Solution
= Solution
At $\theta_0$, the expected Fisher information is
$$
\mathcal I(\theta_0)=\frac{\mathbb E_{\theta_0,\phi_0}[v_+]}{\theta_0^2}.
$$
Requiring it to exceed $I_0$ directly controls the large-sample variance of the <maximum-likelihood estimator>, approximately $\mathcal I(\theta_0)^{-1}$. Choose $I_0$ from the desired standard error, confidence-interval width, or power for clinically relevant alternatives, allowing for any planned significance level.