Measures of Association Dr.Fatima Alkhaledy M.B.Ch.B,F.I.C.M.S/C.M.

Measures of Association Comparing the frequency of disease between exposed and unexposed Measures of association (effect) There are two types of measures of association Absolute measures Relative measures

Measures of Association Show the strength of the relationship between an exposure and outcome Indicate how more or less likely a group is to develop disease as compared to another group Let’s first define each of these terms. A measure of association is a number. It is the result of a calculation that is performed on data collected from an analytic study. The measure of association shows the strength of the relationship between an exposure and the outcome of interest. A larger number generally indicates a stronger association. This measure of association provides evidence as to whether an exposure may cause disease. To do this, the measure indicates how much more or less likely one group is to develop disease compared to another group. Note that in observational studies, we cannot say for certain that an exposure causes an outcome, since we do not have a controlled experiment. Because we cannot assign “bad” exposures, such as smoking, alcohol use, or poor genetics, we cannot actually conduct controlled trials. Instead, we gather information on what we can observe and design a study that allows us to calculate a measure of association. One of the most commonly used measures of association is the relative risk (also known as the risk ratio, and abbreviated RR). The other common measure of association is the odds ratio, abbreviated OR. We will talk about these in a moment.

Absolute Measures of Association Based on DIFFERENCE between two measures of disease frequency May range from -1 to 1 If value of difference measure=0 then no difference between exposed and unexposed Difference measures are useful for assessing the public health impact of an exposure

Relative Measures of Association Relative measures may range from 0 to infinity Relative measures assess the strength of association between exposure and disease and are useful in identifying risk factors

Data Layouts Typically, epidemiologists organize study data as a 2x2 table Column = Disease or Outcome status (Yes or No) Row = Exposure Status (Yes or No) Study participants assigned to one of the four cells according to their individual exposure and disease state Results used to calculate and compare frequency of disease according to exposure

2 x 2 Tables Used to summarize counts of disease and exposure to calculate measures of association Outcome Exposure Yes No Total a b a + b c d c + d a + c b + d a + b + c + d Whether you will be calculating a relative risk or an odds ratio, the first step in calculating measures of association is to organize data on exposures and outcomes in the population into a 2 x 2 table. Once you have data in a 2x2 table, the calculations for obtaining these measures of association are straightforward. Two-by-two tables are used in epidemiology to summarize the counts of those who have the disease and those who have the exposure. This sets up the numbers we need to do the calculations for measures of association. Along one side of the table is the exposure status, and along the top of the table is the outcome status. On the next slide, we’ll talk about each cell of this table.

2 x 2 Tables a = number exposed with outcome b = number exposed without outcome c = number not exposed with outcome d = number not exposed without outcome Outcome Yes No ****************************** a + b = total number exposed c + d = total number not exposed a + c = total number with outcome b + d = total number without outcome a + b + c + d = total study population (N) Yes No a b c d Exposure Refer to the table at the lower right of this slide as we delineate the counts in each of the cells in a two-by-two table. In cell A are the number of people who are exposed and have the outcome. In cell B are the number of people who are exposed and do not have the outcome. In cell C are the number of people who are not exposed and do have the outcome. In cell D are the number of people who are not exposed and do not have the outcome. There are some other quantities from this table that are important as well: a + b = total number who are exposed c + d = total number who are not exposed a + c = total number who have the outcome b + d = total number who do not have the outcome a + b + c + d = total study population

Diseased Non-diseased Example Diseased Non-diseased 100 900 1900 Exposed 1,000 Unexposed 2,000 200 2,800 3,000 * Assume incidence data over 1 year

Cumulative incidence Cumulative incidence in the exposed = Cumulative incidence in the unexposed =

Diseased Non-diseased Example Diseased Non-diseased 100 900 1900 Exposed 1,000 Unexposed 2,000 200 2,800 3,000 * Assume incidence data over 1 year

Example Cumulative incidence in the exposed = Cumulative incidence in the unexposed =

Interpretation Cumulative incidence in the exposed: -10% of the exposed group developed the disease in the study period Cumulative incidence in the unexposed: -5% of the unexposed group developed the disease in the study period

Risk difference and ratio Risk Ratio (Relative Risk, RR) =

Diseased Non-diseased Example Diseased Non-diseased 100 900 1900 Exposed 1,000 Unexposed 2,000 200 2,800 3,000 * Assume incidence data over 1 year

Example Risk Difference = Risk Ratio =

Interpretation Risk Difference: In a population of 100 exposed people, there would be 5 additional cases of disease than what you would observe if exposure was absent in the study period Risk Ratio: The risk of developing the disease in the exposed group is two times the risk of developing the disease in the unexposed group in the study period

