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

Three separate logistic regressions

Three sets of parameters

a 1 vs:< 1 ; b 1 vs:< 1

a 2 vs:< 2 ; b 2 vs:< 2

a 3 vs:< 3 ; b 3 vs:< 3

Logistic models Proportional odds
model
(three parameters) (one parameter)

b1 vs.< 1

b2 vs.< 2 b

b3 vs.< 3

Is the proportional odds assump-
tion met?

 Crude ORs “close”?

(No control of confounding)

 Beta coefficients in separate
logistic models similar?
(Not a statistical test)

Isb 1 vs:< 1 ffib 2 vs:< 2 ffib 3 vs:< 3?

 Score test provides a test of
proportional odds assumption

H 0 : assumption holds

With these three dichotomous outcomes, we

can perform three separate logistic regres-

sions. In total, these three regressions would

yield three intercepts and three estimated beta

coefficients for each independent variable in

the model.

If the proportional odds assumption is reason-

able, then using the proportional odds model

allows us to summarize the relationship

between the outcome and each independent

variable with one parameter instead of three.

The key question is whether or not the propor-

tional odds assumption is met. There are sev-

eral approaches to checking the assumption.

Calculating and comparing the crude odds

ratios is the simplest method, but this does

not control for confounding by other variables

in the model.

Running the separate (e.g., 3) logistic regres-

sions allows the investigator to compare the

corresponding odds ratio parameters for each

model and assess the reasonableness of the

proportional odds assumption in the presence

of possible confounding variables. Comparing

odds ratios in this manner is not a substitute

for a statistical test, although it does provide

the means to compare parameter estimates.

For the four-level example, we would check

whether the three coefficients for each inde-

pendent variable are similar to each other.

The Score test enables the investigator to per-

form a statistical test on the proportional odds

assumption. With this test, the null hypothesis

is that the proportional odds assumption holds.

However, failure to reject the null hypothesis

does not necessarily mean the proportional

odds assumption is reasonable. It could be

that there are not enough data to provide the

statistical evidence to reject the null.

480 13. Ordinal Logistic Regression