Epidemiology quiz

Measures of Association, Part 1

David D. Celentano, ScD, MHS Johns Hopkins University

2

Learning Objectives

► Describe the importance of making comparisons to determine associations

► Calculate and interpret measures of association ► Risk difference (cohort studies) ► Relative risk (cohort studies) ► Odds ratio (case-control studies)

The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.

Making Comparisons in Case-Control Studies

4

Is an Exposure Associated with an Outcome?

► For example, is cigarette smoking associated with the risk of lung cancer?

5

What Is an Association?

► Association: A relationship between an exposure and a disease ► Not necessarily a causal relationship

► We measure associations when we hypothesize that an exposure temporally precedes the disease, and thus could be a cause of the disease

► Associations can be measured as… ► Relative risk ► Risk difference ► Odds ratio

6

Which Groups Are Compared in Case-Control Studies?

► Try to capture history of exposure before the development of disease (in the past)

Cases Controls

7

Relative Measures of Association

► Relative risk ► Calculated in cohort studies ► Cannot be calculated in a case-control study, because risks cannot be calculated

► Odds ratio ● Calculated in case-control studies ● Can be calculated in cohort studies, but rarely done

8

Let’s Talk about “Odds”

► Traditionally used in horse racing betting

► See hypothetical example from Gordis, 5th edition ► Say that the expected probability that a horse will win the race is 60%

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 = 60% 1 −60%

= 60% 40%

= 1.5

► (or 3:2, as usually expressed at the racetrack)

9

What Is the Odds of Exposure?

► The odds of exposure is the proportion exposed divided by the proportion not exposed

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 = 𝑃𝑃 1 −𝑃𝑃

► 𝑃𝑃 = the proportion with the exposure

10

Odds of Exposure in Cases

► 𝑶𝑶𝑶𝑶𝑶𝑶𝑶𝑶 = 𝑷𝑷 𝟏𝟏 −𝑷𝑷

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑪𝑪𝑪𝑪𝑶𝑶𝑪𝑪𝑶𝑶 = 𝑎𝑎

𝑎𝑎 + 𝑐𝑐

1 − 𝑎𝑎 𝑎𝑎 + 𝑐𝑐

= 𝑎𝑎

𝑎𝑎 + 𝑐𝑐 𝑐𝑐

𝑎𝑎 + 𝑐𝑐 = 𝑪𝑪

𝒄𝒄

11

Odds of Exposure in Controls

► 𝑶𝑶𝑶𝑶𝑶𝑶𝑶𝑶 = 𝑷𝑷 𝟏𝟏 −𝑷𝑷

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑶𝑶 = 𝑏𝑏

𝑏𝑏 + 𝑑𝑑

1 − 𝑏𝑏 𝑏𝑏 + 𝑑𝑑

= 𝑏𝑏

𝑏𝑏 + 𝑑𝑑 𝑑𝑑

𝑏𝑏 + 𝑑𝑑

= 𝒃𝒃 𝑶𝑶

12

Odds Ratio in a Case-Control Study

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑎𝑎𝑂𝑂𝑒𝑒𝑂𝑂 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝑜𝑜𝐶𝐶𝑂𝑂

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑎𝑎 𝑐𝑐 𝑏𝑏 𝑑𝑑

= 𝑎𝑎 × 𝑂𝑂 𝑏𝑏 × 𝑐𝑐

(turns out same in a cohort study)

13

Important Fact about the Odds Ratio—1

► The simple calculation of the odds ratio (OR) is the same in a cohort study and a case- control study

14

Important Fact about the Odds Ratio—2

► This fact means that a case-control study may provide similar insight into an association as a cohort study ► Further, under some conditions, the OR calculated in a case-control study may be a

reasonable estimate of the RR that would have been calculated in a cohort study

15

Use the Convenient OR Calculation—1

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑎𝑎𝑂𝑂𝑒𝑒𝑂𝑂 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝑜𝑜𝐶𝐶𝑂𝑂

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑎𝑎 × 𝑂𝑂 𝑏𝑏 × 𝑐𝑐

16

Interpreting the Odds Ratio

► > 1 ► Odds of exposure in those with the disease > odds of

exposure in those without the disease (positive association)

