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All survival (kaplan meier) function graphs must start at the point 1? or Can it start the point which is different from 1?

y-axis cumulative vs. x-axis time

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Let $t_1<t_2<...<t_d$ represent the distinct event times. For each $i=1,...,D$, let $n_i$ be the number of surviving units, the size of the risk set, just prior to $t_i$. Let $d_i$ be the number of units that fail at $t_i$, and let $s_i=n_i-d_i$.

The K-M estimate of the SDF at is the cumulative product $$\hat S(t_i)= \prod_{i=1}^i(1-\frac {d_i}{n_i})$$

From this definition, if $t_1 = 0$ and $d_1 > 0$, then it is reasonable that $S(0) < 1$.

In fact, in my personal experience, I draw the K-M curves with $S(0) < 1$ several times.

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