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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Re: Mixed models for repeated measures |

Date |
Sat, 6 Oct 2012 11:16:58 +0900 |

Avi Zakai wrote: I have data for the comparison of a new treatment for eye disease versus two control groups. My response (Y) is an ordinal variable with 8 levels. I have the group variable (X), and for every subject (S), I have two measurments, representing the two eyes ! I need to run a model to compare the different treatments, while taking into account the inner correlation within a subject, and I need to do it with STATA 12. I was thinking about mixed models, however no matter what I tried, I got error messages. I would like to ask, what is the syntax I need to write in order to run a mixed model of Y=bX+e where e~N(0,R). The correlation between the eyes is 0.6, there is no structure since it's only 2 measurments. This model assumes normallity, it's the best I could think of, is there a better model in STATA for my ordinal scale ? -------------------------------------------------------------------------------- In addition to what Jay and Joerg have mentioned, you can scan through the do-file below to glean some ideas on how to proceed. (Start at the "Begin here" comment. The first portion just sets up a fake dataset for illustration.) If you have reason to believe that there will be a left-right difference (for example, different doses of a topical ophthalmic drug are instilled into each eye), then you can use the treatment-by-side interaction term in the model. Otherwise, I would sum the left and right eyes' scores for a single response per patient. This has a couple of advantages. First, sumscores are more likely to be more normal-like (think: Rensis Likert), albeit, as Jay mentions, with eight categories, you might not need to worry a whole lot about that. (Do check your residuals.) Second, you can use ordinary least squares linear regression. If you're writing clinical protocol's "Statistical Considerations" section or the associated statistical analysis plan, then another consideration is the potential for a clinic-by-treatment interaction. Referees (whether for scientific journals or in government health ministries) usually want this addressed. For the same audience, you'll need to think carefully about the delta, regardless of whether you're conducting so-called noninferiority comparisons between your different treatments. Joseph Coveney version 11.2 clear * set more off set seed `=date("2012-10-06", "YMD")' quietly set obs 210 generate int pid = _n generate byte group = mod(_n, 3) generate double u = rnormal() forvalues side = 0/1 { generate double latent`side' = /// 0.5 * (group != 0) + /// 0 * (`side' - 1/2) + /// 1 * u + /// 1 * rnormal() } quietly reshape long latent, i(pid) j(side) generate double manifest = normal(latent) generate double response = 0 quietly forvalues cut = 1/7 { replace response =`cut' if `cut' / 8 < manifest } label variable response "Therapeutic Response Score" label define Groups 0 Placebo 1 Active 2 Experimental label values group Groups label variable group "Treatment Group" label define Sides 0 L 1 R label values side Sides label variable side Eye tabulate response group if side == "L":Sides sort pid side list group pid side response in 1/6, noobs sepby(pid) * * Begin here * // Linear model xtreg response i.group##i.side, i(pid) mle nolog estimates store Full xtreg response i.group i.side, i(pid) mle nolog lrtest Full test 2.group // "Superiority" (to placebo control treatment) lincom 2.group - 1.group, level(95) // "Noninferiority" (to reference drug) lincom 2.group - 1.group, level(90) // "Therapeutic Equivalence" // Generalized linear model quietly xi i.group*i.side gllamm response _I*, i(pid) family(binomial) link(ologit) adapt // nolog estimates store Full gllamm response _Igroup_? _Iside_1, i(pid) family(binomial) link(ologit) /// adapt // nolog lrtest Full test _Igroup_2 lincom _Igroup_2 - _Igroup_1, level(95) lincom _Igroup_2 - _Igroup_1, level(90) // Alternative (also see -findit gologit2-) ologit response i.group##i.side, cluster(pid) nolog test 1.group#1.side, notest test 2.group#1.side, accumulate ologit response i.group i.side, cluster(pid) nolog test 2.group lincom 2.group - 1.group, level(95) lincom 2.group - 1.group, level(90) exit * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Mixed models for repeated measures***From:*Avi Zakai <aviz@trdf.technion.ac.il>

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