Hi all -
I'm trying to find a good regression model for a project looking at significance of procedure therapies in relation to procedure interval. Your thoughts are much appreciated.
The equation of procedure interval I'm using is (total procedural treatment window/# procedures). I have two sets of data: 11 medications (binary categories yes, no) and 8 perioperative therapies (presented as a percentage: # of times therapy is used/# procedures). My sample size is small (N=25). The y-var, procedure interval, is nonparametric and continuous, but histogram distribution is Poisson-like. So far I'm working with GLM with Poisson family performing two separate regressions for medications and therapies due to the large number of independent variables but am wondering if there is a more correct model to use or way to present the data.
For the perioperative therapy model I'm wondering if it's more correct to use the procedural interval even though Poisson family utilizes counts and not continuous numbers, or if I should multiply both x and y variables by # procedures to work with whole numbers, and procedural window would be considered a count which has Poisson-like distribution.
An additional question - some of the perioperative therapies have some relation to each other. For example, I have use of a balloon dilator or rigid dilator as two separate binary variables. In procedures, either one or the other is used, and very rarely both or none will be used. Another set of variables is use of shaver, laser, cryoablation, or cold incision, where usually only one is used per operation but occasionally none and more rarely two modalities are used in one operation. How can I account for these interactions?
Thanks so much for your thoughts and help with this.
Your experimental setup seems quite complicated to me. Being not in your topic, it will be hard work for a statistician to grasp the important structures in your experiment / data. I therefore suggest to cooperate with a local statistician who can commit sufficient time to understand your problem and the context and work together with you on a solid analysis. I don't think that this will work via RG.
Very generally, my idea for an appropriate probability model for times (time windows - if I understood that correctly) would be the gamma distribution, which is, in fact, the "continuous counterpart" of the Poisson distribution. In contrast to the Poisson, the canonical link of the gamma is the inverse, but you can choose the log as link function as well (log is the canonical link of the Poisson).
And another hint I cannot suppress to give: please don't talk about "non-parametric variables" or "non-parametric data". This is a serious misnomer, producing a lot of confusion. I suppose you mean "non-Gaussian", what is really something different. The Poisson distribution is also a parametric distribution (the parameter is lambda, which determines [and equals] the expected value as well as the variance of the distribution). Essentially, almost any distribution that uses the actual quantity of the response (inlcuding simple counts of events or categories) is parametric. What can be "non-parametric" is the analysis of the data, and that can mean two things: either that the distribution model of the data is not described by any particular (->parametric) function but instead some empirically constructed frequency distribution is used as an approximation of the probability distribution (usually that of the interesting statistic, not of the data), and/or that not the data is used but only the rank-order information of that data.
Your experimental setup seems quite complicated to me. Being not in your topic, it will be hard work for a statistician to grasp the important structures in your experiment / data. I therefore suggest to cooperate with a local statistician who can commit sufficient time to understand your problem and the context and work together with you on a solid analysis. I don't think that this will work via RG.
Very generally, my idea for an appropriate probability model for times (time windows - if I understood that correctly) would be the gamma distribution, which is, in fact, the "continuous counterpart" of the Poisson distribution. In contrast to the Poisson, the canonical link of the gamma is the inverse, but you can choose the log as link function as well (log is the canonical link of the Poisson).
And another hint I cannot suppress to give: please don't talk about "non-parametric variables" or "non-parametric data". This is a serious misnomer, producing a lot of confusion. I suppose you mean "non-Gaussian", what is really something different. The Poisson distribution is also a parametric distribution (the parameter is lambda, which determines [and equals] the expected value as well as the variance of the distribution). Essentially, almost any distribution that uses the actual quantity of the response (inlcuding simple counts of events or categories) is parametric. What can be "non-parametric" is the analysis of the data, and that can mean two things: either that the distribution model of the data is not described by any particular (->parametric) function but instead some empirically constructed frequency distribution is used as an approximation of the probability distribution (usually that of the interesting statistic, not of the data), and/or that not the data is used but only the rank-order information of that data.
Hello Lena W Chen. I'll add two comments to the excellent response you've had from Jochen Wilhelm.
HTH.
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