• Easier definition– Bias that is caused by some kind of systematic problem in the

process of selecting subjects initially or - in a longitudinal study - in the process that determines which subjects drop out of the study

• Problem caused by:

– Investigators: Faulty study design

– Participants: By choosing not to participate/ending participation

– (or both)

Unique to human subjects research

Selection Bias in a Descriptive Study

• Most fulminant: Surveys for 1948 Presidential election– various methods used to find subjects– largest % favored Dewey

• General election results– Truman beat Dewey

• Explanation: Bad Study Design

• Ushered in realization of the importance of representative (random) sampling

N= 894 sample Actual vote

Yes 4,717,006 (55%)No 3,809,090 (45%)

The San Francisco Chronicle

Should Gov. Davis be recalled?

No, retain Davis39%

Yes, recall Davis57%

Undecided4%

Based on a survey conducted in English and Spanish among random samples of people likely to vote in California’s Oct. 7 recall election

Election polls provide rare opportunity to later look at truth and evaluate bias in

study design

Luxury rarely occurs in clinical research

SOURCE POPULATION

STUDY SAMPLE

Descriptive Study: Depiction of No Selection Bias (Unbiased Sampling)

Even dispersion of arrows

SOURCE POPULATION

STUDY SAMPLE

Descriptive Study: Depiction of Selection Bias (Biased Sampling)

Uneven dispersion of arrows

e.g., Dewey backers were

over-represented

Leukemia Among Observers of a Nuclear Bomb Test

Caldwell et al. JAMA 1980• Smoky Atomic Test in Nevada• Outcome of 76% of observing troops at site was later found;

occurrence of leukemia determined

82% contacted by the investigators

18% contacted the investigators on their own

4.4 greater prevalence of leukemia than those

contacted by the investigators

Explanation: Human nature (affected humans like to come forward)

0.0

00

.05

0.1

00

.15

0.2

0P

rop

ort

ion

de

cea

sed

0 .5 1 1.5 2 2.5 3 3.5Time since initiation of antiretroviral therapy (years)

Mortality following initiation of antiretroviral therapy in Uganda

In the presence of 39% loss to follow-up at 3 years

Geng et al. JAMA 2008

0.0

00

.05

0.1

00

.15

0.2

0P

rop

ort

ion

de

cea

sed

0 .5 1 1.5 2 2.5 3 3.5Time since initiation of antiretroviral therapy (years)

Mortality following initiation of antiretroviral therapy in Uganda

Accounting for losses to follow-up by tracking down vital status of a sample of the lost in the community

Naive estimate

Corrected estimate Selection bias

(5-fold change)

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Analytic Study: Depiction of No Selection Bias (Unbiased Sampling)

Given that a person resides in one of the 4 cells in the source population, the selection probability is the probability he/she will be

represented in that cell in the study sample.

Equal weighted arrows = Equal selection probability

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Analytic Study: Depiction of No Selection Bias (Unbiased Sampling)

Equal selection probability in all 4 cells:

No Selection Bias

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

40000

10000

10000

40000

PR = (40,000/50,000)/(10,000/50,000) = 4

1% 1%

1%

1%

400

100

100

400PR = (400/500)/

(100/500) = 4

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Unequal selection probability isolated to one

cell:Underestimate of Exposure Effect

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

40000

10000

10000

40000

PR = (40,000/50,000)/(10,000/50,000) = 4

1% 1%

0.5%

1%

200

100

100

400PR = (200/300)/ (100/500) = 3.3

Analytic Study: Depiction of Selection Bias (Biased Sampling)

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Unequal selection probability:

Overestimate of Effect

Analytic Study: Depiction of Selection Bias (Biased Sampling)

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Unequal selection probability:

Overestimate of Effect

Analytic Study: Depiction of Selection Bias (Biased Sampling)

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Unequal selection probability:

Underestimate of Effect

Analytic Study: Depiction of Selection Bias (Biased Sampling)

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Analytic Study: Depiction of No Selection Bias (Unbiased Sampling)

Unequal selection probability but only

according to exposure:No Selection Bias

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Analytic Study: Depiction of No Selection Bias (Unbiased Sampling)

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

40000

10000

10000

40000

PR = (40,000/50,000)/(10,000/50,000) = 4

1% 1%

0.1%

0.1%

40

100

10

400PR = (40/50)/ (100/500) = 4

Unequal selection probability but only

according to exposure:No Selection Bias

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Analytic Study: Depiction of No Selection Bias (Unbiased Sampling)

Unequal selection probability but only

according to disease:No Selection Bias

For selection bias to occur, selection probabilities must

differ according to both exposure and disease

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Typically, in practice, you don’t know the selection

probabilities

Selection Bias in a Cross-sectional Study: Presence of exposure and disease at outset invites selection bias

?

? ?

?

History of Heart Attack

Hyper-lipidemia

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Selection Bias in a Cross-sectional Study: Effect of Non-Responders

Austin, AJE 1981Survey of S. California adults

OR observed = 3.6

25 347

45 2312

Overall 82% Response?

?

?

?

