Week 4: Multiple regression analysisOverview

Questions from last weekWhat is regression analysis?The mathematical modelInterpreting the β coefficientLeast squares model fitting R and R2

An example using SPSS (ethnicity and LOS)Discussion of the 2 articlesData analysis discussion

What is regression analysis?

• Used to learn more about the relationship between several exposure variables and a continuous outcome variable

• Multiple regression is an extension of bivariate regression with several exposure variables instead of just one

• Used to predict the association

The mathematical model• Y’ (known a Y prime) is the predicted

value on the outcome variable

• A is the Y axis intercept

• β1 is the coefficient assigned through regression

• X1 is the unit of the exposure variable

• Thus the model is:

• Y’=A + β1X1 + β2X2 + β3X3

Interpreting the β coefficient

• The β coefficient is of the most interest to us

• It tells us the predicted change in the association between the exposure variable and the outcome variable

Least squares model fitting

• Most regression models use the least squares method to fit regression models

• Tries to find the best fit for the regression line with the least variance

R and R2

• R is the regression coefficient• R2 is the square of the regression

coefficient• R2 tells you the amount of variance in the

outcome variable explained by the exposure variables

• The adjusted R2 tells you how much of the population variation is likely to be explained by your sample

Sample size calculation

• Sample size calculation is done when planning a research study

• The size of the sample is determined by:– -variability in the data– -the size of difference to be detected

-the smaller the difference to detect, the larger the sample size

– Power and significance level– Practical issues (budget, participant availability)

A linear regression exampleBackground

• Many parents new to Canada use the Emergency Department as the source of primary health care for their children

• Often the parents have limited understanding of English and have difficulty describing their child’s symptoms and understanding treatment modalities

• ED physicians are concerned that language barriers may lead to a longer LOS in the ED

Methods

• A survey was conducted in the ED at the Hospital for Sick Children in Toronto

• Parents whose mother tongue was not English were compared to parents with English as a primary language

• Outcome variable: LOS in the ED in minutes• Exposure variables: Primary language (5 levels

dichotomized into English and other), CTAS (1 to 5, 1= resuscitation, 5 = non-urgent), age in months,

Statistical analysis

• Univariate statistics (histograms for continuous variables, frequency distributions for categorical variables)

• Bivariate statistics (t-tests and chi square statistics)

• Multiple linear regression analysis

• Let’s try it in SPSS

For next week

• Read 2 articles

• Data analysis plan due: background and description of the variables, univariate stats, bivariate comparisons, multivariate analysis

• Start your own data analysis