The Choice of Variables in Observational Studies

SUMMARY A review is given of considerations affecting the choice of explanatory variables in observational studies. Aspects of both design and analysis are considered. In particular the choice of explanatory variables in multiple regression is discussed and some recommendations made. THIS paper reviews some general aspects of the choice of variables in observational studies. To keep the paper concise only outline examples have been included and to be specific these are medical, although the ideas apply widely. Observational studies, where they are not purely descriptive, have as their objective the explanation or prediction of some response in terms of explanatory or predictor variables. It is useful to have two examples in mind. Example 1. Consider an investigation into the incidence of a respiratory disease among a certain group of workers. The response variable may be severity of the disease, with possible explanatory variables being the worker's age, physical status, working conditions, previous employment, etc. Some variables may be more important than others in explaining the severity of the disease. Example 2. A different situation is one of trying to predict the time to death among patients known to be suffering from a progressive and fatal disease. Possible predictive variables are type of treatment, treatment variables such as dose, clinical and biochemical measurements made on diagnosis, etc. Although careful discussion of the most appropriate way to measure response is always important, and often several different measures will be called for, nevertheless what response variables to consider is frequently fairly clearcut. Thus in Example 1, severity may be assessed radiologically and graded according to standard levels. In Example 2, time to death is likely to be measured from time of diagnosis. In this paper we concentrate on the explanatory variables; how many such variables should be measured and, if many are observed, how should the analysis be handled to find the

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