History of Heart Attack

Hyper-lipidemia

+ -

+

-

SOURCE POPULATION

Investigators made the extra effort to track down and question the initial non-

responders

Selection Bias in a Cross-sectional Study: Effect of Non-Responders

Austin, AJE 1981Survey of S. California adults

OR true = 3.3

2807100%100%

63

30100%

401100%

CORRECTED STUDY SAMPLESelection

probability

History of Heart Attack

Hyper-lipidemia

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Investigators made the extra effort to track down and question the initial non-

responders

Selection Bias in a Cross-sectional Study: Effect of Non-Responders

83% 87%

83%72%Austin, AJE 1981Survey of S. California adults

OR biased = 3.6

OR true = 3.325 347

45 2312

2807100%100%

63

30100%

401100%

CORRECTED STUDY SAMPLE

Response % Selection bias

Effect of unequal response (selection) probabilities in a cross-sectional study

Group Exposure Outcome

Bias in OR due to non-

response

Men Family h/o MI Heart failure +63%

Hypertension Stroke -32%

Women Family h/o stroke Stroke +59%

Family h/o diabetes Stroke -34%

Austin, AJE 1981Survey of S. California adults

Explanation: Non-participation among some potential subjects

(Study design is fine)

Another Mechanism for Selection Bias in Cross-sectional Studies

• Finding a diseased person in a cross-sectional study requires 2 things:– the disease occurred in the first place– person survived long enough to be sampled

• Any factor found associated with a prevalent case of disease might be associated with disease development, survival with disease, or both

• Assuming goal is to find factors associated with disease development (etiologic research), bias in prevalence ratio occurs any time that exposure under study is associated with survival with disease

Cross-Sectional Study Design

Selection Bias in a Cross-Sectional Study• Is glutathione S-transferase class deletion (GSTM1-null) polymorphism

associated with increased risk of breast cancer?

• With prevalent breast cancer in cross-sectional study, an association with GSTM1-null is seen depending upon the no. of years since diagnosis

• But not with brand new incident diagnoses (case-control study)

Kelsey et al. Canc Epi Bio Prev 1997

4 - 8 yrCancer

Nocancer

GSTM1-null

52 126

GSTM1-positive

39 119

OR = 1.3

CancerNo

cancer

GSTM1-null

119 115

GSTM1-positive

121 124

OR = 1.08

<4 yrCancer

Nocancer

GSTM1-null

44 126

GSTM1-positive

43 119

OR = 0.97

>8 yrCancer

Nocancer

GSTM1-null

44 126

GSTM1-positive

21 119

OR = 2.0

GSTM1-null is associated with survival after breast cancer, but

not with cancer development

Breast Cancer

GSTM1

+ -

null

SOURCE POPULATION

STUDY SAMPLE

Cross-sectional study of GSTM1 polymorphism and breast cancer

pos.

Bias: overestimate effect of GSTM-1 null polymorphism in causing breast

cancer

Fault: Study design

Selection Bias in Case-Control Studies: Presence of Exposure & Disease at Outset Also Invites Selection Bias

Coffee and cancer of the pancreas MacMahon et al. N Eng J Med 1981; 304:630-3

Cases: patients with histologic diagnosis of pancreatic cancer in any of 11 large hospitals in Boston and Rhode Island between October 1974 and August 1979

What study base gave rise to these cases?

How should controls be selected?

Selection Bias in a Case-Control Study

Coffee and cancer of the pancreas MacMahon et al. N Eng J Med 1981; 304:630-3

Controls: • Other patients without pancreatic cancer under the care of the

same physician of the cases with pancreatic cancer.

• Patients with diseases known to be associated with smoking or alcohol consumption were excluded

207 275

9 32

Case Control

Coffee: > 1 cup day

No coffee

OR= (207/9) / (275/32) = 2.7 (95% CI, 1.2-6.5)

Coffee and cancer of the pancreasMacMahon et al., (N Eng J Med 1981; 304:630-3)

216 307

Biased?

Relative to the hypothetical study base that gave rise to the cases, the selected controls were depleted of coffee users

Selected controls were: • Other patients under the care of the same physician at the time of

an interview with a patient with pancreatic cancer

Most of the MDs were gastroenterologists whose other patients were likely advised to stop using coffee

• Patients with diseases known to be associated with smoking or alcohol consumption were excluded

Smoking and alcohol use are correlated with coffee use; therefore, sample is relatively depleted of coffee users

Conclusion: Controls vastly depleted of coffee users compared to true study base

Fault: Investigators (Poor study design)

Cancer No cancer coffee

no coffee

SOURCE POPULATION

STUDY SAMPLE

Case-control Study of Coffee and Pancreatic Cancer: Depiction of Selection Bias

Bias: overestimate effect of coffee in

causing cancer

1410

8284

Case Control

Coffee: > 1 cup day

No coffee

OR= (84/10) / (82/14) = 1.4 (95% CI, 0.55 - 3.8)

