I also found the word "censoring" to be confusing when I first started survival analysis.
"Censored" individuals aren't removed from analysis; they're just treated differently from those with events/deaths. If censoring is non-informative, as @swmo discussed, then a censored individual provides information that the event did not occur up to the censoring time. Just doesn't provide the exact time.
A standard survival curve includes the censored patients, noting the censoring times with a mark on the curve at the censoring time. The survival curve only drops at times of (noncensored) events, with a drop given by the ratio of events at that time to the total at risk at that time, including those with later censoring times. So the survival curves for the wonder drug in your example would in fact look quite good, with the few early events leading to small drops in the curve (as the fraction of individuals dying early was small) and then a high survival fraction thereafter.
Also, you're not usually comparing censored to uncensored patients within a single treatment group, as the question seems to suggest. Rather, you're comparing the timing of events in treatment group A to those in treatment group B. So in a test of a poor drug A versus wonder drug B, there would be many events/deaths in group A and few in group B, or at least events would tend to happen earlier in group A.
If most patients in group B are "cured" and they are not otherwise at high risk of death, then the "survival times" of the censored individuals in that group would mostly be determined by the duration of the study. A longer survival time for censored versus non-censored individuals may just mean that the study went on long enough to pick up most of those who were not "cured" by drug B.
For left censored data, they are excluded from follow-up at the point of censoring and coded as a non-event. That is in fact the definition of censoring. Also, you need to know what "time 0" is. So if you don't understand that, you can't include right censored data. You will get different results if the time under observation goes from 0 to 6 as compared to 12 to 18. The last consideration is that you can't just sample observations on the basis of being failures. It will inflate the incidence and bias the hazard ratios. Cox regression works, but I think you need a clearer understanding of how censoring is encountered. A practical description of the data is warranted.
Best Answer
In this situation, the "survival days" for all individuals is the difference between the last observation date and the date of entry into the study. To that extent, you are correct in your calculation for Patient B. Remember, however, that all you know is that Patient B survived at least that long. Thus that is a right-censored observation.
What's important is to include for each patient, along with those "survival day" values, an indicator of whether there was an event at the end of that time period (Patient A) or if the individual had not yet experienced the event (Patients B and C). In the R survival package, that's done with a
Surv()object that, in its simplest form, combines the survival time with the event indicator.