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Table 2 Kaplan-Meier and cumulative incidence estimators of probability of clinical stability for artificial data

From: How to handle mortality when investigating length of hospital stay and time to clinical stability

     Kaplan-Meier Cumulative Incidence
t i y i s i d i S ^ c s ( t i ) 1 - S ^ c s ( t i ) SE S ^ ( t i ) C I ^ c s ( t i ) SE
2 10 2 0 1-2/10 = 0.80 0.20 0.126 1-2/10 = 0.8 2/10 = 0.2 0.133
3 8 0 1 0.80 0.20 0.126 0.8*(1-1/8) = 0.7 0.2+0/8*(0.8) = 0.2 0.133
4 7 1 0 0.8*(1-1/7) = 0.69 0.31 0.151 0.7*(1-1/7) = 0.6 0.2+1/7*(0.7) = 0.3 0.154
5 6 1 1 0.69*(1-1/6) = 0.57 0.43 0.164 0.6*(1-2/6) = 0.4 0.3+1/6*(0.6) = 0.4 0.167
7 4 1 0 0.57*(1-1/4) = 0.43 0.57 0.174 0.4*(1-1/4) = 0.3 0.4+0/4*(0.4) = 0.5 0.172
>7 3    0.43 0.57   0.3 0.5  
  1. t i = ith time point; y i = number at risk at time t i ; s i = number clinically stable at time t i ; d i = number who died at time t i ; Ŝ ( t i ) = event free survival at time t i = event free survival at time t i ; SE = standard error