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If I have total $n$ patients with two sub-groups of size $n_1$ and $n_2$ in a clinical trial and I wish to find the variance of the estimator $\hat{S^c}(t)=\frac{n_1}{n} \times \hat{S_1}(t)+\frac{n_2}{n} \times \hat{S_2}(t)$, will that simply be $V(\hat{S^c}(t))=(\frac{n_1}{n})^2 \times V(\hat{S_1}(t))+(\frac{n_2}{n})^2 \times V(\hat{S_2}(t))$ or I need any adjustment? I know, it's better to present results for two sub-groups separately. But I am curious about such an estimator to find out how a single combined estimate compares with that found by ignoring the presence of such sub-groups.

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