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Example 1
Osteogenic Sarcoma Study
In a 46-patient study of non-metastatic osteogenic sarcoma, (Goorin et al., 1987), the investigators were interested in determining the predictors for a three year disease free interval (DFI3). The covariates of interest were SEX, any osteoid pathology (AOP), and lymphocytic infiltration (LI). The complete data set is displayed below. The FREQ (frequency count) variable shows the number of copies of each row in the data set.
| DFI3 |
LI |
SEX |
AOP |
FREQ |
| 1 |
0 |
0 |
0 |
3 |
| 1 |
0 |
0 |
1 |
2 |
| 1 |
0 |
1 |
0 |
4 |
| 1 |
0 |
1 |
1 |
1 |
| 1 |
1 |
0 |
0 |
5 |
| 1 |
1 |
0 |
1 |
3 |
| 1 |
1 |
1 |
0 |
5 |
| 1 |
1 |
1 |
1 |
6 |
| 0 |
1 |
0 |
1 |
2 |
| 0 |
1 |
1 |
0 |
4 |
| 0 |
1 |
1 |
1 |
11 |
Individually each of the covariates, LI, SEX, and AOP, has a statistically significant effect on DFI3. For example the p-value for LI is 0.0075 from Fisher's exact test. But try to fit the logistic regression model DFI3=SEX+AOP+LI by maximum likelihood, using a standard package like SAS, BMDP or GLIM. You will get no convergence. Although maximum likelihood fails, exact inference works. The exact option in LogXact is able to fit the above model and reveals that after adjusting for SEX and AOP, LI has an exact p-value of 0.074.
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