FIGURE 1.

Sample size calculated to detect a risk difference of ${\mu }_1-{\mu }_0=0.375-0.275$ with 90% power at a two-sided 5% significance level using the $n_{\text{IPRW}}$, $n_{\text{known}}$, $n_{\text{approx}}$ and $n_{\text{standard}}$ formulas. The within-category prevalence of the outcome in the intervention group (${\mu }_{11}$ and ${\mu }_{21}=2{\mu }_1-{\mu }_{11}$) is varied on the x-axis, and within-category prevalence of the outcome in the control group is held fixed at the displayed values of ${\mu }_{10}$ and ${\mu }_{20}=2{\mu }_0-{\mu }_{10}$. The probability of the outcome being observed in each category and intervention group is as displayed for $P\left(R_i=1\mid X_i=1,Z_i=1\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{11}\right)$, $P\left(R_i=1\mid X_i=2,Z_i=1\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{21}\right)$, $P\left(R_i=1\mid X_i=1,Z_i=0\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{10}\right)$ and $P\left(R_i=1\mid X_i=2,Z_i=0\right)=\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{i}\mathrm{t}\left({\beta }_{20}\right)$.