retention comparison

[skk_2011]

how to compare the retention of 2 drugs, data is like:

Drug      week1    week2    week3 ...............................week20

drugA     100         82          55                                        26

drugB     810        580         460                                     312 

The numbers are the patient count who keep using the the drug starting week1.

question: retention statistically significant?

Thanks.

[Doc_Duke]

I don't think that you can test that hypothesis with these data.  Since this is aggregate data, each data element can represent some fo the same and different people from the previous column.  For instance, drugB shows somewhere between 80 and 230 people were taking the drug on Week3 who were not taking it on week 2.

With some severly simplifying assumptions, you could do a test, but I am not sure how much trust you could put into it. 

If you forced the data to be monotonically non-increasing, you could assume that each person took the drug until they stopped and generate a duration for each person.  Then you would have a total of 910 records (100+810) and could do a test (e.g. Wilcoxon).  However, it appears that you have people going on and off and on the drugs from week to week and that assumption is likely unfounded. 

Alternatively, you could assume that the likelihood of taking a drug on any given week is independent of any other week (within a person) and apply a time series analysis.  That assumption is generally false in the medication adherence studies.

Doc Muhlbaier

Duke