Patricia Cohen, Ph.D.

Henian Chen, M.D., Ph. D.

Teaching Assistants

Julie Kranick Sylvia TaylorChelsea Morroni Judith Weissman

Applied Epidemiologic Analysis

Outline Lecture 2

1) Measures of effect/measures of association

2) Review of Study Design

3) Introduction to Data Handling

Learning Objectives

• To understand the relationship between and among absolute and relative measures.

• To understand the relationship between measures of effect and measures of association

• To understand some of the features of measures of effect including effect measure modification and noncollapsibility

Measures of effect

• Effect– endpoint of a causal mechanism– amount of change in a population disease frequency

caused by a specific factor

• Absolute effects– differences in incidence rates, proportions, prevalences

or incidence times

• Relative effect– ratios of these measures

Causal rate difference

Absolute measures

Causal risk difference

0

0

1

1

T

A

TA

NA

NA 01

Causal Rate Ratio

Causal Risk Ratio

Relative measures

0

1

0

0

1

1

II

TAT

A

0

1

0

1

0

1

RR

AA

NAN

A

Relationship between Ratio Measures

0 0

1 1

0

1

0

1

0

1

TI

TI

A

A

N R

N R

R

R

Risk Ratio

because R = A/N and I=A/T

Risk Ratio = Rate Ratio * Ratio of Persontime

0

0

1

1

SRS

R

0

0

1

1

1

1

RR

RR

= =

=

0

0

1

1

ANA

ANA

Odds Ratio

NA

NA

NA

NA

0

0

1

1

1

1

Scenarios when relative measures approximate relative risk

Time period sufficiently small that average T for exposed population is only slightly smaller than T for unexposed

–means T1 and T0 are approximately equal and rate ratio approximates risk ratio

0

0

1

1

0

1

00

11

0

1

SRS

R

I

I

TI

TI

R

R

Sufficiently small proportion of onsets– means R1 and R0 are small, S1 and S0 are close to 1 (odds ratio

approximates risk ratio)

Odds Ratio will overestimate the risk ratio

Scenario 1 where factor increases risk R1 > R0

0011 11 SRRS

11

0 SS

0

0

1

1

10

01

0

11

SRS

R

SR

SR

RR

Scenario 2 where factor decreases risk R1 < R0

0011 11 SRRS

11

0 S

S

0

0

1

1

10

01

0

11

SRS

R

SR

SR

RR

Odds Ratio will underestimate the risk ratio

Scenario 1 where factor increases risk

Rate Ratio with respect to Risk Ratio

01 TT

10

1 TT

0

1

00

11

0

1

0

1

0

11II

TITI

AA

NAN

A

RR

The risk ratio will be closer to null than the rate ratio.

If R1 > R0 then

Scenario 2 where factor decreases risk

Rate Ratio with respect to Risk Ratio

10

1 TT

0

1

00

11

0

1

0

1

0

11II

TITI

AA

NAN

A

RR

The risk ratio will be closer to null than the rate ratio.

If R1 < R0 then

10

1 TT

Magnitude of effect ratios

• If exposure increases disease:

1.0 < Risk ratio < Rate ratio < Odds ratio

• If exposure prevents disease:

1.0 > Risk ratio > Rate ratio > Odds ratio

Because, given equal N, disease occurance shortens cumulative time of exposed subjects.

Cohort dataCases Noncases Total

Exposed 200 99,800 100,000Unexposed 100 99,900 100,000

Risk ratio = (200/100,000)/(100/100,000) = 2.0

Case-controlCases Noncases Total

Exposed 200 99.8 299.8Unexposed 100 99.9 199.9

Odds ratio = (200*99.9)/(100*99.8) = 2.0

Rate = ln (1.0-risk)/time assume time = 1 yearRate (unexposed) = .001Rate (exposed) = .002Rate ratio = 2.0

Example 1: Rare disease

Case-controlCases Noncases Total

Exposed 40,000 60 40,060Unexposed 20,000 80 20,080

Risk ratio = (40,000*80)/(20,000*60) = 2.67

Cohort dataCases Noncases Total

Exposed 40,000 60,000 100,000Unexposed 20,000 80,000 100,000

Risk ratio = (40,000/100,000)/(20,000/100,000) = 2.0

Rate = ln (1.0-risk)/time assume time = 1 yearRate (unexposed) = .22Rate (exposed) = .51Rate ratio = 2.29

Example 2: Non-rare disease

Effect measure modification

If exposure has any effect on an occurrence measure, at most one of the ratio or difference measures of effect can be uniform across strata

Two Examples: Effect Measure Modification

Example 1

Here you see that the risk ratio is constant but therisk difference varies by strata.

