Wald statistic:Z¼
^bSMKNS
s^bSMKNS, which is approximately
normal (0, 1) underH 0 , or alternatively,
Z^2 is approximately chi square with one degree of
freedom underH 0 ; test computation:
Z¼ 01 : 5997 :^1128 ¼ 1 : 856 ; alternatively,Z^2 ¼3.44; the
P‐value for the Wald test is 0.0635, which gives
borderline significance.
The LR statistic is 3.51, which is approximately equal
to the square of the Wald statistic; therefore, both
statistics give the same conclusion of borderline
significance for the effect of the interaction term.
- The formula for the estimated odds ratio is given
byORdadj¼expðb^SMKþ^dSMKNSNSÞ¼expð 1 : 9381
1 : 1128 NSÞ, where the coefficients come from Model
II and the confounding effects of NS and AS are
controlled.
- Using the adjusted odds ratio formula given in
Question 7, the estimated odds ratio values for NS¼ 1
and NS¼0 are
NS¼1: exp[1.93811.1128(1)]¼exp(0.8253)¼2.28;
NS¼0: exp[1.93811.1128(0)]¼exp(1.9381)¼6.95
- Formula for the 95% confidence interval for the
adjusted odds ratio when NS¼1:
exp^l 1 : 96
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dvar^l
q
;where^l¼b^SMKþ^dSMKNSð 1 Þ
¼b^SMKþ^dSMKNS
and
dvar^l
¼dvarb^SMK
þð 1 Þ^2 dvar^dSMKNS
þ 2 ð 1 Þdcov^bSMK;^dSMKNS
;
wheredvar ^bSMK
;dvar^dSMKNS
, and
covd ^bSMK;^dSMKNS
are obtained from the printout of
the variance–covariance matrix.
- ^l¼^bSMKþ^dSMKNS¼ 1 : 9381 þð 1 : 1128 Þ¼ 0 : 8253
dvar^l
¼ 0 : 1859 þð 1 Þ^2 ð 0 : 3596 Þþ 2 ð 1 Þð 0 : 1746 Þ
¼ 0 : 1859 þ 0 : 3596 0 : 3492 ¼ 0 : 1963 :
The 95% confidence interval for the adjusted odds
ratio is given by
exp^l 1 : 96
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Vard^lÞ
q
¼exp 0 : 8253 1 : 96
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 : 1963
p
¼expð 0 : 8253 1 : 96 0 : 4430 Þ
¼ e^0 :^0430 ;e^1 :^6936
¼ð 0 : 96 ; 5 : 44 Þ:
Chapter 5 673