► = 1 ► Odds of exposure in those with the disease = odds of

exposure in those without the disease (no association)

► < 1 ► Odds of exposure in those with the disease < odds of

exposure in those without the disease (inverse association)

17

Use the Convenient OR Calculation—2

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑎𝑎𝑂𝑂𝑒𝑒𝑂𝑂 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝑎𝑎 ℎ𝑖𝑖𝑂𝑂𝑖𝑖𝑜𝑜𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑂𝑂𝑒𝑒𝑖𝑖𝑒𝑒 𝑖𝑖𝑖𝑖 𝑖𝑖ℎ𝑒𝑒 𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝑜𝑜𝐶𝐶𝑂𝑂

► 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑖𝑖𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 𝑎𝑎 × 𝑂𝑂 𝑏𝑏 × 𝑐𝑐

= 100 × 475 25 × 400

= 4.75

18

Interpretation of the Odds Ratio

► 𝑂𝑂𝑂𝑂 = 𝑎𝑎 × 𝑂𝑂 𝑏𝑏 × 𝑐𝑐

= 100 × 475 25 × 400

= 4.75

► The odds of exposure is 4.75-times higher in the cases compared with the controls

► Because the exposure odds = disease odds, can also say… ► The odds of disease is 4.75-times higher in the exposed compared with the non-

exposed

19

Summary

► Described the importance of making comparisons to determine associations

► Learned how to calculate and interpret measures of association ► Risk difference (cohort studies) ► Relative risk (cohort studies) ► Odds ratio (case-control studies)

The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.

Making Comparisons in Cohort Studies

2

Which Groups Are Compared in Cohort Studies to Estimate Associations?

Cohort study

3

Calculate Risk of Disease in the Exposed and Not Exposed Groups

Cohort study

Calculate risk of disease in those who are exposed

Calculate risk of disease in those who are not exposed

4

Compare Risk of Disease between Groups

► In cohort studies, how do we determine if an exposure is associated with a disease? ► We compare the risk of disease between the exposed group and a comparison group

► The purpose of selecting a comparison group is to obtain an estimate of the risk the exposed group would have had, had they not had been exposed ► In other words, the background risk

5

Risks in the Exposed and Non-exposed

6

Non-exposed Group Provides an Estimate of Background Risk

*Select the comparison group to be similar to the exposed group on all factors other than exposure so that we can assume that the background risk in the non-exposed is the risk the exposed would have had if they had not been exposed

7

Misunderstanding of Background Risk?

“Women need to understand that just because they don’t have a family history, that doesn’t mean they’re not at risk.”

Source: Baltimore Sun. (2007, October 1).

8

Misunderstanding of Background Risk

“Women need to understand that just because they don’t have a family history, that doesn’t mean they’re not at risk.”

Excess risk of breast cancer in women with a family history of breast cancer due to their family history

“I don’t have a family history of breast cancer, so I am not at risk for breast cancer”

9

Correct Interpretation of Background Risk

“Women need to understand that just because they don’t have a family history, that doesn’t mean they’re not at risk.”

Excess risk of breast cancer in women with a family history of breast cancer due to their family history Risk of breast cancer

in women without a family history

10

October Is Breast Cancer Awareness Month

Source: C101. Accessed November 13, 2018, at http://cancer101.org/where-do-i-start/navigating-cancer/

► Female breast cancer ► US, 2016

● 246,000 new cases ● 40,450 deaths

► Global, 2012 ► 1.7 million new cases ► 521,900 deaths

Source: American Cancer Society. Accessed November 13, 2018, at http://www.cancer.org/research/cancerfactsstatistics/cancerfactsfigures2016/

11

Who Is the Comparison in a Cohort Study?

► The non-exposed group ► E.g., nonsmokers (for smokers)

► If everyone is exposed, then the group with the lowest level of exposure ► E.g., low vitamin D intake (for high

vitamin D intake)

► The group that has the normal clinical exposure status in a population ► E.g., normal serum cholesterol

concentration (for elevated serum cholesterol)

The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.

