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

The Choice:

Unconditional – preferred if the
number of parameters issmall
relative to the number of subjects

Conditional – preferred if the
number of parameters islarge
relative to the number of subjects

Small vs. large? debatable

Guidelines provided here

In making the choice betweenunconditional

andconditional ML approaches, the researcher

needs to consider the number of parameters

in the model relative to the total number of

subjects under study. In general,unconditional

ML estimation is preferred if the number of

parameters in the model issmall relative to

the number of subjects. In contrast,conditional

ML estimation is preferred if the number of

parameters in the model is largerelative to

the number of subjects.

Exactly what is small vs. what is large is debat-

able and has not yet nor may ever be precisely

determined by statisticians. Nevertheless, we

can provide some guidelines for choosing the

estimation method.

An example of a situation suitable for an

unconditional ML program is a large cohort

study that does not involve matching, for

instance, a study of 700 subjects who are fol-

lowed for 10 years to determine coronary heart

disease status, denoted here as CHD. Suppose,

for the analysis of data from such a study, a

logistic model is considered involving an expo-

sure variableE, five covariablesC 1 throughC 5

treated as confounders in the model, and five

interaction terms of the formECi, whereCi

is theith covariable.

This model contains a total of 12 parameters,

one for each of the variables plus one for the

intercept term. Because the number of para-

meters here is 12 and the number of subjects

is 700, this is a situation suitable for using

unconditional ML estimation; that is, the num-

ber of parameters issmallrelative to the num-

ber of subjects.

EXAMPLE: Unconditional Preferred

Cohort study: 10 year follow-up

n¼ 700

D¼CHD outcome

E¼exposure variable

C 1 ,C 2 ,C 3 ,C 4 ,C 5 ¼covariables

EC 1 ,EC 2 ,EC 3 ,EC 4 ,EC 5

¼interaction terms

Number of parameters¼ 12

(including intercept)

small relative ton¼ 700

108 4. Maximum Likelihood Techniques: An Overview