Chapter 15.1

### Introduction

Investigators are sometimes interested in the relationship among different measures or variables. They may pose questions related to the correlation of these variables. For example, they might ask, “How well does the clinical impression of symptoms in a child with asthma relate to the parents' perception?” “How strong is the relationship between a patient's physical and emotional functions?”

By contrast, other investigators may be primarily interested in predicting individuals at high risk of having a subsequent event. For instance, can we identify patients with asthma who are at high risk for exacerbations that require hospitalization?

Still other investigators may seek the causal relations among biologic phenomena. For instance, they might ask, “What determines the extent to which a patient with asthma will experience dyspnea when exercising?” Finally, investigators also may pose causal questions that could directly inform patient management. For example, “Does use of long-acting β-agonists in asthma really increase the likelihood of dying?”

Clinicians may be interested in the answers to all 3 sorts of questions—those of correlation, prediction, and causation. To the extent that the relationship between child and parental perceptions is weak, clinicians must obtain both perspectives. If physical and emotional functions are only weakly related, then clinicians must probe both areas thoroughly. We may target patients at high risk of subsequent adverse events with prophylactic interventions. If clinicians know that hypoxemia is strongly related to dyspnea, they may be more inclined to administer oxygen to patients with dyspnea. The clinical implications of the causal questions are more obvious. We may avoid long-acting β-agonists if they really increase the likelihood of dying.

We refer to the degree of association among different variables or phenomena as correlation.1 If we want to describe the relationship among different variables and subsequently use the value of a variable to predict another or make a causal inference, we use a technique called regression.1 In this chapter, we provide examples to illustrate the use of correlation and regression in the medical literature.

### Correlation

Correlation is a statistical tool that permits researchers to examine the strength of the relationship between 2 variables when neither variable is necessarily considered the dependent variable.

Traditionally, we perform laboratory measurements of exercise capacity in patients with cardiac and respiratory illnesses by using a treadmill or cycle ergometer. Approximately 30 years ago, investigators interested in respiratory disease began to use a simpler test that is related more closely to day-to-day activity.2 In the walk test, patients are asked to cover as much ground as they can during a specified period (typically 6 minutes) walking in an enclosed corridor. For several reasons, we may be interested in the strength of the relationship between the walk test and conventional laboratory measures of exercise capacity. If the tests relate strongly enough to one another, we might ...

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