FDMAT 222



FDMAT 222

Odds Ratio and Relative Risk Module

Learning Model Principles

Learners and teachers at BYU–Idaho. . .

1. Exercise faith in the Lord Jesus Christ as a principle of action and power

2. Understand that true teaching is done by and with the Holy Ghost

3. Lay hold upon the word of God as found in the holy scriptures and in the words of the Prophets in all disciplines

4. Act for themselves and accept responsibility for learning and teaching

5. Love, serve, and teach one another

Data file

Download the following file:

Risk and Odds Ratio.xls

You will use the file as part of this module.

Prepare

Risk and Odds

Before getting into relative risk and odds ratios, let’s first tie it in to what have covered earlier in this class on probability and introduce the concepts of risks and odds.

Risk corresponds to the probability of an undesirable event such as death, disease, or side effects. The risk of a given adverse event, like the probability, is defined by the frequency of that adverse event in a population or sample of interest. For instance, in Dr. Jonas Salk’s experiment on his polio vaccination in the 1950’s, 200,000 children were given the vaccination and 33 children still got the Polio disease even with the vaccination. Then, the risk of children getting polio even with the vaccination is 33/200,000 or 0.000165.

Odds, on the other hand, are ratios of two probabilities where the numerator represents the probability of an event occurring and the denominator represents the probability of the event not occurring. Each probability can be obtained from the frequency of the event in a population or sample of interest. For instance, if you did a study on HIV patients to determine the odds of a HIV patient being an IV drug user. You sampled 50 HIV patients and found that 32 were IV drug users. The odds of finding an HIV patient that is an IV drug user would be the probability of that happening (32/50 = 0.64) divided by probability of the event not happening (18/50 = 0.36). So the odds would be 0.64/0.36 = 1.778. Another way to calculate the odds is by merely taking the number of HIV patients who are IV drug users in the sample divided by the number of HIV patients who are not drug users (32/18 = 1.778)

Relative Risk

Both observational and experimental studies, particularly in the health sciences, typically compare a sample from a population of interest with another sample from a population of interest, usually from a control population. The comparison is represented by either a relative risk or an odds ratio.

When comparing two groups, the relative risk is simply the ratio of the two risks with typically the risk of the control group in the denominator. For instance, referring to Dr. Salk’s polio experiment on his polio vaccination in the 1950’s, 200,000 children were given the vaccination and 33 children from that group still got the polio disease. Also, another 200,000 children were given a placebo and 150 children from the group got the polio disease. The relative risk can be calculated by taking the risk or probability of getting the disease in the vaccination group (33/200,000 = 0.000165) and dividing by the risk or probability of getting the disease in the control group (150/200,000 = 0.007500). The relative risk of getting polio with the vaccination compared to the placebo would be (0.000165/0.007500 = 0.22). Relative risks are typically used in randomized control experiments or prospective cohort studies.

What does that relative risk number mean? For this example, if relative risk was greater than 1, then the vaccination group would have a greater percentage of children with polio than the control group. If relative risk was close to or equal to 1, then the vaccination group would have about the same percentage of children with polio than the control group. If relative risk was less than 1, then the vaccination group would have a fewer percentage of children with polio than the control group, which is the case in this example.

Confidence Interval for Relative Risk

Earlier this semester, this class has covered confidence intervals from several different types of statistical procedures (e.g. One Sample t, Matched Paired Samples, Two Independent Samples, One Proportion and Two Proportion). We can also construct a confidence interval for relative risk. However, distributions of ratios (like relative risk) are not normally distributed and the distribution of a sample statistic is assumed to be normally distributed for a confidence interval to work. However, the distribution of the natural log of ratios is normally distributed. So, we will use natural logs to calculate the confidence intervals. To calculate them, however, we will be using an excel program for these confidence intervals (Relative Risk and Odds Ratio.xls).

The main purpose of creating a confidence interval for relative risk is to see if the ratio value 1 is within or outside the confidence interval. If the value 1 is within the confidence interval, then there is no statistical difference in the risks between of the two groups. If the value 1 is outside the confidence interval, then there is a statistical difference in the risks between the two groups.

To show an example of calculating a confidence interval for relative risk, let’s go back to the Dr. Salk’s vaccination experiment in the 1950’s. To create a 95% confidence interval, we will input in the excel program the sample sizes for both groups, the number of children who got polio from both groups, and the level of confidence. The following are the inputs for excel (see print screen below – the inputs are in the red boxes):

X1– The number of children who got polio in the vaccination group (33 children)

N1 – The number of children in the Vaccination group (200,000 children)

X2 - The number of children who got polio in the placebo group (150 children)

N2 – The number of children in the Placebo group (200,000 children)

Level of Confidence – 95% for a 95% confidence interval

[pic]

The 95% confidence interval for the relative risk is (0.1509, 0.3207), which implies that the true RR is significantly different than the value of one and it appears that the children in the vaccination group have significantly much lower risk of getting polio than the placebo group. Note that the risks from both groups and the relative risk are also calculated in this program.

