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Transcript
```Week 5: Logistic regression analysis
Overview
Questions from last week
What is logistic regression analysis?
The mathematical model
Interpreting the β coefficient and odds ratios
Maximum likelihood model fitting
An example using SPSS (with our Ottawa
hospital data)
Discussion of the 2 articles
Data analysis discussion
What is logistic regression
analysis?
between several exposure variables and a
dichotomous outcome variable
• Logistic regression is an extension of the
2X2 table with several exposure variables
• No assumptions about the distribution of
the variables
The mathematical model
• In linear regression Y’ (known as 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
• But for logistic regression the model is:
• ln
•
(
Y’
1-Y’
)
=A + β1X1 + β2X2 + β3X3
Interpreting the coefficient
• The regression equation in logistic regression
tells us the (natural log of the) probability of
being in one group divided by the probability of
being in the other group
• The exponentiated coefficient gives us the odds
ratio
• The significance of each coefficient is tested by
dividing the coefficient by its standard error
Maximum likelihood model fitting
• Most logistic regression models use the
maximum likelihood model to fit regression
models
• The log-likelihood is calculated based on
predicted and actual outcomes
• A goodness-of-fit chi-square is calculated
(usually compares a constant-only model to the
one you created)
• Tries to find the best fit for the variables included
A logistic regression example
Background
• Remember our Ottawa CHIRPP data
• We want to compare the odds of going to
a children’s hospital with going elsewhere
• The outcome variable is pediatric hospital
compared to other hospital
• The exposure variables are:
• Age group, disposition, others?
Statistical analysis
• Univariate statistics (histograms for
continuous variables, frequency
distributions for categorical variables)
• Bivariate statistics (t-tests and chi square
statistics)
• Logistic regression analysis
• Let’s try it in SPSS
For next week