\(\hat F(t)= \sum_{i=1}^{n}\frac{I(T_i<C_i)(1-R_i+R_iZ_i/p)I(U_i\le t)}{\hat S(U_i)},\)

where \(I(.)\) is an indicator function.

Now it is written that, with no censoring \(\hat F(t)\) becomes

\(\hat F(t)= \sum_{i=1}^{n}(1-R_i+R_iZ_i/p)I(T_i\le t).\)

I understand that if there is no censoring, then \(I(T_i<C_i)=1\), that is, we will always observe the survival time. Also, with no censoring \(U_i=T_i\) and hence \(I(U_i\le t)=I(T_i\le t)\).

But I do not understand why does Kaplan-Meier estimator for the censoring distribution, \(\hat S(U_i)\), which appears in the above first equation vanish in the second equation with no censoring?

Thanks in advance.