# ESTIMATION

If an epidemiologic study is thought of as an exercise in measurement, the result of the study should be an estimate of an epidemiologic quantity. Ideally, the analysis of data and the reporting of results should report the magnitude of that epidemiologic quantity and portray the degree of precision with which it is measured. For example, a case-control study may be undertaken to estimate the incidence rate ratio *(RR)* between use of cellular telephones and the occurrence of brain cancer. The report on the results of the study should present a clear estimate of the *RR,* such as *RR =* 2.5. When an estimate is presented as a single value, we refer to it as a *point estimate.* In this example, the point estimate of 2.5 quantifies the estimated strength of the relation between the use of cellular telephones and the occurrence of brain cancer. To indicate the precision of the point estimate, we use a *confidence interval,* which is a range of values around the point estimate. A wide confidence interval indicates low precision, and a narrow interval indicates high precision.

Chance

In ordinary language, the word *chance* has a dual meaning. One meaning refers to the outcome of a random process, implying an outcome that could not be predicted under any circumstances; the other refers to outcomes that cannot be predicted easily but are not necessarily random phenomena. For example, if you unexpectedly encounter your cousin on the beach at Cape Cod, you may describe it as a chance encounter. Nevertheless, there were presumably causal mechanisms that can explain why you and your cousin were on the beach at Cape Cod at that time. It may be a coincidence that the two causal mechanisms led to both of you being there together, but randomness does not necessarily play a role in explaining the encounter.

Flipping a coin is usually considered to be a randomizing event, one that is completely unpredictable. Nevertheless, the flip of a coin can be predicted with sufficient information about the initial conditions and the forces applied to the coin. The reason we consider it a randomizing event is that most of us do not have the necessary information nor the means to figure out from it what the outcome of the flip would be. Some individuals, however, have practiced flipping coins enough to predict the outcome of a given toss almost perfectly. For the rest of us, the flip of a coin appears random, despite the fact that the underlying process is not actually random. As we practice flipping or learn more about the sources of error in a body of data, we can reduce errors that may appear random at first. Physicists tell us that we will never be able to explain all components of error, but for the problems that epidemiologists address, it is reasonable to assume that much of the random error that we observe in data could be explained with better information.