## Matched pairs analysis

Suppose we are interested in pairs of siblings, one whose has been treated for cancer (case) and one who has not (control). We wish to see if cancer treatment increases the risk of acquiring a psychiatric disorder when corrected for a covariate, IQ. Such an analysis is possible in SPSS using the Cox regression procedure (outlined under the section entitled conditional logit models about two-thirds of the way down the page) The straightforward generalisation to three or more dichotomous matched responses is also described.

Below is an illustrative example of the described procedure on the sibling cancer data.

Case/Control |
Disorder |
Pair |
Duplicate |
IQ |
|||||

2 |
0 |
1 |
2 |
23 |
|||||

1 |
1 |
1 |
1 |
12 |
|||||

2 |
0 |
2 |
2 |
11 |
|||||

1 |
1 |
2 |
1 |
39 |
|||||

2 |
0 |
3 |
2 |
23 |
|||||

1 |
1 |
3 |
1 |
12 |
|||||

2 |
0 |
4 |
2 |
63 |
|||||

1 |
1 |
4 |
1 |
12 |
|||||

2 |
1 |
5 |
2 |
17 |
|||||

1 |
0 |
5 |
1 |
34 |
|||||

2 |
1 |
6 |
2 |
29 |
|||||

1 |
0 |
6 |
1 |
11 |

Running the Cox Model below

COXREG case_con /STATUS=duplic(1) /STRATA=pair /CONTRAST (disorder)=Indicator /METHOD=ENTER iq /METHOD=ENTER disorder /PRINT=CI(95) /CRITERIA=PIN(.05) POUT(.10) ITERATE(20) .

The disorder term, obtained by taking the reciprocal of the regression estimates, gives the relative risk of 1/0.553 = 1.81 with 95% confidence interval(1/3.192, 1/0.096) = (0.31,10.42). Given one sibling has the psychiatric disorder it is 1.8 times more likely to be the one whose has been treated for cancer. This is not a statistically significant association. (chi-square(1)=0.45, p=0.50).

Another example of the above technique (also known as conditional logistic regression) using the syntax above in SPSS is given here. Hosmer and Lemeshow (2000) whilst not mentioning SPSS do state that the proportional hazards model may be adapted to fit conditional logistic models for case-control matched data.

Relationship to McNemar's test for 2x2 interaction tests

Alternatively you can use the Multinomial Logistic Regression procedure in SPSS

For three or more repeated measures you need to use a specialist procedure

Reference

Hosmer DW and Lemeshow S (2000). Applied logistic regression. 2nd Edition. Wiley:New York. In CBSU library. A third edition is due to be published in 2013.