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I have 2 groups of patients and I'm looking at what percentage were discharged from the hospital at different time points after surgery.

            Day 1     Day 2     Day 3     Day 4
Group 1     12%       10%       25%       12%
Group 2     50%       20%       20%       15%

What is the most appropriate statistical test for this? These are two separate groups of patients and the total number of patients in each group is different. As far as the raw numbers, some of the values are less than 5 so I don't think I can use chi-square. I would appreciate your thoughts.

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    $\begingroup$ When you say "I'm looking at what percentage were discharged from the hospital at different time points after surgery" you're asking a question about point estimation. When you say "What is the most appropriate statistical test for this?" you're asking an entirely different question. You should be clear whether your interest is in estimation of values or testing for differences. $\endgroup$
    – Glen_b
    Commented Dec 24, 2013 at 2:28
  • $\begingroup$ My interest is in comparing the two groups. $\endgroup$
    – area51
    Commented Dec 24, 2013 at 16:21
  • $\begingroup$ In comparing discharge-rate estimates (e.g. that one occurs a certain amount earlier) or in saying whether they're more different that would occur by chance? $\endgroup$
    – Glen_b
    Commented Dec 24, 2013 at 16:23

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To clarify, the hypothesis you are testing is, "is there a difference between group 1 and 2 in the time to discharge post-surgery?" if so, you are looking at a survival analysis.

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  • $\begingroup$ Yes that's the hypothesis: that the discharge efficiency was better in group 2 (due to some interventions). $\endgroup$
    – area51
    Commented Dec 23, 2013 at 20:00
  • $\begingroup$ So you need to perform a Cox Proportional Hazards test. Googling survival analysis and cox proportional hazards test should give you some background information - you will need your data to be in a different structure from what you have above. $\endgroup$
    – Bosley
    Commented Dec 23, 2013 at 20:09
  • $\begingroup$ @Bosley 's suggestion would be very constructive except for the fact that cell sample sizes are too small even for chi-square testing. Sometimes Ns are so small that no hypothesis test is going to be appropriate in the sense of adequately powered. And you may want to look up 'statistical power.' $\endgroup$
    – rolando2
    Commented Dec 24, 2013 at 3:14
  • $\begingroup$ @Rolando2, I interpreted the comment that cell sizes were <5 as Area51 setting up his data in a group (1,2)x day of discharge(1-4) format. If some of those 8 cells are less than 5 but the overall N is decent, then there is not a problem in using survival analysis. Even a chi square could be done via a Fisher's exact test, but that did not seem to be the best treatment of his data. Area51 - if your overall group N is <5 then Rolando2 is correct that statistical testing is not appropriate here. But if a single cell is < 5 then it should be fine;a power analysis may be performed to check. $\endgroup$
    – Bosley
    Commented Dec 24, 2013 at 14:50
  • $\begingroup$ Thank you. The overall Ns are 21 and 27 respectively. There are several cell sizes that are <5. However, not all the subjects are included in the analysis as they were discharged at later time points that are not of interest to us (beyond Day 4). $\endgroup$
    – area51
    Commented Dec 24, 2013 at 16:22

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