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

Presentation

I. Overview

Assessing discriminatory

performance (DP) of a binary

logistic model

Focus

Good DP:model discriminates

casesðY¼ 1 ÞfromnoncasesðY¼ 0 Þ

Example: Blunt knee trauma)
X-ray?
Predictor variables:
ability to flex knee
ability to put weight
on knee
patient’s age
injury to knee head
injury to patella
Outcome variable:
knee fracture status

Approach 1
Use fitted model to predict which
subjects will be cases or non-
cases e.g.,
IfP^ðXÞ> 0 : 2 , predict subjXto be
case,
ifP^ðXÞ 0 : 2 , predict subjXto be
noncase, wherecut-point¼0.2

Note: Rare outcome ) 0 : 2 ,or

even 0.02, high

Classification/Diagnostic Table

True (Observed) Outcome

Y¼1Y¼ 0

Predicted Y¼ 1 nTP¼ 70 20
Outcome Y¼ 030 nTN¼ 80
n 1 ¼ 100 n 0 ¼ 100
nTP¼#of trueþ,
nTN¼#of true,

This presentation describes how to assessdis-

criminatory performance(DP) of a binary logis-

tic model.

We say that a model providesgood DPif the

covariates in the model help to predict (i.e.,

discriminate) which subjects will develop the

outcome (Y¼1, or thecases) and which will

not develop the outcome (Y¼0, or thenon-

cases).

For example, we may wish to determine

whether or not a subject with blunt knee

trauma should be sent for an X ray based on a

physical exam that measures ability to flex

knee, ability to put weight on knee, injury to

knee head, injury to patella, and age. The out-

come here is whether or not the person has a

knee fracture.

One way to measure DPinvolves using the

fitted model to decide how to predict which

subjects will be cases and which will be non-

cases. For example, one may decide that if the

predicted probability for subjectX(i.e.,^PðXÞ)

is greater than 0.2, we will predict that subject

Xwill be a case, whereas otherwise, a noncase.

The value of 0.2 used here is called acut-point.

Note that for a very rare health outcome, a

predicted probability of 0.2, or even 0.02,

could be considered a high “risk.”

The observed and predicted outcomes are com-

bined into aclassification or diagnostic table,an

example of which is shown at the left, In this

table, we focus on two quantities: the number

of true cases (i.e., we are assuming that the

observed cases are the true cases) that are pre-

dicted to be cases (true positives or TP), and the

number of true noncases that are predicted to

be noncases (true negatives or TN).

348 10. Assessing Discriminatory Performance of a Binary Logistic Model