Measures Used To Compare Groups

Dr. N. Birkett,School of Epidemiology, Public Health and Preventive Medicine,

University of Ottawa

SUMMER COURSE:INTRODUCTION TO

EPIDEMIOLOGY

AUGUST 25, 1330-1500

Session OverviewMethods of comparing studies

• Risk/rate ratios• Odd ratios• Difference measures• Number needed to treat• Attributable risk

ONE BIG WARNING!!!!!The textbook (4th edition) has rotated their 2X2 tables from the normal approach.

That is, they have the outcomes as the rows and the exposure as the columns.

BE WARNED. This could cause confusion with my tables which use the more common approach.

Comparing studies (1)• Two main types of outcome measures

• Incidence (either risk or rate)• Prevalence

• How do you determine if an exposure is related to an outcome?• Study 2 groups• Need to compare the measure in the two groups.

• Differences• Ratios (we’ll start with this one).

Comparing studies (2)• Ratios (we’ll start with this one).

• Ratio measures have NO units.• All ratio measures have the same interpretation

• 1.0 = no effect• < 1.0 protective effect• > 1.0 increased risk

• Values over 2.0 are of strong interest

Comparing studies: Cohorts (3)RISK RATIORisk in exposed = 1,000/10,000Risk in Non-exposed = 100/10,000If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other:

Disease

Exp

Yes No

Yes 1,000 9,000 10,000

No 100 9,900 10,000

1,100 18,900 20,000

Comparing studies: Cohorts (4)RISK RATIORisk in exposed = a/(a+b)Risk in Non-exposed = c/(c+d)

If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other:

Disease

Exp

Yes No

Yes a b a+b

No c d c+d

a+c b+d N

Comparing studies: Cohorts (5)RISK RATIORisk in exposed = 42/122 = 0.344Risk in Non-exposed = 43/345 = 0.125

Death

Apgar

Yes No

0-3 42 80 122

4-6 43 302 345

85 382 467

0-3: Very low4-6: Moderate7-10: Normal

Comparing studies: Cohorts (6)RISK DIFFERENCERisk in exposed = 1,000/10,000Risk in Non-exposed = 100/10,000If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the difference between the two:

Disease

Exp

Yes No

Yes 1,000 9,000 10,000

No 100 9,900 10,000

1,100 18,900 20,000

Comparing studies: Cohorts (7)RISK DIFFERENCERisk in exposed = a/(a+b)Risk in Non-exposed = c/(c+d)

If exposure increases risk, you would expect the risk in the exposed to be larger than risk in the unexposed. How much larger can be assessed by the difference between the two:

Disease

Exp

Yes No

Yes a b a+b

No c d c+d

a+c b+d N

Comparing studies: Cohorts (8)RISK DIFFERENCERisk in exposed = 42/122 = 0.344Risk in Non-exposed = 43/345 = 0.125

Death

Apgar

Yes No

0-3 42 80 122

4-6 43 302 345

85 382 467

Comparing studies: Cohorts (9)Which comparative measure do you use?• Depends on the circumstances.

• Risk Ratio RELATIVE risk measure• Risk Difference ABSOLUTE risk measure

• Post-menopausal estrogens & endometrial cancer• RR = 2.3• RD = 2/10,000

Comparing studies: Cohorts (10)RATE RATIORate in exposed = 1,000/9,500Rate in Non-exposed = 100/9,950

If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other:

Exp

# Diseased

Person-years

Yes 1,000 9,500

No 100 9,950

1,100 19,450

Comparing studies: Cohorts (11)RATE RATIORate in exposed = A/Y1

Rate in Non-exposed = B/Y2

If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other:

Exp

# Diseased

Person-years

Yes A Y1

No B Y2

A+B Y1+Y2

Comparing studies: Cohorts (12)RATE RATIORate in exposed = 42/101 = 0.416Rate in Non-exposed = 43/323.5 = 0.133

Apgar

# Diseased

Person-years

0-3 42 101

4-6 43 323.5

85 424.5

Comparing studies: Cohorts (13)RATE DIFFERENCERate in exposed = 1,000/9,500Rate in Non-exposed = 100/9,950

If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two:

Exp

# Diseased

Person-years

Yes 1,000 9,500

No 100 9,950

1,100 19,450

Comparing studies: Cohorts (14)RATE DIFFERENCERate in exposed = A/Y1

Rate in Non-exposed = B/Y2

If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two:

Exp

# Diseased

Person-years

Yes A Y1

No B Y2

A+B Y1+Y2

Comparing studies: Cohorts (15)RATE DIFFERENCERate in exposed = 42/101 = 0.416Rate in Non-exposed = 43/323.5 = 0.133

Apgar

# Diseased

Person-years

0-3 42 101

4-6 43 323.5

85 424.5

Comparing studies: Cohorts (16)Some Issues• What does RR mean

• Can mean either• risk ratio or • rate ratio.

