Regression
models are frequently used in medical research. Regression models
relate independent variables, denoted as X variables, to a dependent
variable, Y. A regression formula can be constructed which takes
the form: Y ~ a + biXi,
where a denotes a constant or intercept and bi
denotes the regression coefficients for the independent
variables Xi.
Example
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| To
predict the pain score after one week based on age,
sex and pain at admission, where pain is quantified
by the score of a standard questionnaire (e.g. McGill
pain questionnaire)... |
|
...the
regression formula might look like this:
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Pain
at 1 week ~ a + b1age + b2sex + b3pain at admission
|
|
Estimation
of the regression formula requires empirical (actual observed)
data from individual patients. Statistical packages estimate
the regression formula with methods that maximally reduce the
deviance between observed and expected value. For linear regression,
least squares are calculated and optimized, for other models
maximum
likelihood estimates are used.