Observational Studies

"The curious associations with lung cancer found in relation to smoking habits do not, in the minds of some of us, lend themselves easily to the simple conclusion that the products of combustion reaching the surface of the bronchus induce, though after a long interval, the development of a cancer." - Ronald Aymler Fisher

R.A. Fisher was, arguably, the most important statistician of the twentieth century yet, according to the above quote, he did not believe that studies had shown that smoking causes lung cancer. Though the link between smoking and lung cancer has now been firmly established, it is instructive to look at how a study would be constructed to test such a relationship and why such studies might not have been convincing to Fisher.

A controlled experiment can be used to establish that a certain treatment causes a specific response. However, to conduct a controlled experiment, a researcher must assign people to receive a treatment. This is not always ethical and is sometimes not even possible. Consider designing a study to look at the relationship between smoking and lung cancer. To implement a controlled experiment, the researcher would have to assign subjects to the treatment group. The treatment in this case is smoking!

It would be difficult to find people who would agree to let a researcher determine whether or not they will smoke (and, if we think smoking does cause lung cancer, it would be highly unethical). People who choose not to smoke are unlikely to take up the habit for the sake of an experiment and those who already smoke would probably be unwilling or even unable to stop for the sake of the investigation. Thus, this relationship must be studied through an observational study. That is, subjects are recruited and their behaviors and characteristics are observed and monitored without direct intervention on the part of the researcher.

In an observational study, a researcher observes individuals and measures variables of interest but does not impose any intervention or treatment.

Observational studies cannot show that change in one variable causes change in the other because the researcher cannot rule out the presence of extraneous variables that confuse the relationship. A variable that influences the response variable but that is not one of the explanatory or response variables is called a lurking variable. When two variables are related in a way that their effects on the response variable are not distinguishable, we say that there is confounding. A counfounding factor is a difference, other than the treatment, between the treatment and control groups that affects the response of interest. A counfounding factor is associated both with the exposure and with the response.

Confounding factor: a difference, other than the treatment, between the treatment and control groups that affects the response of interest.

There are three conditions that must be present for confounding to occur:

The confounding factor must be associated with both the explanatory and the response variables.
The confounding factor must be distributed unequally among the groups being compared.
A confounder cannot be an intermediary step in the causal pathway from the explanatory variable to the response variable.

In order to have a confounding factor, it must be something that could be causing a change in both the explanatory and response variables. In this case, something can only be a confounding factor if it might cause having personal calculators and higher achievement.

One possible confounding factor here could be socioeconomic status. Having a higher socioeconomic status could make a person more likely to have a personal calculator, and having a higher socioeconomic status also often provides opportunity for higher achievement. So, socioeconomic status could confound the relationship between calculator ownership and academic success.

One possible confounding factor is the health of the mother. Mothers who are experiencing certain health problems find it much more difficult -- or sometimes even impossible -- to breastfeed, and so must resort to bottle-feeding. However, mothers experiencing health problems are more likely to give birth to a child with health problems, or her health problems could result in less clean/sterile living conditions, which could contribute to diarrhea in the infant. Since the health of the mother could be affecting the decision to bottle-feed and could affect instances of diarrhea in the infant, it qualifies as a possible confounding factor.

In well-designed observational studies, researchers take steps to avoid confounding. They control for confounding factors by identifying possible lurking variables and making comparisons between subjects that are similar on that variable. For instance, if age or sex confounds the relationship between smoking and lung cancer, then the researchers would compare subjects that are similar in age or that are the same sex.

Researchers control for confounding factors by making comparisons between subjects that are similar for different levels of the factor.