Measuring Association in Case-Control Studies

T. Dhasaratharaman*

Statistician, Kauvery Hospitals, India

The cohort studies or clinical trials in which we compared either cumulative incidence ada-reference or incidence rates among two or more exposure groups. However, in a true case-control study we don’t measure and compare incidence. There is no “follow-up” period in case-control studies.

Variables	Diseased	Non-diseased	Total
Exposed	7	1,000	1,007
Non-exposed	6	5,634	5,640

This view of the population is hypothetical because it shows us the exposure status of all subjects in the population. We therefore know the total number of exposed and non-exposed people (in the “Total” column). If we know all this, we could compute the incidence in each group (the incidence in the exposed individuals would be 7/1007 = 0.70%, and the incidence in the non-exposed individuals would be 6/5640 = 0.11%), and we could compute the risk ratio (RR = 6.53). All of our computations involved the “Diseased” column and the “Total” column.

Another way of looking at this association is to consider that the “Diseased” column tells us the relative exposure status in people who developed the outcome (7/6 = 1.16667), and the “Total” column tells us the relative exposure status of the entire source population (1007/5640 = 0.1785). The ratio of these two distributions (7/6)/(1007/5640) = 6.53, because it is just an algebraic rearrangement of the same four numbers we used to compute the cumulative incidences and the risk ratio. Note also that the relative exposure distribution in the “Total” population is very similar the relative exposure distribution in the “Non-diseased” portion of the source population, because the disease is rare. Consequently, in order to estimate the risk ratio we could use the relative distribution of exposure in the “Non-diseased” subjects – OR, to be more efficient, we could just take a sample of non-diseased subjects in order to estimate their exposure distribution. We could for example, just sample 1% of the non-diseased people and I then determine their exposure status. The data might look something like this:

Variables	Diseased	Non-diseased	Total
Exposed	7	10	unknown
Non-exposed	6	56	unknown

The Odds Ratio

The relative exposure distributions (7/6) and (10/56) are really odds, i.e. the odds of exposure among cases and non-diseased controls. If we compute the ratio of these two odds we would get:

ada-reference

i.e., almost identical to the risk ratio we calculated when we had all the information for the source group. Note that we would get the same answer if we computed the odds ratio by dividing the odds of disease in the exposed (7/10) by the the odds of disease in the non-exposed group (6/56).

ada-reference

because this expression is just an algebraic rearrangement of the previous equation.

Mr. T. Dhasaratharaman

Statistician

Kauverian Bookshelf

Applied Medical Statistics

Measuring Association in Case-Control Studies

Measuring Association in Case-Control Studies

Kauverian Bookshelf

Journals