ssizeCT.default(power, k, pE, pC, RR, alpha = 0.05)RR.Suppose we want to compare the survival curves between an experimental group ($E$) and a control group ($C$) in a clinical trial with a maximum follow-up of $t$ years. The Cox proportional hazards regression model is assumed to have the form: $$h(t|X_1)=h_0(t)\exp(\beta_1 X_1).$$ Let $n_E$ be the number of participants in the $E$ group and $n_C$ be the number of participants in the $C$ group. We wish to test the hypothesis $H0: RR=1$ versus $H1: RR$ not equal to 1, where $RR=\exp(\beta_1)=$underlying hazard ratio for the $E$ group versus the $C$ group. Let $RR$ be the postulated hazard ratio, $\alpha$ be the significance level. Assume that the test is a two-sided test. If the ratio of participants in group E compared to group C $= n_E/n_C=k$, then the number of participants needed in each group to achieve a power of $1-\beta$ is $$n_E=\frac{m k}{k p_E + p_C}, n_C=\frac{m}{k p_E + p_C}$$ where $$m=\frac{1}{k}\left(\frac{k RR + 1}{RR - 1}\right)^2\left( z_{1-\alpha/2}+z_{1-\beta} \right)^2,$$ and $z_{1-\alpha/2}$ is the $100 (1-\alpha/2)$ percentile of the standard normal distribution $N(0, 1)$.
Rosner B. (2006). Fundamentals of Biostatistics. (6-th edition). Thomson Brooks/Cole.
ssizeCT# Example 14.42 in Rosner B. Fundamentals of Biostatistics.
# (6-th edition). (2006) page 809
ssizeCT.default(power = 0.8, k = 1, pE = 0.3707, pC = 0.4890,
RR = 0.7, alpha = 0.05)Run the code above in your browser using DataLab