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From |
ymarchenko@stata.com (Yulia Marchenko, StataCorp) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Sample size for four-level logistic regression |

Date |
Fri, 21 Jun 2013 17:48:36 -0500 |

Clyde Schechter <clyde.schechter@gmail.com> asks several questions about sample-size determination for a four-level random-effects logistic model. I will address some of Clive's questions below. > Our intervention would be randomized at the level of institutions, which > have a few levels of outcome-relevant internal hierarchy themselves. The > outcome is dichotomous and is fairly rare: around 2.5 "successes" per 1,000 > observations. (Observations within institutions will be relatively > plentiful and inexpensive to obtain electronically, although limited by the > number of discharges per year they handle. The limit on feasibility will be > the number of institutions, each of which will need resources to implement > the intervention and program their data collection.) Ultimately, the > analysis will require a 4-level logistic regression. > > I need to get a sense of how many institutions would need to be recruited > for the study: if too large, it's a dead letter. > > ... > > By any chance, will the expanded sample size calculations supported in > Stata 13 handle this? The new -power- command does not provide a sample-size computation for the design that Clive describes. > ... > Plan A was to do simulations. > ... If Clive decides to pursue the simulation approach, he may benefit from a forthcoming feature of the -power- command that will allow access to -power-'s tables and graphs for user-specified power computations. I will talk more about this feature at the upcoming Stata Conference in New Orleans. This feature is not yet available in Stata 13, so Clive would not be able to benefit from it immediately. > ... > The problem is that in the simulations, each replication (analysis of a > single simulated sample) takes 2 hours to run on my setup, even with the > Laplace approximation. For even one candidate number of institutions and > set of assumptions about variance components, I will need about 500 > replications to get reasonable precision on the power. So we're talking > months here. > ... > Or is its (Stata 13) speedup in runtime for xtmelogit so great that it will > deliver me from this problem? In general, we find the new -melogit- command to be approximately 4 to 10 times faster than the old -xtmelogit- command. There are models for which the speed increase is greater. It is difficult, however, to comment on the speed increase in Clive's situation without running timings for his design. We ran a quick comparison of the timings from the new -melogit- command and the old -xtmelogit- command fitting a 4-level nested random-intercept logistic model with a rare outcome using adaptive Gaussian quadrature with 7 integration points. The model had 30 groups at the fourth level, 150 groups at the third level, and 600 groups at the second level. The number of observations per group varied between 4 and 60. The total number of observations was 1800. The new command took 100 seconds to execute and the old command took 739 seconds to execute. We also considered models with a smaller and larger total numbers of observations. We found the new command to be approximately 5 to 7 times faster than the old command for the considered models. --Yulia ymarchenko@stata.com * * 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/

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