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From |
Matthew Bombyk <bomby001@umn.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Overlapping averages |

Date |
Mon, 27 Jun 2011 22:16:31 -0500 |

Dear Statalist, I have a pretty long and complicated question: My research group has data on the level of average treatment compliance per day (average hours of use of a personal medical device) for a number of subjects over various time intervals. So we might have a subject that was observed from day 3 to 10 and had an average daily usage of 5 hours over that period. We don't have the actual usage data on a given day. We have other panel data on these subjects and want to assign an average treatment compliance number to each day. Many subjects have two time intervals that overlap, say one starts on day 3 and ends day 10, the other starts day 7 and ends day 20. We have average usage over both of these periods. I've done some algebra and found that it is impossible to calculate the average exactly for the overlapping time interval, 7 to 10 in our example. But, I am wondering if there is a "best way" to incorporate the information I have into a better estimate than just assigning one of the period's values to the overlap, or doing a simple average? I have a few criteria that I thought would be useful: 1) if the two intervals have the same start or end date, we CAN calculate the overlap exactly (namely the shorter interval). So the weighted average should collapse to this when appropriate. 2) If the intervals are the same length, we should just get a simple average. 3) if interval 1 is smaller than interval 2, interval 1 should get more weight. I thought about using w1=t22/(t11+t22) and w2=t11/(t11+t22), where w1 is the weight on the first average, and t11 and t22 are the lengths of the nonoverlapping portions of the first and second time intervals, respectively, and t12 is the length of the overlap. Period 1 ____________ t11_____ t12______ t22___________________ Period 2 _________________________ (These might turn out poorly, if so sorry, just ignore them!) The problem with this is that if the overlap is really large compared to the non-overlapping portions, we can put way too much weight on the shorter interval if the nonoverlapping portions have a very high ratio, even if they only differ absolutely by a small amount. We also thought about using w1=t12/(t12+t11) but this fails on criterion #1 above. Any comments appreciated. Thanks! Matt Bombyk * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Overlapping averages***From:*Austin Nichols <austinnichols@gmail.com>

**st: RE: Overlapping averages***From:*"Mak, Timothy" <timothy.mak07@imperial.ac.uk>

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