• Some people think this is pedantic rather than correct • Need to tell which from context.• Sometimes referred to as Relative Risk (generic term).

• Are risk differences or ratios preferred?• RR’s are much more common• Both have a role to play.

Comparing studies: Case-control (1)CAN NOT COMPUTE A RISK RATIO!• Can not estimate incidence from a case-control study.• Can not directly compute risk differences.• Why? We choose the subjects based on their outcome status.

Usually, that means making the number of cases and controls equal. Hence, the ‘incidence’ in the case-control study is fixed at 0.50. In real world, it is most likely much lower (1/100,000).

So, what do we do?• Cornfield & Haenzel provided solution in 1960.

• They looked at the ODDS of exposure.• The ratio of the odds of exposure in the cases and controls is almost the same as the

RR, if the disease is rare.

Comparing studies: Case-control (2)ODDS RATIOOdds of exposure in cases = 900/100Odds of exposure in controls = 400/600If exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for cases would be higher. How much higher can be assessed by the ratio of one to the other:

Disease

Exp

Yes No

Yes 900 400 1,300

No 100 600 700

1,000 1,000 2,000

Comparing studies: Case-control (3)ODDS RATIOOdds of exposure in cases = a/cOdds of exposure in controls = b/dIf exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for case would be higher. How much higher can be assessed by the ratio of one to the other:

Disease

Exp

Yes No

Yes a b a+b

No c d c+d

a+c c+d N

Comparing studies: Case-control (4)Death

Apgar

Yes No

0-3 42 18 60

4-6 43 67 110

85 85 170

NOTE:Risk ratio = 2.76Rate ratio = 3.13

ODDS RATIOOdds of exposure in cases = 42/43 = 0.977Odds of exposure in controls = 18/67 = 0.269

Comparing studies: Case-control (5)Cohort aside:• You can compute an OR for a cohort. Why would you do

so?• OR’s are the key outcome measure for logistic regression, one of

the most common analysis methods used in epidemiology• Unless disease is common, the OR and the RR from the cohort will

be very similar.• But, where possible, rate ratios are preferred.

Number needed to treat (1)Consider a clinical trial of a new drug. How many people do we need to treat to prevent one death?

• Incidence rate for the control group is 2 cases per 5 person years. • Incidence rate for the experimental group is 1 case per 5 person

years.

Number needed to treat (2)• Treat five people for one year:

• Control therapy: 2 deaths• Exp therapy: 1 death• PREVENTED = 1 death

NNT = 5.

• What is the risk difference:• 2/5 – 1/5 = 1/5

Number needed to treat (3)For diseases with rare outcomes, you will need to treat many people to prevent one outcome, even if the reduction in risk is high:

Relative risk reduction = 0.1IR (Old Rx) = 10/1,000IR (New Rx) = 1/1,000RD = 9/1,000NNT = 1000/9

= 111

Attributable risks (1)• How much lung cancer can be attributed to smoking?• Measure of exposure IMPACT rather than strength.• There are many AR measures, often with similar names.

Makes things confusing. One book used the same abbreviation for 4 different measures in five pages!

Attributable risks (2)In exposed subjects

ExpUnexp

RD or Attributable Risk Iexp

Iunexp

Attributable risks (3)• In the exposed group, the impact of the exposure on

outcome depends on RR only:

• A value of ‘0’ shows no impact.• You shouldn’t compute AR’s unless causation has been

established.

Attributable risks (4)However, my actual interest was:

In the general population, how much lung cancer was due to smoking?

Depends on two factors:• Strength of the smoking/lung cancer relationship (RR).• How common smoking is in the population (exposure prevalence).

Attributable risks (5)

ExpUnexp

Attributable Risk,population

Iexp

Iunexp

Population

Ipop

Attributable risks (5)

ExpUnexp

Attributable Risk,population

Iexp

Iunexp

Population

Ipop

Exposure is uncommon

Attributable risks (5)

ExpUnexp

Attributable Risk,population

Iexp

Iunexp

Population

Ipop

Exposure is common

Attributable risks (6)• Risk in the population is a weighted average of

• risk in exposed people• risk in unexposed people.

• The weight is the prevalence of the risk factor in the population:

Attributable risks (6)Formulae for Population Attributable Risk (PAR)• Usually expressed as a %

• The percent reduction in risk in the population if the risk factor could be completely eliminated:

Summary: comparisons• Cohort studies

• Relative risk• Relative rate• Risk/rate differences

• Case-control study• Odds-ratio

• Number needed to treat• Attributable risk/fraction

• Measure of the impact of exposure to exposed people or to general population.