Part of the retrospective evaluation of a pathology "XY" is the question "Since when did you realize those symptoms?".
As answers I get a variety of answers, like:
- "since 6 days
- since 2-3 month
- since 7 weeks
- since 4-6 weeks
- since 3-4 month
- since 1 year
- since more than 1 year"
etc.
Now I need to calculate the mean and SD of those various periods. How to cope with the variety and inaccuracy of the answers? I thought about calculating all periods into days and always take the minimum period (e.g. 2-3 month = 2 month = 2 x 30 = 60 days; 4-6 weeks = 4 weeks = 4 x 7 = 28 days). Is there any correct way how to proceed in such a case? Any literature to rely on?
Thank you for your help!
In my opinion for an interval of time with limits the midpoint or class mark should be adopted. For instance 4-6 weeks should be 5 weeks or 5x7 days and 2-3 months should be 5/2x30 = 75 days. Open ended intervals should be represented by their closed ends. For example not earlier than two weeks ago should be represented by 2 weeks or 2x7=14 days.
You can calculate a maximum likelihood estimate also for "censored data". See: Pavitan: In all Likelihood.
@Mathias
I have tried with Najim Jamal to answer in demography to your more general question on: How to deal with imprecise/vague information on time periods in statistics?, and we have applied these methods to demographic data artificially rendered imprecise. We called such data interval-censored and we used event history analysis to analyse them. Let me give more precise information about our methods, and you can read the joint file for more details: Interval-censored event history analysis.
These problems occur when we have a Demographic Panel Survey giving the information obtained at different censuses for the same individuals: in this case for example you have only the place of residence or occupation at each census to infer migration or job changes between them. In this case the density of events defining the individual’s position may be sufficient for few migrations or job changes to slip through. Another hypothesis is also necessary to estimate durations of stay from such a panel: the events defining the individual’s spatial or social position must be independent of the geographical and or occupational mobility we wish to measure.
We applied these methods to two data sets: a complete retrospective data set and these data artificially interval-censored.
You will have also application of these methods in my ResearchGate website: An attempt to analyse individual migration histories from data on place of usual residence at the time of certain vital events (1993); Reconstruire des trajectoires de mobilité résidentielle (1998).
You could always convert the time periods to the same metric, for example, days. In your example, it would be 6-365 days or more. Of course, if the distribution is skewed, which it certainly may be in this case, use the median rather than the mean. For some journals, they allow you to report both.
Cheers
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