Coffee and cancer of the pancreas:Use of population-based controls

•Gold et al. Cancer 1985

Selection Bias in Cohort Studies/RCTs

• Among initially selected subjects, selection bias “on the front end” less likely to occur compared to case-control or cross-sectional studies

– Reason: study participants (exposed or unexposed; treatment vs placebo) are selected before the outcome occurs

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Cohort Study/RCTAt the outset, since disease has not occurred yet among initially selected subjects, there is typically no opportunity for unequal sampling with respect to exposure and disease. (We cannot yet draw the 4 arrows)

Disease

Exposure

+ -

+

-

SOURCE POPULATION

STUDY SAMPLE

Cohort Study/RCTAll that is sampled at the beginning is exposure status (the “margins”)

Even if unequal sampling of exposed or unexposed groups occurs, it will not

result in selection bias when forming measures of

association

A + B

C + D

a + b

c + d

Selection Bias: Cohort Studies

• Selection bias can occur on the “front-end” of the cohort if:

– diseased individuals are unknowingly entered into the cohort; and

– being diseased is a cause of the exposure

• e.g.:

– Consider a cohort study of effect of exercise on all-cause mortality in persons initially thought to be completely healthy.

– If some participants were enrolled had undiagnosed cardiovascular disease and as a consequence were more likely to exercise less, what would happen to the measure of association?

Death No death

exercise

no exercise

SOURCEPOPULATION

STUDY SAMPLE

Cohort Study of Exercise and Survival

Selection bias will lead to spurious protective effect of exercise (assuming truly no effect)

Selection Bias: Cohort Studies/RCTs

• Most common form of selection bias does not occur with the process of initial selection of subjects

• Instead, selection bias most commonly caused by forces that determine length of participation (i.e., who ultimately stays in the analysis; losses)

– When those lost to follow-up have a different incidence of the outcome than those who remain (i.e. informative censoring) in at least one of

the exposure groups

AND

– Rate of informative censoring differs across exposure groups

• Selection bias results

When losses are associated with both exposure and outcome

Selection Bias: Cohort Studies

e.g., Cohort study of progression to AIDS: IDU vs homosexual men

All the ingredients are present for selection bias:

• Informative censoring is present– getting sick with AIDS is a common reason for loss to follow-up

– persons who are lost to follow-up have greater AIDS incidence than those who remain (i.e., informative censoring)

• Informative censoring is differential across exposure groups– IDU more likely to become lost to follow-up - at any level of feeling sick

– i.e., the magnitude of informative censoring differs across exposure groups (IDU vs homosexual men)

• Result: selection bias -- underestimates the incidence of AIDS in IDU relative to homosexual men

Effect of Selection Bias in a Cohort Study

Survival assuming no informative censoring and no difference between IDU and homosexual men (superimposed lines)

Effect of informative censoring in IDU group

Effect of informative censoring in homosexual men group

Time

Pro

bab

ilit

y of

bei

ng

AID

S-f

ree Selection

bias

AIDS No AIDS

IDU

Homo-sexual men

SOURCE POPULATION

STUDY SAMPLE

Cohort Study of HIV Risk Group and AIDS Progression: Depiction of Selection Bias

Selection bias will lead to spurious underestimation of AIDS incidence in both exposure groups, more so in IDU group

Explanation: Sick subjects stopped coming

(Study design is fine)

Effect of losses to follow-up in a cohort study

Bisson, PLoSOne, 2008

Naively Ignoring Losses

Tracking Down Vital Status on Losses

Determinants of survival after initiation

of antiretroviral therapy in Africa

1.0 1.0

1.0 1.0

1.0 1.0

Selection bias

Selection Bias in a Randomized Clinical Trial

• If randomization is performed correctly, then selection bias on the “front-end” of the study (i.e., differential inclusion of diseased individuals between arms) is not possible (other than by chance)

– even if diseased individuals are unknowingly included, randomization typically ensures that this occurs evenly across treatment groups

Selection Bias in a Clinical Trial

• Losses to follow-up are the big unknown in clinical trials and the major potential cause of selection bias

• e.g., Assume that:– a symptom-causing side effect of a drug is more common in

persons “sick” from the disease under study– occurrence of the side effect is associated with more losses to

follow-up • Then:

– Compared to placebo, drug treatment group would be selectively depleted of the sickest persons (i.e., informative censoring)

– Would make drug treatment group appear better

Effect of Selection Bias in an RCT

Survival assuming no informative censoring and no difference between drug and placebo (superimposed curves)

Effect of informative censoring in drug group

Time

Pro

bab

ilit

y of

non

-d

isea

se

Selection bias

Managing Selection Bias• Prevention and avoidance are critical

– Unlike confounding where there are solutions in the analysis of the data, once the subjects are selected and their follow-up occurs, there are usually no easy fixes for selection bias

• In descriptive studies:– Need random sampling

• In cross-sectional studies:– Strive for high response percentages– Be aware of how exposure in question affects disease survival

• In case-control studies:– Follow the study base principle

• In longitudinal studies (cohorts/RCTs):– Carefully screen for disease at baseline (front end)– Avoid losses to follow-up (back end)– Consider approaches to tracking down the lost