two way within-subject Anova for Centile results on categorical data
Statalisters-
I'd appreciate advice on the following data.
We are studying drug dosages used in two types of operations, using data taken from 30 different hospitals.
Operation 1 generally requires more drug than operation 2, and the distribution of drug used is very skewed. Thus we chose to use median, 80th percentile, and other centile results to describe the distribution for drug used at each hospital for each operation.
Hospitals have different cultures; some use lots of drug, some less drug, but in general, operation 1 requires more drug than operation 2, though the "low-drug" operation at one hospital may be higher than the high-drug operation at another hospital. It's all relative to local culture.
Initially I performed a paired t-test at each centile, which compared, for example, the 80th percentile drug dose for operation 1 against the same percentile drug dose for operation 2, which basically looked at the difference at each hospital, calculated the mean and SD of the difference across all hospitals and showed that it was not 0. All of the centile comparisons were highly significant, but we had 6 centiles, thus 6 paired t-tests and I needed to reduce the SDs and p values for multiple comparisons. Bonferroni seems overly conservative since the centile results are related.
I thought that my paired t-test approach was theoretically the same as a one-level within-subject Anova, limiting the anova to one centile at a time. Wonder if the different centiles are a form of Repeated Measure.
Thus, how can I use a 2-way within-subject anova (my guess at the structure) to comment about the overall difference between Operation 1 and Operation 2 (step 1), then perform a post-hoc analysis to look at individual centiles. I don't care about the differences between hospitals for this Operation1 vs Operation2 analysis.
I have performed kruskal Wallis comparing Operation 1 to Operation 2 over all the primary data not separated by hospital before generating centile data, but this seems to miss the extra information contained by knowing the difference at each hospital. (There are other reasons, too, that I need to perform the analysis on a per-hospital basis)
Demonstration data is below-- can't include the real data. I specifically made the 90th percentile data not different Operation1 vs Operation2, to see if I can detect that.
Sorry about the length of the question.
Thanks much.
Mitchell Berman
Columbia University
I'd appreciate advice on the following data.
We are studying drug dosages used in two types of operations, using data taken from 30 different hospitals.
Operation 1 generally requires more drug than operation 2, and the distribution of drug used is very skewed. Thus we chose to use median, 80th percentile, and other centile results to describe the distribution for drug used at each hospital for each operation.
Hospitals have different cultures; some use lots of drug, some less drug, but in general, operation 1 requires more drug than operation 2, though the "low-drug" operation at one hospital may be higher than the high-drug operation at another hospital. It's all relative to local culture.
Initially I performed a paired t-test at each centile, which compared, for example, the 80th percentile drug dose for operation 1 against the same percentile drug dose for operation 2, which basically looked at the difference at each hospital, calculated the mean and SD of the difference across all hospitals and showed that it was not 0. All of the centile comparisons were highly significant, but we had 6 centiles, thus 6 paired t-tests and I needed to reduce the SDs and p values for multiple comparisons. Bonferroni seems overly conservative since the centile results are related.
I thought that my paired t-test approach was theoretically the same as a one-level within-subject Anova, limiting the anova to one centile at a time. Wonder if the different centiles are a form of Repeated Measure.
Thus, how can I use a 2-way within-subject anova (my guess at the structure) to comment about the overall difference between Operation 1 and Operation 2 (step 1), then perform a post-hoc analysis to look at individual centiles. I don't care about the differences between hospitals for this Operation1 vs Operation2 analysis.
I have performed kruskal Wallis comparing Operation 1 to Operation 2 over all the primary data not separated by hospital before generating centile data, but this seems to miss the extra information contained by knowing the difference at each hospital. (There are other reasons, too, that I need to perform the analysis on a per-hospital basis)
Demonstration data is below-- can't include the real data. I specifically made the 90th percentile data not different Operation1 vs Operation2, to see if I can detect that.
Sorry about the length of the question.
Thanks much.
Mitchell Berman
Columbia University
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input byte inst float operation byte centiles int dose 1 1 50 30 1 2 50 28 1 1 80 45 1 2 80 46 1 1 90 55 1 2 90 55 1 1 95 76 1 2 95 70 2 1 50 60 2 2 50 40 2 1 80 90 2 2 80 91 2 1 90 120 2 2 90 120 2 1 95 160 2 2 95 155 3 1 50 15 3 2 50 15 3 1 80 20 3 2 80 21 3 1 90 30 3 2 90 36 3 1 95 38 3 2 95 36 4 1 50 50 4 2 50 45 4 1 80 60 4 2 80 55 4 1 90 63 4 2 90 67 4 1 95 85 4 2 95 84 end
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