Essentials of Biostatistics. 11. Statistical relationships and the concept of multiple regression

Abstract

Relationships are inherent in medicine and health. For example, lung functions are related to height, and greater weight gain in childhood among low birth weight children is associated with a higher chance of myocardial infarction. The methods for studying relationships are different for qualitative variables than for quantitative variables. You know by this time that a variable is considered quantitative when it is measured on a metric scale (continuous or discrete), whereas variables on nominal and ordinal scales as well as those that have broad categories on a metric scale are considered qualitative for most statistical purposes(1). There are two aspects in the study of relationships. One is the form or type of relationship and the other is the strength of relationship. The strength is generally measured by correlation in quantitative type of variables and by association in qualitative type. For example, different anthropometric measurements in children such as weight, height, mid-arm and calf circumferences are correlated. Symptoms in children of age 6 months to 1 year such as increased biting, ear-rubbing, decreased appetite for solid foods and mild temperature elevation are associated with teething. Some measures of strength of relationships for both qualitative and quantitative variables are discussed in Section 11.1. What do we actually mean by form of relationship? The form of relationship between weight gain during pregnancy and birth weight would be able to indicate how much increase in birth weight (y) to expect when the pregnancy weight gain (x₁) is 10 kg in one women opposed to 8 kg in another. This is an example of what is called simple regression in statistical sense because there are a total of only two variables in this case. The variables y and x₁ are called dependent and independent, respectively. Thus, the form of relationship is an expression of quantitative change in one variable per unit change in the other. It becomes from simple to multiple regression when the number of independent variables is more than one. For example, birth weight is also related to the other parameters such as maternal Hb level (x₂) and calorie intake during pregnancy (x₃). The type and expression of the regression may vary depending on the number of independent variables and whether the dependent variable (y) is quantitative or qualitative. These are discussed in Section 11.2. Computation of regressions, especially multiple type, involves intricate mathematical expressions. We avoid discussing these and advise use of computer programs to obtain such regressions. Our emphasis is mainly on the concepts and interpretation of such regressions. There is another type of relationship that is frequently encountered in the practice of medicine and health. This is between two or more measurements on the same variable obtained on the same subjects. Examples of this are: (i) presence or absence of a disease in a group of children diagnosed by two clinicians, and (ii) measurement by two devices, a newly devised and a conventional, for a nutritional anthropometry, such as mid-arm circum-ference. The problem under study in these situations basically is that of agreement between two or more observers, methods, laboratories, etc. Methods of assessing such agreement in both quantitative and qualitative variables are presented in Section 11.3.