Risk Difference and Relative Risk

2

Comparing Risks between Groups

► In cohort studies, how do we determine if an exposure is associated with a disease? ► We compare the risk of disease between the exposed group and a comparison group

► We’ve identified the exposed and comparison groups

► Next, we make comparisons between the two groups in their risks or rates ► By calculating measures of association

● Difference ● Ratio

3

Measures of Disease Frequency: Risks

► If all people at risk in the population are observed for the full time period…

► Cumulative incidence = risk

4

Measures of Disease Frequency: Rates

► If people at risk in the population are observed for different lengths of time…

► Incidence rate = rate

5

Calculating Measures of Association—Risks

1. Difference in risks ► (Risk in exposed) – (Risk in non-exposed)

2. Ratio of risks ► (Risk in exposed) / (Risk in non-exposed)

► Incidence or mortality

6

Calculating Measures of Association—Rates

1. Difference in rates ► (Rate in exposed) – (Rate in non-exposed)

2. Ratio of rates ► (Rate in exposed) / (Rate in non-exposed)

► Incidence or mortality

7

Interpreting the Risk (or Rate) Difference

► > 0 ► Risk in exposed > risk in non-exposed ► Exposure may increase risk (excess risk)

► = 0 ► Risk in exposed = risk in non-exposed ► Exposure does not affect risk (no excess risk)

► < 0 ► Risk in exposed < risk in non-exposed ► Exposure may decrease risk (reduced risk)

8

Interpreting the Relative Risk or Risk Ratio (or Rate Ratio)

► > 1 ► Risk in exposed > risk in non-exposed ► Exposure may increase risk (positive association)

► = 1 ► Risk in exposed = risk in non-exposed ► Exposure does not affect risk (no association)

► < 1 ► Risk in exposed < risk in non-exposed ► Exposure may reduce risk (inverse association)

9

Interpreting the Relative Risk

► The direction of the association provides information on the nature of the influence of the exposure on the disease ► Positive (RR>1) vs. inverse (RR<1)

► The magnitude of the association provides information about the strength of the relationship between an exposure and disease ► Big RR, strong association ► Small RR, weak association

10

Naming Measures of Association

1. Difference in risks (rates) ► Risk difference (rate difference) ► Attributable risk

2. Ratio of risks (rates) ► Relative risk ► Risk ratio (rate ratio)

11

A 2x2 Table Is Helpful for Calculating Measures of Association: Comparing Risks—Closed Cohort Study

► Risk difference = [a / (a + b)] – [c / (c + d)] ► (Specify the time period)

► Risk ratio = [a / (a + b)] / [c / (c + d)]

12

A 2x2 Table Is Helpful for Calculating Measures of Association: Comparing Risks—Closed Cohort Study with 1-Year Follow-up Period ► Risk difference = [100 / 1000] – [50 / 1000] = 50 / 1000 people

over 1 year ► Risk ratio = [100 / 1000] / [50 / 1000] = 2

13

Interpretation—Comparing Risks

► Risk difference = [100 / 1000] – [50 / 1000] = 50 / 1000 people over 1 year ► The excess risk of disease in the exposed compared with the non-exposed is 50 / 1000

persons over 1 year

► Risk ratio = [100 / 1000] / [50 / 1000] = 2 ► Risk of disease is 2-times higher in the exposed compared with the non-exposed ► The exposed have twice the risk of disease than the non-exposed

14

A 2x2 Table Is Helpful for Calculating Measures of Association: Comparing Rates—1

► Rate difference = [a / PYE] – [c / PYNotE]

► Rate ratio = [a / PYE] / [c / PYNotE]

15

A 2x2 Table Is Helpful for Calculating Measures of Association: Comparing Rates—2

► Rate difference = [50 / 5000] – [25 / 10,000] = 75 / 10,000 PY

► Rate ratio = [50 / 5000] / [25 / 10,000] = 4

16

Interpretation—Comparing Rates

► Rate difference = [50 / 5000] − [25 / 10,000] = 75 / 10,000 PY ► The excess rate of disease in the exposed compared with the non-exposed is 75 /

10,000 person-years

► Rate ratio = [50 / 5000] / [25 / 10,000] = 4 ► The rate of disease is 4-times higher in the exposed compared with the non-exposed ► The exposed have 4-times the rate of disease than the non-exposed

