How to determine the average or expected time duration of an event to a group statistically correct, if this event has not happened to everybody yet?

One could consider only those to whom the event occurent and simply to statistics for this sub-group, however then it is neglected that there is the complementary sub-group which provides reason to shift the expected event occurence time to the right.

Example: In a group of people owning a smartphone, we want to find out for each brand, when on average the display breaks. Of course, there are people who posess a mobile phone that did not get damaged (yet?). Shall we include this sub-group as well, and how?

Sample data:

Person | display broke after x years
1      | 1.0
2      | 1.5
3      | 2.0
4      | never and has the phone for 0.5 years
5      | never and has the phone for 3.0 years

Only considering the first 3 persons who suffered a phone damage, we might think, the expected lifetime is 1.5 years, however there is a person (nr 5) who has his phone for 3 years and no problem occured (yet?). Shall we even consider person nr 4 that supports the thesis that the phone will at least last for 0.5 years?


You should look into Kaplan Meier analysis, which is a way of handling this type of "right censored" data. In these cases, you want to leverage every data point as much as you can, so you'll still want to use the fact that Person 5's phone hasn't broken in 3 years, even though we don't know how long it will actually last (but we know it's at least 3 years).

One measure for average survival time is called the median survival, which is the time at which 50% of the phones have broken (excluding ones we don't know whether they broke or not). At 1.5 years, for example, 2 people's phone's have broken, 2 people's phones have not broken, and 1 person's phone we don't know whether it broke or not. From this data, we can say that the median survival time of phones is 1.5 years. To visualize this, you can use a Kaplan Meier survival plot as shown below:

enter image description here

  • $\begingroup$ That means, person nr 4 does not play any role in the result? He does not affect the outcome since his event did not happen before any of another person's event time (the minimum event time of events happened)? $\endgroup$
    – pas-calc
    Apr 20 '21 at 17:52
  • $\begingroup$ @pas-calc They play a role up until the point they are censored, although it's tough to see in this example. Had this person been censored at 1y and the first phone breakage occurred at 0.5y, survival at 0.5y would be 80% rather than 75%, since 4 of 5 phones survived to 0.5y, not 3 of 4 phones. The censored datapoint doesn't get removed entirely, but you don't really notice the difference when it occurs before any event. It can make a difference for statistical significance, as that person counts toward your sample size until they are censored. $\endgroup$ Apr 20 '21 at 18:06

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