Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Influential observations:

 Individual data may influence
regression coefficients, e.g.,
outlier
 Coefficients may change if
outlier is dropped from analysis

IV. Variable Specification
Stage

 Define clinically or biologically
meaningful independent
variables

 Provide initial model

SpecifyD,E,C 1 ,C 2 ,...,Cpbased
on:

 Study goals

 Literature review

 Theory

SpecifyVs based on:

 Prior research or theory

 Possible statistical problems

Influential observationsrefer to data on indivi-

duals that may have a large influence on the

estimated regression coefficients. For example,

an outlier in one or more of the independent

variables may greatly affect one’s results. If a

person with an outlier is dropped from the

data, the estimated regression coefficients

may greatly change from the coefficients

obtained when that person is retained in the

data. Methods for assessing the possibility of

influential observations should be considered

when determining a best model.

At the variable specification stage, clinically or

biologically meaningful independent variables

are defined in the model to provide the largest

model to be initially considered.

We begin by specifying theDandEvariables of

interest together with the set of risk factorsC 1

throughCpto be considered for control. These

variables are defined and measured by the

investigator based on the goals of one’s study

and a review of the literature and/or biological

theory relating to the study.

Next, we must specify theVs, which are func-

tions of theCsthatgointothemodelaspotential

confounders. Generally, we recommend that the

choice of Vsbebasedprimarilyonprior

research or theory, with some consideration of

possible statistical problems like multicollinear-

ity that might result from certain choices.

For example, if theCs are AGE, RACE, and

SEX, one choice for theVs is theCs themselves.

Another choice includes AGE, RACE, and SEX

plus more complicated functions such as AGE^2 ,

AGERACE, RACESEX, and AGESEX.

We would recommend any of the latter four

variables only if prior research or theory sup-

ported their inclusion in the model. Moreover,

even if biologically relevant, such variables

may be omitted from consideration to avoid a

possible collinearity problem.

EXAMPLE

Cs: AGE, RACE, SEX

Vs:

Choice 1: AGE, RACE, SEX

Choice 2: AGE, RACE, SEX, AGE^2 ,

AGERACE, RACESEX,

AGESEX

Presentation: IV. Variable Specification Stage 173