Corporalagan, you can calculate a MOS with your example. In your example you can actually obtain a MOS with the two 'evented' patients of 9 mos and 11 mos (MOS would be 10 mos), because the two that are alive are censored, and MOS reported is only on evented patients.
Kaplan-Meier is a statistical method of approximating chance of survival by multiple probabilities of survival between time intervals (e.g. every month). In your example, the first time interval of 0 mos - 1 mos would have a survival rate of 100%. The rest goes as follows:
time interval(i)___At risk____ dead____censored___survival for(i)
0-1 mos_________ 4________ 0_______ 0______ 100% (4/4)
>1-2 mos_________ 4________ 0_______ 0______ 100% (4/4)
>2-3 mos_________ 4________ 0_______ 0______ 100% (4/4)
>3-4 mos_________ 4________ 0_______ 0______ 100% (4/4)
>4-5 mos_________ 3________ 0_______ 1______ 100% (3/3)
>5-6 mos_________ 3________ 0_______ 0______ 100% (3/3)
>6-7 mos_________ 3________ 0_______ 0______ 100% (3/3)
>7-8 mos_________ 2________ 0_______ 1______ 100% (2/2)
>8-9 mos_________ 1________ 1_______ 0______ 50% (1/2)
>9-10 mos________ 1________ 0_______ 0______ 100% (1/2)
>10-11 mos_______ 0________ 1_______ 0______ 0% (0/1)
You obtain the survival data point for each time interval by multiplying the survival for that interval by each preceding interval. So, this is easy for up to <9 mos as it is 100% in each interval, so 100% survival. Then, patient dies at 9 mos, and the chance of surviving that interval is 50%, so cumulative survival would be 50% times the preceding intervals of 100%, would give you 50%. Of course, the next interval is 100% chance of surviving, so K-M data point is 50% * 100% or 50%. And only in the next interval, >10-11 mos, do you get 0% of survival.
As mentioned, the MOS would be calculated by taking the median of the two 50% K-M data points, 9 mos and 11 mos, so 10 months.
The key here is the censored patients at 5 mos and 8 mos. If brought back into the study, they could impact MOS calculation (remember censored is also patients lost to the study because of various reasons and are not eligible to be brought back in). However, that is why companies wait to report interim results to prevent multiple censored patients that are in the study and are currently to the left of the MOS estimation
IMO
AI