Relative Risk Example a / (a + b) 23 / 33 RR = = = 6.67 Escherichia coli? Pink hamburger Yes No Total 23 10 33 7 60 67 30 70 100 Let’s walk through an example of a relative risk calculation. The exposure in this scenario is pink (undercooked) hamburger. The outcome is infection with the bacteria Escherichia coli, or simply E. coli. The cells in the table are already filled in with the counts from our study. For example, 23 people in the study ate pink hamburger AND were diagnosed with E. coli. To calculate the relative risk, we want to compare the risk in the exposed to the risk in the unexposed. The risk in the exposed is the number who ate pink hamburger and had E. coli, Cell A with a value of 23, divided by the total number Exposed to pink hamburger, which is A+B, or 33. The risk in the unexposed is the number of those who did not have pink hamburger but still had E. coli, which is Cell C with a value of 7, divided by the total number Unexposed to pink hamburger, which is C+D or 67. The calculation is shown below the table, and the answer comes to 6.67. Therefore, we would say that the risk of E. coli infection among those who ate pink hamburger is 6.67 times the risk of E. coli infection in those who did not eat pink hamburger. a / (a + b) 23 / 33 RR = = = 6.67 c / (c + d) 7 / 67

Odds Ratio Used with case-control studies Population at risk is not known (selected participants by disease status) Calculate odds instead of risks a x d OR = b x c Now let’s talk about the other measure of association we mentioned, the odds ratio. The odds ratio is the measure of effect used in case control studies. Remember that in a case-control study, we have selected study participants based on whether or not they had disease, not based on their membership in a population. Therefore, the risk of disease cannot be directly calculated because the population that we draw the case-patients from is not known or defined. Instead, we calculate the odds ratio. The numbers for the odds ratio calculation come from the same type of 2x2 table that we use for the risk ratio. When you set up a 2x2 table like we have demonstrated in this lesson, the odds ratio equals A times D divided by B times C. Let’s walk through an example calculation.

Diseased Non-diseased 2x2 tables Diseased Non-diseased a b c d Exposed a+b Unexposed c+d a+c a+d a+b+c+d = N * Assume incidence data over 1 year

Odds Odds of disease in the exposed = Odds of disease in the unexposed =

Odds Ratio a/b c/d Odds Ratio = = a/b x d/c = a x d / b x c

Diseased Non-diseased Example Diseased Non-diseased 100 900 1900 Exposed 1,000 Unexposed 2,000 200 2,800 3,000

Example Odds of disease in the exposed = Odds of disease in the unexposed =

Example Odds Ratio =

Interpretation Odds Ratio: (OR as an estimate of RR) The risk of developing the disease in the exposed group is 2.11 times the risk of developing the disease in the unexposed group during the study period

Increased Blood Pressure Odds Ratio Example Increased Blood Pressure Caffeine intake “high”? Yes No Total 130 115 245 120 135 255 250 500 Let’s suppose that we want to calculate the measure of an association between the hypothetical outcome of high blood pressure and the exposure of caffeine intake classified as “high”, with both the exposure and outcome having specific criteria that are met. A case-control study is conducted, with the results shown in the table. To calculate the OR, we multiply cell A, which is 130, times cell D, which is 135. When we multiply 130 x 135, we get 17,550. Next we divide 17,550 by the quantity of cell B (120) times cell C (115). When we multiply 120 x 115, we get 13,800. So, 17,550 divided by 13,800 gives an OR of 1.27. From this, we can say that the odds of being exposed to high caffeine levels were 1.27 times higher in those who had high blood pressure than in those who did not have high blood pressure. a x d 130 x 135 OR = = = 1.27 b x c 115 x 120

Interpreting Risk and Odds Ratios RR or OR < 1 Exposure associated with decreased risk of outcome = 1 No association between exposure and outcome > 1 Exposure associated with increased risk of outcome How do we interpret risk and odds ratios? We use the following general rules, which can also be used to interpret any other type of relative measure: A risk ratio of less than 1.0 means that the exposure is associated with a decreased risk of the outcome, or that the exposure is protective. It is also called a negative association. A risk ratio of 1.0 means that there is no association between the exposure and the outcome. This is also called the null value. A risk ratio of greater than 1.0 means that the exposure is associated with an increased risk of developing the outcome. It is also called a positive association. In our high blood pressure example, the odds ratio was 1.27, which is greater than 1, indicating that the exposure, high caffeine intake, is associated with the outcome, high blood pressure.

Interpretation RR = 5 RR = 0.5 RR = 1 People who were exposed are 5 times more likely to have the outcome when compared with persons who were not exposed RR = 0.5 People who were exposed are half as likely to have the outcome when compared with persons who were not exposed RR = 1 People who were exposed are no more or less likely to have the outcome when compared to persons who were not exposed Here are a few example interpretations: If the relative risk = 5 People who were exposed are 5 times more likely to have the outcome when compared with persons who were not exposed If the relative risk = 0.5 People who were exposed are half as likely to have the outcome when compared with persons who were not exposed If the relative risk = 1 People who were exposed are no more or less likely to have the outcome when compared to persons who were not exposed

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