A question about the effective sample size in life tables I am currently studying basic methods of survival analysis and I came across this strange estimator of the effective sample size at a given interval. For the jth interval say, the estimator $n^{\prime}_j$ is given by
$$n^{\prime}_j=n_j-\frac{c_j}{2}$$
where $n_j$ is the number of individials who are at risk of death at the start of the jth interval and $c_j$ is the number of censored survival times. The estimator is used under the assumption of uniformity of the censored survival times throughout the jth interval. 
My question is then, how is that estimator justified? Why not use the simpler and more intuitive $n^{\prime}_j=n_j-c_j$? I suspect that there is a bias argument that can be made, exactly as in the case of the sample variance but I have not been able to figure it out yet. 
To be more precise, here is the exact extract from the book on Survival Analysis by Xian Liu:

All help is greatly appreciated, thank you.
 A: Observations censored within the interval under consideration are not at risk of death for the whole period. 
They don't count as a whole person-period of exposure, but only the fraction to which they were exposed. Under the uniformity assumption, on average they're exposed half a period. So on average each of the $c_j$ censored people will lose half a person-period of exposure.
The text is a little awkwardly worded, but it's treating the $c_j$ people unexposed for on average half the period as equivalent to half of the $c_j$ people who were censored being unexposed to risk of death in the study (equivalently, not in the study) -- it's the same number of person-periods of exposure. 
In the diagram below, censored observations are marked with an "o" when censored and uncensored observations that died are marked with an "x at death". The uncensored ones count just as they would if there were no censoring at all, but the censored ones have reduced exposure:

I've split the censored values off separately and then sorted them by exposure. If you took the censored values with shorter exposure times, you could (on average) use them to "fill up" the exposure time of the ones with longer exposure, leaving it as half the censored lives had full exposure and half had none.
That is, you lose $c_j/2$ person-periods of exposure on average, but you could treat that as equivalent to simply losing half the censored people at the start of the period (and the other half being exposed for the entire period), reducing the count by $c_j/2$.
A: thank you for this discussion, I'm also dubitative regarding this denominator correction. When you estimate a rate you have to consider the total time spent by subject during a given period of time, so one usually assumes that censored (as well as dying) people have lived half of the period on average. But this is not the case when you are estimating a conditional probability, i.e. the probability of dying during the period given that a subject is still alive at the beginning of the period. In this case at the denominator one has the number of subject entering the period- Why to correct ith the half of censoring in this case?
