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

Association of Predicted Probabilities and Observed Responses

Percent Concordant 65.2 Somers’ D 0.518

Percent Discordant 13.4 Gamma 0.660

Percent Tied 21.5 Tau‐a 0.144

Pairs 25205 c 0.759

Partition for the Hosmer and Lemeshow Test

Event Nonevent

Group Total Observed Expected Observed Expected

1 179 8 11.83 171 167.17

2 114 12 8.17 102 105.83

3 25 13 9.17 12 15.83

4 108 38 41.83 70 66.17

Hosmer and Lemeshow Goodness‐of‐Fit Test

Chi‐Square DF Pr>ChiSq

6.3576 2 0.0416

Chapter 11 True‐False Questions:

1. T


2. F: information may be lost from matching: sample
   size may be reduced by not including eligible controls


3. T


4. T


5. T


6. McNemar’s chi square: (X  Y)^2 /(X þ Y)¼
   (125121)^2 /(125þ121)¼16/246¼0.065, which is
   highly nonsignificant. The MOR equalsX/Y¼125/121¼
   1.033. The conclusion from this data is that there is no
   meaningful or significant effect of exposure (Vietnam
   veteran status) on the outcome (genetic anomalies of
   offspring).


7. logit PðXÞ¼aþbEþå

8501

i¼ 1

g 1 iV 1 i;

where theV 1 idenote 8,501 dummy variables used to

indicate the 8,502 matched pairs.

8. The Wald statistic is computed asZ¼0.032/0.128¼
   0.25. The square of this Z is 0.0625, which is very close
   to the McNemar chi square of 0.065, and is highly
   nonsignificant.


9. The odds ratio from the printout is 1.033, which is
   identical to the odds ratio obtained using the formula
   X/Y.


10. The confidence interval given in the printout is com-
    puted using the formula

exp^b 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vard ^b

r 

;

where the estimated coefficient^bis 0.032 and the square

root of the estimated variance, i.e.,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

dvarð^bÞ

q

,is0.128.

Chapter 11 685