## Power for Multilevel Analysis ## 1. [Centre for Multilevel Modelling: Sample sizes for multilevel models][1] using `MLPowSim` 2. [Introducing `powerlmm` an R package for power calculations for longitudinal multilevel models][2] * The purpose of `powerlmm` is to help design **longitudinal treatment studies**, with or without higher-level clustering (e.g. by therapists, groups, or physician), and missing data. * Currently, `powerlmm` supports two-level models, nested three-level models, and partially nested models. * Additionally, unbalanced designs and missing data can be accounted for in the calculations. * Power is calculated analytically, but simulation methods are also provided in order to evaluated bias, type 1 error, and the consequences of model misspecification. * For novice R users, the basic functionality is also provided as a Shiny web application. 3. [Power for linear models of longitudinal data with applications to Alzheimer’s Disease Phase II study design][3] using `longpower` * We will discuss power and sample size estimation for randomized placebo controlled studies in which the primary inference is based on the **interaction of treatment and time** in a **linear mixed effects model** (Laird and Ware, 1982). * We will demonstrate how the sample size formulas of (Liu and Liang, 1997) for **marginal** or model fit by generalized estimating equation (GEE) (Zeger and Liang, 1986) can be adapted for mixed effects models. * Finally, using mixed effects model estimates based on data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), we will give **examples of sample size calculations** for models with and without baseline covariates which may help explain **heterogeneity** in cognitive decline and improve power. 4. [`simR` an R package for power analysis of generalized linear mixed models by simulation][4] * The R package `simR` allows users to calculate power for **generalized linear mixed models** from the `lme4` package. The power calculations are based on Monte Carlo simulations. * It includes to 'ols' for * running a power analysis for a give n model and design * calculating powe rcurves to assess trade-offs between power and sample size * This paper presents a tutorial using a simple example of count data with mixed effects (with structure represen-tative of environmental monitoring data) to guide the user along a gentle learning curve, adding only a few com-mands or options at a time. [1]: http://www.bristol.ac.uk/cmm/learning/multilevel-models/samples.html [2]: http://rpsychologist.com/introducing-powerlmm [3]: https://cran.r-project.org/web/packages/longpower/vignettes/longpower.pdf [4]: http://xz6kg9rb2j.search.serialssolutions.com/?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.jtitle=Methods%20in%20Ecology%20and%20Evolution&rft.stitle=Methods%20Ecol%20Evol&rft.atitle=SIMR:%20an%20R%20package%20for%20power%20analysis%20of%20generalized%20linear%20mixed%20models%20by%20simulation&rft.volume=7&rft.issue=4&rft.spage=493&rft.epage=498&rft.date=2016-04-01&rft.aulast=Green&rft.aufirst=Peter&rft.issn=2041-210X&rft.eissn=2041-210X&rfr_id=info:sid/wiley.com:OnlineLibrary