## Considering the data as binary

If interest focuses on the proportion of responders ( complete response + partial response) in the three groups the results in Table 9.9 are seen.

 de Gramont Lokich raltitrexed (control) (%) (%) (%) Response rate (excluding deaths) 28 28 23 Response rate (including deaths) 23 25 18

It can be seen that excluding the patients who die, increases the response rate for all three treatments, particularly for the raltitrexed therapy which had the largest number of deaths. Using the nomenclature introduced in Section 9.3.1, we have

^experimental(excluding deaths) = praltitrexed (excluding deaths) = 46/(250 - 50) = 0.23, pexperimental (including deaths) = praltitrexed (including deaths) = 46/250 = 0.18, pcontrol(excluding deaths) = pdeGramont(excluding deaths) = 59/(252 - 39) = 0.28, pcontrol (including deaths) = pde Gramont (including deaths) = 59/252 = 0.23,

Thus, praltitrexed (including deaths) - pdeGramont (including deaths) = 0.18 - 0.23

SE(praltitrexed — pde Gramont) = J -2jq--+--252- = 0.036.

Thus a 95 per cent confidence interval for the estimated difference of —0.05 is given by —0.05 — 1.96 x 0.03644 to —0.05 +1.96 x 0.036. When this is evaluated this gives —0.121 to 0.021, i.e.—12 per cent to +2 per cent. To perform a test of the hypothesis that the proportion of responders in the two groups is similar, we calculate the following:

250 252

The Z-statistic to test the null hypothesis of no difference in the response rate between the two treatments is given by:

If we look up this Z-statistic in the tables at www.anu.edu.au/nceph/surfstat/surfstat-home/tables.html then the p-value of 0.084 is obtained. This indicates that although the estimate ofthe response rate is higher in the de Gramont treatment when compared with the raltitrexed treatment, from these data there is no clear evidence that it is significantly better. We need to ensure that this result is not a consequence of how the data have been analysed - we have collapsed the five ordered categories into two (binary) categories. This is addressed below.

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