Odds Ratio

Likewise when comparing two groups, the odds ratio is the ratio of the two odds. For instance, you would like to conduct a case control study and determine that you need 50 people with HIV for your study. You also decide to select one control for every case in your study. So your study has 100 people in it and 50 of them have HIV and the other 50 do not. You find that 32 of the 50 people in the HIV group are IV drug users, and 19 of the 50 people in the non-HIV group are IV drug users. The odds ratio for the two groups can be calculated by taking the odds of someone in the HIV group that are IV drug users (32/18 = 1.7778) and dividing by odds of someone in the non-HIV group that are drug users (19/31 = 0.6129). The odds ratio for this analysis would be (1.7778/0.6129 = 2.90). What does this mean? In this study, it means that if you have HIV you are 2.9 times more likely to have been an IV drug user than if you do not have HIV. Odds ratios are typically used in observational and case-control studies.

Confidence Interval for an Odds Ratio

Just like relative risk, we can also construct a confidence interval for odds ratios. Odds ratios are also not normally distributed. However, the distribution of the natural log of ratios is normally distributed. So, we will use natural logs to calculate the confidence intervals. We will again be using an excel program for these confidence intervals (Relative Risk and Odds Ratio.xls).

The main purpose of creating a confidence interval for odds ratios is to see if the odds ratio value one is within or outside the confidence interval. If the value one is within the confidence interval, then there is no statistical difference between the odds of the two groups. If one is outside the confidence interval, then there is a statistical difference between the two odds.

To show an example of calculating a confidence interval for odds ratio, let’s go back to the study looking at the association between HIV and IV drug usage. To create a 95% confidence interval, we will input in the excel program the sample sizes for both groups, the number of people who are IV drug users in each group, and the level of confidence. The following are the inputs for excel (see print screen below – the inputs are in the red boxes):

X1– The number of people in the HIV group who are IV drug users (32 people)

N1 – The number of people in the HIV group (50 people)

X2 - The number of people in the non-HIV group who are IV drug users (19 people)

N2 – The number of people in the non-HIV group (50 people)

Level of Confidence – 95% for a 95% confidence interval

[pic]

The 95% confidence interval for the odds ratio is (1.286, 6.534), which implies that the true odds ratio is significantly different than one and it appears that the people in the HIV group are significantly more likely to be IV drug users than people in the non-HIV group.

Teach One Another

Answer the following questions in your groups:

1) Define Relative Risk. Define what an Odds Ratio is.

2) In what settings do you use relative risk? In what settings do you use odds ratios?

3) How can you know if a relative risk measure or an odds ratio measure is statistically significant?

Do the following:

1) Go through the polio vaccination example with your group. Be sure to calculate the relative risk and the confidence interval of the relative risk. Be able to explain in your group how to interpret the confidence interval of the relative risk.

2) Go through the HIV/IV drug users example with your group. Be sure to calculate the odds ratio and the confidence interval of the odds ratio. Be able to explain in your group how to interpret the confidence interval of the odds ratio.

Ponder/Prove

Relative Risk Problem

The Physicians’ Health Study randomly assigned 22,071 healthy male physicians at least 40 years old to take either an aspirin every other day or a placebo pill every other day. Of the 11,037 physicians who took aspirin regularly for 5 years, 10 had a fatal heart attack. Of the 11,034 who took the placebo, 26 suffered a fatal heart attack [1].

a) What are the proportions (or risks) of physicians who suffered a fatal heart attack in the two groups?

b) Calculate the relative risk and the 95% confidence interval of the relative risk.

c) Interpret the results from problem b.

The Physicians’ Health Study also recorded the number of nonfatal heart attacks in the two groups. Of the 11,037 physicians who took aspirin regularly for 5 years, 129 had a nonfatal heart attack. Of the 11,034 who took the placebo, 213 suffered a nonfatal heart attack [1].

a) What are the proportions (or risks) of physicians who suffered a nonfatal heart attack in the two groups?

b) Calculate the relative risk and the 95% confidence interval of the relative risk.

c) Interpret the results from problem b.

d) Were there any different conclusions when examining fatal vs. non fatal heart attacks in this study?

Odds Ratio Problem

The Woman-to-Woman Study is a 4-year randomized controlled trial designed to evaluate the impact of a work-site based breast and cervical cancer education project. In the study they looked at how many women got a mammogram and whether the women had other characteristics. We are first interested knowing whether women get mammograms more frequently if they go to graduate school rather than just college. Out of 305 women who obtained graduate degrees, 156 of them got a recent mammogram. Out of 198 women who obtained just a college degree, 102 of them got a recent mammogram [2].

a) What are the odds of a woman getting a recent mammogram for both two groups?

b) Calculate the odds ratio and the 95% confidence interval of the odds ratio.

c) Interpret the results from problem b.

d) Does there appear to be a difference in the odds that a woman who attends graduate school will get a mammogram compared to one who does not attend graduate school?

Also in this study, they looked at whether the doctors for each of the women recommended a mammogram. So, we are also interested knowing whether women get mammograms more frequently if their doctors recommend it to them. Out of 1190 women who were recommended by their doctors, 610 of them got a recent mammogram. Out of 140 women who were not recommended by their doctors, 79 of them got a recent mammogram [2].

a) What are the odds of a woman getting a recent mammogram for both two groups?

b) Calculate the odds ratio and the 95% confidence interval of the odds ratio.

c) Interpret the results from problem b.

d) Is there a difference in the odds that a woman will get a mammogram if her doctor recommends it compared to if her doctor does not recommend it?

References

[1] Baldi, B., & Moore, D. (2009). The Practice of Statistics in the Life Sciences (2nd ed.). W. H. Freeman and Company

[2] Allen, J. D., Stoddard, A. M., Sorensen, G. (2008). Do social network characteristics predict mammography screening practices? Health Education and Behavior, 35 (6), 763-776.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download