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From |
Rebecca Pope <rebecca.a.pope@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: odd simulation results for ICC with binary outcomes |

Date |
Fri, 15 Feb 2013 11:19:15 -0600 |

For background, I'm in the midst of a project to assess the reliability of measures of physician quality. These quality measures are scored 0 (recommended care not provided) or 1 (recommended care provided). The powers that be suggested using -loneway- to find the reliability of the different measures. In the interest of full disclosure, ANOVA is not in my usual toolkit, but my understanding is that it is a linear random effects model and something didn't seem right about this for binary data. With performance here being a series of binomial trials (yes/no recommended care), the beta-binomial is a natural fit. I decided I'd run some simulations and see how the results differ. I focused on the intraclass correlation (ICC) for now. My thinking was that the ICC would make the best comparison since expected values can be calculated directly from beta shape parameters (Guimaraes, 2005) and I would have a known true value to test against. However, while the two estimates of the ICC are different, the ICC estimate produced by the beta-binomial simulations is not the correct ICC while the ANOVA analysis does converge to the correct value. The data was generated by a beta-binomial process, so if anything should produce that value, it should be a beta-binomial model, no? My code is below. I ran this for different sample sizes (for which I can also send the code if that is helpful), but except for very small sample sizes, the results regarding the ICC are invariant to the number of observations per group. I would be inclined to attribute this to an as yet undiscovered error in my code, but the a, b, mean, and variance parameters are appropriately recovered. The mean of the beta(5,5) is 0.5. The variance is approximately 0.0227. The ICC of a sample drawn from a beta(5,5) should be about 0.091 (see Guimaraes, 2005). Are these results surprising to anyone else? Does any one see any error in my code to which this could be attributed? Thanks so much for any help, Rebecca *** begin code *** set seed 72114 set more off capture program drop betabinsim program define betabinsim, rclass version 12 syntax [, a(real 5) b(real 5) groups(integer 135) n(real 100)] drop _all tempvar group foo event set obs `groups' gen `group' = _n // pseudo-identifiers for physician groups gen y1 = rbinomial(`n', rbeta(`a',`b')) // draw successes for each group around beta(a,b) gen y0 = `n'-y1 // failues for each PFSA // Set-up for beta-binomial reshape long y, i(`group') j(`event') // Guimaraes (2005) procedure for estimating beta-binomial parameters xtnbreg y `event', i(`group') fe nolog local alpha exp(_b[_cons]+_b[`event']) local beta exp(_b[_cons]) return scalar n = `n' return scalar a = `alpha' return scalar b = `beta' return scalar mu = `alpha'/(`alpha'+`beta') return scalar icc = 1/(`alpha'+`beta'+1) // Set-up for ANOVA expandcl y, cluster(`group' `event') generate(`foo') // Run ANOVA & save ICC loneway `event' `group' return scalar icc_anova = `r(rho)' end simulate sampsi=r(n) alpha=r(a) beta=r(b) mu=r(mu) icc=r(icc) icc_anova=r(icc_anova), reps(10000): betabinsim local truerho = 1/(1+5+5) ttest icc==icc_anova, unpaired ttest icc ==`truerho' ttest icc_anova == `truerho' *** end *** References: Guimaraes, P. (2005) A simple approach to fit the beta-binomial model. The Stata Journal, 5(3), 385-394. Available at: http://www.stata-journal.com/article.html?article=st0089 * * 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/

**Follow-Ups**:**Re: st: odd simulation results for ICC with binary outcomes***From:*Austin Nichols <austinnichols@gmail.com>

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