Strata 1 Strata 2

Exposed .2 .3

Unexposed .1 .15

Risk Ratio 2 2

Risk difference

.1 .15

Two Examples: Effect Measure Modification

Example 2

Risk Ratio 2 1.67

Risk difference

.1 .1

Strata 1 Strata 2

Exposed .2 .25

Unexposed .1 .15

Here you see that the risk ratio varies by stratabut the risk difference remains constant.

Relation of Stratum-specific measures to overall

• Risk differences and ratio– entire cohort measure must fall in the midst of stratum

specific measures

• Causal odds ratio and rate ratio– entire cohort measure can be closer to null than any of

the causal odds ratios for the strata

•noncollapsibility of the causal odds ratio

•odds ratio not a weighted average

Men Women

% of population 50% 50%

Risk (exposed) .5 .08

Risk (unexposed) .2 .02

Odds ratio 4

(.5/.5)/(.2/.8) 4.3

(.08/.92)/(.02/.98)

Risk ratio 2.5 4

CombinedRisk (exp) = .5*.5 + .5*.08 = .29

Risk (unexp) = .5*.2 +.5*02 = .11

Example of Non-collapsability

Odds ratio = (.29/71)/(.11/89) = 3.3

Risk ratio = .29/.11 = 2.6

– Non-collapsibility can also occur for rate ratio– Only a problem if the outcome is common in a

particular strata

Combining Strata for Rate Ratios

Causation and Causal Attributable Fraction

Assume 2 sufficient causes

Without exposure, can get disease only through C’.

If exposed, can get disease through either sufficient cause (whichever acts first).

Rate difference (I1- I0) does not necessarily equal the proportion of onsets attributable to exposure.

C’EC

Excess fraction:

RRRR

A

AA 1

1

01

Causation and Causal Attributable Fraction

Preventable fraction:

RRA

AA 1

0

10

Generalizing Exposure in Definition of Effect

A sample of three people smoke one pack of cigarettes daily at the start of a 5 year period.

What is the effect of different patterns of mailing anti-smoking literature to them?

Generalizing Exposure in Definition of Effect

Person Pattern 0 A0 T0 Pattern 1 A1 T1

1

Quarterly Dies at year 4 of lung cancer

1 4 No mailing Same

1 4

2

Yearly Dies at year 1 of heart attack

1 1 Yearly Same 1 1

3

No mailing Dies of stroke at year 1

1 3

Quarterly Quits smoking and survives all 5 years

0 5

3 8 2 10

I 3/8 yr-1 3/10 yr-1

R 3/3 =1 2/3 = .67

Causal rate difference 3/8 yr-1 - 2/10 yr-1= .175

Causal rate ratio (3/8)/(2/10) = 1.875

Causal risk difference 1-2/3 = 1/3 = .33

Causal risk ratio 1/(2/3) = 1.5

Example cont.

Key points:Even though same overall portion of the sample are exposed to the three types of mailing in the two patterns,

• effects on I are not same as effect on R

• not all individuals respond alike to exposures or

treatments

Therefore• effects are defined for populations, not

individuals.• Individual characteristics affecting exposure

response are used to stratify analyses

Measures of Association

Given separate exposed and unexposed populations:

Confounding is defined by observed rate differences not equal to the causal rate difference.

– true for ratio measures, average risks, incidence times, or prevalences

– odds are risk-based measures, odds ratios are confounded under same circumstances as risk ratio

A Counterfactual Approach to Causal Reasoning

• Considers the experience of an exposed cohort if, contrary to fact, was unexposed

• and/or the experience of an unexposed cohort if, contrary to fact, was exposed.

