Q.no: 9 A study of the mortality of 12 laboratory-bred insects was undertaken. The insects were observed from birth until either they died or the period of study ended, at which point those insects still alive were treated as censored. The following table shows the Product-Limit estimate of the survival function, based on data from the 12 insects. t (weeks) S(t) 0 t < 1 1.0000 1 t < 3 0.9167 3 t < 6 0.7130 6 t 0.4278 ii) Calculate the number of insects dying at durations 3 and 6 weeks. Can anyone please help me solving this question. Thank you.
Product-limit estimate is another way of saying the more familiar Kaplan-Meier estimate. The tricky part is that it's not explicitly mentioned that some insects are censored before 6 weeks are up. So at one week, 0.9167/1.0000 (91.67%) of the original insects remain alive (i.e. 1 insect died, 11 survived) At 3 weeks, 0.7130/0.9167 (77.78%) of the remaining insects then remain alive (2 are right-censored between weeks 1 to 3; of the 9 left, 2 insects died, 7 survived) At 6 weeks, 0.4278/0.7130 (60.00%) of the remaining insects then remain alive (2 are right-censored between weeks 3 to 6; of the 5 left, 2 insects died, 3 survived which are then right-censored) This incidentally also affects the total number of insects that get right-censored (7 altogether); if calculated in a way such that all censoring is only at the end of week 6, then only 5.1334 insects get right-censored. I believe that you are supposed to know that only an integer number of insects can die at any point, so you would use the ratios to determine what the possible numerators and denominators are, then the difference between the denominator and the number of surviving insects from last time period would naturally have to be right-censored.
In the question they have mentioned insects are censored only at the end, there is no other way they are censored in between the study. Then how do we suppose they are right censored during the study period. Solution provided in IAI site considers insects are right censored in between. Now, if i suppose they are censored only at the end of the study, i would get fractional value for deaths. For example 2.44 deaths, can't i take 2 deaths and remaining are alive beacuse there is no other way of censoring mentioned in the question. How do i assume they are censored, when is there is no way mentioned?
Strictly speaking, the censoring is not only at the end, and can exist elsewhere. "...the period of study ended, at which point those insects still alive were treated as censored" means that all insects alive then are censored, but does not mean that they are the only insects censored. It's just that I find the question could have been phrased better to mention more explicitly that censoring isn't limited to just those insects surviving for the full 6 weeks.
Sir, For example 2.44 deaths, can't i take 2 deaths and remaining are alive and censored at the end. Is this approach wrong ? Solutions didn't give any explanation for this approach.
I believe that (at least based on past markschemes from IFoA) should there be this sort of ambiguity within the question, then your alternative approach should get significant credit as long as you can justify it.
