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

V. The Wald test(pages 138–140)

A. Requires one parameter only to be tested, e.g.,

H 0 :b 3 ¼0.

B. Test statistic:Z¼^b=s^bwhich is approximately

N(0, 1) underH 0.

C. Alternatively,Z^2 is approximately chi square with

one df underH 0.

D. LR andZare approximately equal in large

samples, but may differ in small samples.

E. LR is preferred for statistical reasons, althoughZ

is more convenient to compute.

F. Example of Wald statistic forH 0 :b 3 ¼0inModel2:

Z¼^b 3 =s^b 3.

VI. Interval estimation: one coefficient

(pages 140–142)

A. Large sample confidence interval:

estimatepercentage point ofZestimated

standard error.

B. 95% CI forb 3 in Model 2:^b 3  1 : 96 s^b 3 :

C. IfX 3 is a (0, 1) exposure variable in Model 2, then

the 95% CI for the odds ratio of the effect of

exposure adjusted forX 1 andX 2 is given by

exp ^b 3  1 : 96 s^b 3



D. IfX 3 has coding other than (0, 1), the CI formula

must be modified.

VII. Interval estimation: interaction(pages 142–146)

A. Model 3 example:dOR¼e^l;where^l¼b^ 3 þ^b 4 X 1 þ^b 5 X 2

100(1a)% CI formula for OR:expl^Z 1 a 2

ffiffiffiffiffiffiffiffiffiffiffiffiffi

vard^l



Þ

q

;

where

dvar^l



Þ¼vard ^b 3



þðÞX 12 dvar ^b 4



þðÞX 22 dvar^b 5



þ 2 X 1 covd bb 3 ;^b 4



þ 2 X 2 covd ^b 3 ;b^ 5



þ 2 X 1 X 2 covd ^b 4 ;^b 5



:

B. General 100(1a)% CI formula for OR:

exp^lZ 1 a 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vard^l



Þ

q

whereORd¼e

^l

;

^l¼~

k

i¼ 1

^b

iðÞX^1 iX^0 i andvar^l



Þ¼var Sb^iðÞX 1 iX 0 i

|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}

linearsum

0

B

@

1

C

A:

Detailed Outline 155