Disease under   Proportion in

ExposureNo

exposureDescription

Cohort 1(exposed)

Cohort 0(unexposed)

D D Doomed(other causes sufficient)

p1 q1

D 0 Exposure is causal p2 q2

0 DExposure is preventive

p3 q3

0 0 Immune p4 q4

Sum 1.0 1.0

)()(

)()(

ratio Odds Causal

)()(

differencerisk Causal

42

31

43

21

323121

pppp

pppp

pppppp

Note: null value no effect, unless no preventiveeffect is possible, rather null means balancebetween causal and preventive effects

If Cohort 1 represented the population:

)()(

)()(

observed ratio Odds

42

31

43

21

qqqq

pppp

Associational measure = causal counterparts if andonly if q1 + q3 = p1 + p3

Confounder explains a discrepancy between the desired(but unobservable) counterfactual risk or rate and theunexposed risk or rate that was its substitute

In an actual study:

A Counterfactual Approach to Causal Reasoning, cont.

Consider the effect of child abuse on young adult depression:

Counterfactual:

a) abused children had not been abused

b) not abused children had been abused

What are barriers to assuming observed association

Is causal?

Types of Epi Studies

• Experimental

• Non-experimental

• The ideal design, where only one factor varies, is unrealistic (because of biologic variation).

• Settle for amount of variation in key factors that might affect outcome small in comparison to the variation of the key factor under study

Experimental Studies

• Classifications– Clinical treatment or prevention trials

• patients as subjects– Field trial

• non-patient subjects– Community intervention trials

• interventions assigned to the whole community

• Characteristics– Investigator assigns exposure based only on study

protocol, not needs of patient

– ethical only when adherence to protocol does not conflict with subject’s best interest

– all treatment alternatives should be equally

acceptable under present knowledge

Non-experimental studies

• Cohort– classified (& possibly selected on) exposure– direct analog of the experiment but investigator does

not assign exposure

• Case-control– can be more efficient (sample on outcome)– introduces avenues for bias not present in cohort

studies– the critical issue is defining a source population

Non-experimental studies (cont)

• Control group

– main purpose is to determine relative (not absolute) size of exposed and unexposed denominators within the source population

– to do so, controls must be sampled independently of exposure status: do not select on exposure or potential confounders

• Use of prospective & retrospective– use these terms for timing of the disease

occurrence with respect to exposure measurement

– in cohort studies, usually involves follow-up for disease occurance

– in case-control studies, prospective exposures are usually measured via pre-existing records

Non-experimental studies (cont)

Non-experimental studies (cont)

• Cross-sectional

– can classify under case-control

– main problem is with assessing sequencing and timing

– consequently, emphasis is often on prevalence

– but, current exposure may be too recent to be etiologically relevant

• Proportional Mortality Rate – best to think of as a type of case-control study

– main problem is that cannot distinguish whether exposure causes the index causes of death or prevents the reference causes of death

– cannot distinguish between the extent to which exposure causes disease or worsens prognosis

Non-experimental studies (cont)

Introduction to Data Handling

1) Collection

2) Coding

3) Entry

4) Repeat entry

5) Checking & Editing (logic checks, outliers, fix where possible)

6) Reduction (creation of global variables)

7) Analysis

Types of variables

• Quantitative– e.g., height, weight, body mass index, age

• Qualitative– e.g., gender, race, ICD codes, case/control status,

smoker/non-smoker status

• Ordinal– age in discrete years, low/medium/high consumption

Data coding

1) Make enough categories to avoid non-responses

2) Code all responses (even for don’t know or refusal or not applicable responses)

3) Avoid open-ended questions

4) Record exact values rather than categories

5) Record exact date (of birth, death, diagnosis) rather than ages

Data editing

1) Check for illegal or unusual values for each variable

2) Check codes for unknown or missing values

3) Check distribution of variables

- expected proportion of subjects in each category

- check ranges of values

4) Check consistency of variable distribution (e.g., whether nonsmokers have recorded values for the number of cigarettes per day of duration of smoking etc.)

Learning Objectives

• To understand the relationship between and among absolute and relative measures.

• To understand the relationship between measures of effect and measures of association

• To understand some of the features of measures of effect including effect measure modification and noncollapsibility