Speaking Notes
PADM 5324
October 20, 2009
Dr. Neubauer

WHERE WE ARE:

-- Please turn in homework 1 assignment if you have it and have not already turned it in.
-- It is apparent that the distinction between COHORT STUDIES and CASE-CONTROL STUDIES is VERY IMPORTANT. 
-- I am still learning with the Chapter 11 material.
-- We are at the place where the material we learned in previous weeks is now being built upon.

CHAPTER 11 MATERIAL

The key question this chapter addresses is, "How do we determine whether a certain disease is associated with a certain exposure?" (page 202)

The quick and easy answer is to calculate the DISEASE RISK IN THE EXPOSED and THE DISEASE RISK IN THE NONEXPOSED.  The resulting numbers are called RISKS or INCIDENCE RATES.

If we know the group of those EXPOSED and the group of those NOT EXPOSED we can calculate the two risks and then EITHER USE DIVISION to create a ratio of the risks or USE SUBSTRACTION to calculate the difference in the risks (incidence rates).  (see page 202)

If the RELATIVE RISK (ratio) = 1 then there is no evidence that the exposure had anything to do with the incidence of the disease.

If the RELATIVE RISK (ratio) is greater than 1 there is evidence that the exposure MAY HAVE caused (or contributed to the cause of) the disease.

If the RELATIVE RISK (RATIO) is less than 1 the exposure MAY HAVE served to help prevent the disease.

The key to understanding THE MESSAGE of this chapter is at the bottom of page 205 and also begins at the bottom of page 208 and the top of 209.

"We have seen that in order to calculate a relative risk, we must have values for the incidence of the disease in the exposed and in the nonexposed, as can be obtained from a cohort study.  In the case-control study, however, we do not know the incipence in the exposed population or the incidence in the nonexposed population because we start with diseased people (cases) and nondiseased people (controls).  Hence, in a case-control study we cannot calculate the relative risk directly.  In this section we shall see how another measure of association, the odds ratio, can be obtained from either a clhort or a case-control study and can be used instead of the relative risk.  We will also see that even though we cannot calculate a relative risk from a case-control study, under many conditions, we can obtain a very good estimate of the relative  risk from a case-control study using the odds ratio."

As shown in Figures 11-6 and 11-7, the odds ratio is a good estimate of the relative risk when a disease is NOT FREQUENT.  However, it is not a good estimate of the relative risk when a disease IS FREQUENT.

http://www.childrens-mercy.org/stats/journal/oddsratio.asp

The writer of the site above gives an example in which the risk ratio is 2.5 and the odds ratio is 9.986 -- in the same study.  Most people would become more alarmed by an odds ratio of 9.986 because it looks so much more serious than the risk ratio of "only" 2.5. 

The following example is based on the numbers used on the web site cited above.

 

Figure 1

 

No Disease

Got Disease

Total

Not exposed to X

308

154

462

Exposed to X

142

709

851

Total

450

863

1,313

Figure 2

 

 

No Disease

Got Disease

Total

Relative Risk

Not exposed to X

308

154

462

0.3333

Exposed to X

142

709

851

0.8331

Total

450

863

1,313

 

Figure 3

So, we started with a cohort of 1,313 people.  We waited a few years to see which ones would expose themselves to some possibly harmful thing and 851 of them did.  The other 462 did not have (report) the exposure.  We waited a few more years (or decades) and observed which people got the disease and which did not, as shown above.

So, we have all the information needed to calculate the RELATIVE RISK, which is sometimes called the  risk ratio.  We can calculate the probability of getting the disease among those who were exposed BECAUSE WE KNOW THE NUMBER OF THOSE EXPOSED WHO DID NOT GET THE DISEASE.  Among those NOT EXPOSED (n=462) the probability of getting the disease was 154/452 = 0.3333. 

Among those EXPOSED (n=851) the probability of getting the disease was 709/851 = 0.8331. 

The relative risk of getting the disease if exposed is 0.8331/0.3333 = 2.5.  There is a 2.5 greater probability of getting the disease if exposed than if not exposed to X.

Now, we can also calculate the ODDS. 

The ODDS RATIO for THOSE EXPOSED was 709/142 = 4.993. 

The ODDS for THOSE NOT EXPOSED was 154/308 = 0.500

So I think the ODDS RATIO for getting the disease was 4.994/0.5 = 9.986. 

Two ways of expressing the same information:

Relative Risk

Odds Ratio

2.5

9.986

In either case, exposure to X appears to cause (or contribute to causing) the disease. 


MAJOR "TAKE AWAYS" from Chapter 11

1)         The key question this chapter addresses is, "How do we determine whether a certain disease is associated with a certain exposure?"

2)         The most intuitive way is to calculate a RELATIVE RISK (ratio).  If the ratio is greater than 1 there is at least some evidence that the exposure causes the disease.

3)         It is not always possible to calculate a relative risk (ratio).  You can calculate it when using the COHORT research design.  You CANNOT calculate it directly when using the CASE-CONTROL research design.

4)         You can calculate an ODDS RATIO using either research design. 

5)         The difference has to do with the values used in the denominator. 

6)         If a disease is NOT FREQUENT then the ODDS RATIO is an accurate estimator of the RELATIVE RISK (ratio).

7)         If a disease IS FREQENT then the ODDS RATIO is NOT AN ACCURATE estimator of the RELATIVE RISK (ratio).

8)         People who don't read this literature frequently may be confused by the use of odds ratios.  The confusion may lead to incorrect interpretations of the reported findings.