Question

In Health service administration identify and describe how regression analysis and basic probability theory these branches of mathematics might be used in health service administration Be specific.  If you find examples through research, cite your sources.

Answer 1

Statistical concepts, methods and techniques are useful in Health service administration. Among them regression analysis and basic probability theory are two of the important concepts that play a major role in various aspects of health service administration such as determining the relationship between variables like age and impact of disease(severity on 1-10 scale); determining the proportion of variance in the dependent variable by the change in independent variable through R-squared (R²) obtained from regression analysis; determining the probability of presence of disease when the test result is positive, thereby knowing the impact of test on healthy people. Various probability distributions are useful in knowing the patients arrival and departure times, knowing the density of patients on different days of a week and thereby planning for extra staff required and relaxation of staff if not required, planning the number of beds needed for the patients, etc,. so that the costs are efficiently managed.

As a simple example - If we want to find the relationship between age of drivers and back pain severity, we take a sample of drivers, collect data and use regression analysis and construct scatter plot by taking X: Age as the independent (also called explanatory) variable and Y: Severity of back pain (0 to 10 scale) as the dependent (also called response) variable. We shall then find out the correlation(r), slope(b0), R-squared value, and regression equation to evaluate the relationship and see for any other confounding variables.

As an example for using probability theory - let the incidence of a disease(D) among the population is 0.10; Let P=Probability; Let P(test +ve/D) =0.70; Let P(+ve) =0.50; then by Baye's rule of probability we have P(D/+ve) =P(+ve/D)*P(D)/P(+ve) =0.70*0.10/0.50 =0.14​​​​​​, that is, 14% of people who test positive will actually have the disease.