To perform the matched case-control analysis using the SPSS Multinomial logistic procedure we compute differences between each pair of cases and controls on each predictor. So, for example, for the sibling data on the previous webpage the first pair of observations consists of a cancer patient with an IQ of 23 and their healthy sibling control with an IQ of 12 so the case-control IQ difference is 23-12=11. Similarly the cancer patient has the psychiatric disorder (code=1) whereas their healthy control does not (code=0) so the case-control difference on disorder is 1-0=1. These are entered on the first row of the table below. The differences in case-control disorders and IQs are worked out similarly for the other 5 sibling pairs giving the table below which has six rows, one for each pair.
Disorder Difference |
IQ Difference |
Constant |
|||
-1 |
11 |
1 |
|||
-1 |
-28 |
1 |
|||
-1 |
11 |
1 |
|||
-1 |
51 |
1 |
|||
1 |
-17 |
1 |
|||
1 |
18 |
1 |
|||
We also need to add a constant row which takes the value one for all observations.
All these operations can be easily achieved in SPSS, using the compute statement in the transform menu, if the data is structured so that each row represents a sibling pair with data columns denoting sibling pair characteristics.
We are now ready to do the matched pairs analysis. We go to analyze:regression:multinomial logistic and enter the constant term as the dependent variable with disorder and iq as covariates. We also need to click on the model button and unclick the "include intercept in model" box. We then run the procedure and get exactly the same results as using the Cox model method. Given that one sibling has a psychiatric disorder it is 1/0.55 = 1.82 times more likely to be the one who has been treated for cancer.
This approach is called a conditional logistic regression as this approach is equivalent to the probability of the cancer patient having the disorder given a disorder is associated with either the cancer patient or their control.
Categorical predictors with 3 or more levels need to be converted into dummy variables before being differenced and entered as predictors into the multinomial logistic procedure. A Macro is available to do this
References
Agresti A. (2002) Categorical Data Analysis. Second Edition. Wiley:New York.
Hosmer DW, Lemeshow S. (1989) Applied Logistic Regression. New York: Wiley.
SPSS Regression Models version 10.0 (1999) Chicago:SPSS Inc.