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Example 6
Tests of Trend
A study, conducted in mice, tested a potentially harmful drug at the following doses: 0, 1, 10, 100 mg/kg. There were 96 litters with a total sample size of 1248. Table 3 displays the binary response rates at different dose levels, which increase from 1.39% at control level to 3.05% at the highest dose level.
Table 3. Summary Data on Response Rates
Now the question is whether this trend in the response rates is statistically significant. Figure 7 shows the different options available in ToxTools for trend and pairwise tests.
Figure 7. Test Menu
Figure 8 shows the dialog box after the variables are appropriately allotted to different categories. Notice again that the correlation due to clustering is automatically accounted for simply by specifying the cluster variable (ClusterID) in the appropriate box.
Figure 8. Trend Test: Dialog Box
The results obtained from running the trend test are given in Table 4. Two asymptotic tests and one exact test were computed.
Table 4. Trend Test: Results
Note the considerable difference in the p-value obtained from the exact method (p = .059, 1-sided), compared to the p-values obtained from the two asymptotic methods (p = .111, 1-sided, Rao-Scott and p = .198, 1-sided, GEE score). Despite the large overall sample size, you can see that the unequal spacing of dose levels, as well as the low response rates, lead to this discrepancy between the exact p-value and the p-values obtained through asymptotic approximations.
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