17

What Do Tables Look Like in Published Papers?—1

Source: Platz, Drake, Wilson et al. (2015). Asthma and risk of lethal prostate cancer in the Health Professionals Follow-Up Study. Int J Cancer, 137(4), 949–958. http://dx.doi.org/10.1002/ijc.29463

18

What Do Tables Look Like in Published Papers?—2

19

Difference vs. Relative Measures of Association—1

► When should the difference versus relative measures of association be calculated? ► Risk difference

● Describes the public health impact of exposure ● Use for public health planning, including prioritizing interventions

► Relative risk ● Use for establishing etiologic relationships ● Stronger associations imply greater contributions to the etiology of the outcome

20

Difference vs. Relative Measures of Association—2

► A major foundation has funds to support an intervention to reduce childhood mortality in one country. Which country should they pick?

► Country 1 ► Problem: Exposure A ► Prevalence of exposure:

A = 0.1 ► Number of children:

20,000 ► RateA = 5 / 100 PY ► Ratenot A = 1 / 100 PY ► RR = 5 ► RD = 4 / 100 PY

► Country 2 ► Problem: Exposure B ► Prevalence of exposure:

B = 0.1 ► Number of children:

20,000 ► RateB = 50 / 100 PY ► Ratenot B = 10 / 100 PY ► RR = 5 ► RD = 40 / 100 PY

► Fund the intervention on Exposure B in Country 2 to save the most children

21

What Does the 2x2 Table Look Like for More Than Two Groups?

Recall Activity 2, Measuring Disease Frequency

22

Interpreting Measures of Association: Excess Risk

► Measures of association provide information about excess risk ► Risk difference—how much higher (or lower) is the risk in one group than the

comparison group ● Difference conveys the excess (or reduced) risk

► Relative risk—how many times greater (or lower) is the risk in one group than in the comparison group ● Times higher (or lower) conveys excess (or reduced) risk

23

Excess Risk

24

Excess Risk and Disease Prevention

► Excess risk in exposed group when compared with the comparison group tells us about the opportunity for prevention ► How much of the risk could have been avoided if the exposed had not been exposed?

● This interpretation is why the risk difference is often called the attributable risk ● Lots of assumptions are required to draw this interpretation, including that the

association is causal

25

Difference: Excess Risk = Attributable Risk

► Risk difference = Risk of disease in the exposed minus risk of disease in the

non-exposed = Excess risk of disease in the exposed due to their exposure = Attributable risk

26

Attributable Risk

Measure Annual risk

Risk in exposed = 25 / 100 persons

Risk in non-exposed = 10 / 100 persons

Risk difference = 15 / 100 persons

► The excess risk of disease in the exposed due to their exposure is 15 / 100 persons per year

► The risk of disease attributable to the exposure in the exposed is 15 / 100 persons per year

► The risk of disease that potentially could be prevented in the exposed if they were not exposed is 15 / 100 persons per year

27

Attributable Risk Percent

► Proportion of the disease risk in the exposed that potentially could be prevented in the exposed if they were not exposed…

= 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑖𝑖 𝑡𝑡𝑡𝑡𝑡 𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑅𝑅𝑡𝑡𝑒𝑒 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑖𝑖 𝑡𝑡𝑡𝑡𝑡 𝑖𝑖𝑒𝑒𝑖𝑖𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑅𝑅𝑡𝑡𝑒𝑒

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑖𝑖 𝑡𝑡𝑡𝑡𝑡 𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑅𝑅𝑡𝑡𝑒𝑒

► When multiplied by 100, attributable risk percent (AR%)

28

Attributable Risk Percent Interpretation

Measure Annual risk

Risk in exposed persons = 25 / 100 persons

Risk in non-exposed persons = 10 / 100 persons

► Attributable risk percent…

► = 𝟐𝟐𝟐𝟐∕𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟏𝟏𝟏𝟏∕𝟏𝟏𝟏𝟏𝟏𝟏 𝟐𝟐𝟐𝟐∕𝟏𝟏𝟏𝟏𝟏𝟏

► = 0.6

► = 60%

► 60% of the disease risk in the exposed is potentially preventable in the exposed if they were not exposed. This assumes the association is causal!