For example: if the true response rate is 50% for the best arm and 40% for the other arms, there are 3% and 5% chances of erroneously dropping the best arm after 50 and 75 patients/arm, respectively; the cumulative probability of 8%.
In order to employ the linear regression model for the true response surface, it can be written as Eq. (1).
For the primary analysis, a 95% CI for the true response rate was calculated using the normal approximation to the binomial distribution.
This sample size was considered sufficient to estimate 95% confidence intervals for the true response rate with a maximum width of 30%.
The circuit is simulated using our SAT formulation in the fault-free and drug-free model for a specified primary input value, and the resulting primary output value for the true response is saved as Z.
A total of sample size of 55 evaluable patients was calculated using a one-sample multiple testing procedure (Fleming, 1982) and was based on a null hypothesis for the true response rate of 15% and an alternative hypothesis of 30% with a type I error alpha of 5% and type II error beta of <20%.
The procedure tests, the null hypothesis (H0) as formulated for this study that the true response rate is ⩽5% vs the alternative hypothesis (HA) that the true response rate is ⩾25%, with a significance level of 6% and a power of 96%.
This calculation assumes that the true response probability for the best treatment is 10% better than that for the others.
The results are summarised in Table 2-wrap> where all the corresponding Stage 1 and 2 posterior distributions strongly suggest that the true response proportion for these patients (θp) exceeds the R1=0.2 threshold.
The design tested the null hypothesis that the true response rate for this population would improve by approximately 40%, that is, from 30% to the clinically relevant alternative of 50%, using an α error of 0.05 and a β error of 0.1.
The Host assumes that this true response implies that, for now, there is a real schism among conservatives.
