powerlmm
powerlmm 0.4.0
縦方向のマルチレベル/線形混合効果モデルの電力分析。
powerlmmの目的は、高レベルのクラスタリング（例えば、セラピスト、グループ、または医師によって縦断的にクラスター化された）、および欠落データの有無にかかわらず、縦断的治療研究（並列グループ）の設計を支援することです。パッケージの主な機能は次のとおりです。
powerlmm 、CranとGithubからインストールできます。
# CRAN, version 0.4.0
install.packages( " powerlmm " )
# GitHub, dev version
devtools :: install_github( " rpsychologist/powerlmm " )これは、主題レベルとクラスターレベルの両方でランダムな勾配を使用して、3レベルの縦方向モデルをセットアップし、治療群ごとに異なるデータパターンを失います。相対標準化された入力が使用されますが、標準化されていない生パラメーター値も使用できます。
library( powerlmm )
d <- per_treatment( control = dropout_weibull( 0.3 , 2 ),
treatment = dropout_weibull( 0.2 , 2 ))
p <- study_parameters( n1 = 11 ,
n2 = 10 ,
n3 = 5 ,
icc_pre_subject = 0.5 ,
icc_pre_cluster = 0 ,
icc_slope = 0.05 ,
var_ratio = 0.02 ,
dropout = d ,
effect_size = cohend( - 0.8 ,
standardizer = " pretest_SD " ))
p
# >
# > Study setup (three-level)
# >
# > n1 = 11
# > n2 = 10 x 5 (treatment)
# > 10 x 5 (control)
# > n3 = 5 (treatment)
# > 5 (control)
# > 10 (total)
# > total_n = 50 (treatment)
# > 50 (control)
# > 100 (total)
# > dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
# > 0, 0, 1, 3, 6, 9, 12, 16, 20, 25, 30 (%, control)
# > 0, 0, 1, 2, 4, 5, 8, 10, 13, 17, 20 (%, treatment)
# > icc_pre_subjects = 0.5
# > icc_pre_clusters = 0
# > icc_slope = 0.05
# > var_ratio = 0.02
# > effect_size = -0.8 (Cohen's d [SD: pretest_SD]) plot( p )get_power( p , df = " satterthwaite " )
# >
# > Power Analyis for Longitudinal Linear Mixed-Effects Models (three-level)
# > with missing data and unbalanced designs
# >
# > n1 = 11
# > n2 = 10 x 5 (treatment)
# > 10 x 5 (control)
# > n3 = 5 (treatment)
# > 5 (control)
# > 10 (total)
# > total_n = 50 (control)
# > 50 (treatment)
# > 100 (total)
# > dropout = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (time)
# > 0, 0, 1, 3, 6, 9, 12, 16, 20, 25, 30 (%, control)
# > 0, 0, 1, 2, 4, 5, 8, 10, 13, 17, 20 (%, treatment)
# > icc_pre_subjects = 0.5
# > icc_pre_clusters = 0
# > icc_slope = 0.05
# > var_ratio = 0.02
# > effect_size = -0.8 (Cohen's d [SD: pretest_SD])
# > df = 7.971459
# > alpha = 0.05
# > power = 68%不均等なクラスターサイズもサポートされており、クラスターサイズはランダム（サンプリング）か、周辺分布を指定できます。
p <- study_parameters( n1 = 11 ,
n2 = unequal_clusters( 2 , 3 , 5 , 20 ),
icc_pre_subject = 0.5 ,
icc_pre_cluster = 0 ,
icc_slope = 0.05 ,
var_ratio = 0.02 ,
effect_size = cohend( - 0.8 ,
standardizer = " pretest_SD " ))
get_power( p )
# >
# > Power Analyis for Longitudinal Linear Mixed-Effects Models (three-level)
# > with missing data and unbalanced designs
# >
# > n1 = 11
# > n2 = 2, 3, 5, 20 (treatment)
# > 2, 3, 5, 20 (control)
# > n3 = 4 (treatment)
# > 4 (control)
# > 8 (total)
# > total_n = 30 (control)
# > 30 (treatment)
# > 60 (total)
# > dropout = No missing data
# > icc_pre_subjects = 0.5
# > icc_pre_clusters = 0
# > icc_slope = 0.05
# > var_ratio = 0.02
# > effect_size = -0.8 (Cohen's d [SD: pretest_SD])
# > df = 6
# > alpha = 0.05
# > power = 44%クラスターサイズはポアソン分布に続きます
p <- study_parameters( n1 = 11 ,
n2 = unequal_clusters( func = rpois( 5 , 5 )), # sample from Poisson
icc_pre_subject = 0.5 ,
icc_pre_cluster = 0 ,
icc_slope = 0.05 ,
var_ratio = 0.02 ,
effect_size = cohend( - 0.8 ,
standardizer = " pretest_SD " ))
get_power( p , R = 100 , progress = FALSE ) # expected power by averaging over R realizations
# >
# > Power Analyis for Longitudinal Linear Mixed-Effects Models (three-level)
# > with missing data and unbalanced designs
# >
# > n1 = 11
# > n2 = rpois(5, 5) (treatment)
# > - (control)
# > n3 = 5 (treatment)
# > 5 (control)
# > 10 (total)
# > total_n = 24.96 (control)
# > 24.96 (treatment)
# > 49.92 (total)
# > dropout = No missing data
# > icc_pre_subjects = 0.5
# > icc_pre_clusters = 0
# > icc_slope = 0.05
# > var_ratio = 0.02
# > effect_size = -0.8 (Cohen's d [SD: pretest_SD])
# > df = 8
# > alpha = 0.05
# > power = 48% (MCSE: 1%)
# >
# > NOTE: n2 is randomly sampled. Values are the mean from R = 100 realizations.たとえば、電力曲線を作成するためのいくつかの利便性関数も含まれています。
x <- get_power_table( p ,
n2 = 5 : 10 ,
n3 = c( 4 , 8 , 12 ),
effect_size = cohend(c( 0.5 , 0.8 ), standardizer = " pretest_SD " ))plot( x )パッケージには、さまざまなモデルのパフォーマンスを簡単に調査できる柔軟なシミュレーション方法が含まれています。例として、2レベルのLMMのパワーの違いを、ポストテストでANCOVAを実行する11の繰り返し測定と比較しましょう。 sim_formulaを使用すると、シミュレーション中に異なるモデルが同じデータセットに適合できます。
p <- study_parameters( n1 = 11 ,
n2 = 40 ,
icc_pre_subject = 0.5 ,
cor_subject = - 0.4 ,
var_ratio = 0.02 ,
effect_size = cohend( - 0.8 ,
standardizer = " pretest_SD " ))
# 2-lvl LMM
f0 <- sim_formula( " y ~ time + time:treatment + (1 + time | subject) " )
# ANCOVA, formulas with no random effects are with using lm()
f1 <- sim_formula( " y ~ treatment + pretest " ,
data_transform = transform_to_posttest ,
test = " treatment " )
f <- sim_formula_compare( " LMM " = f0 ,
" ANCOVA " = f1 )
res <- simulate( p ,
nsim = 2000 ,
formula = f ,
cores = parallel :: detectCores( logical = FALSE ))次に、 summaryを使用して結果を要約します。治療効果を特に見てみましょう。
summary( res , para = list ( " LMM " = " time:treatment " ,
" ANCOVA " = " treatment " ))
# > Model: summary
# >
# > Fixed effects: 'time:treatment', 'treatment'
# >
# > model M_est theta M_se SD_est Power Power_bw Power_satt
# > LMM -1.1 -1.1 0.32 0.32 0.93 0.93 .
# > ANCOVA -11.0 0.0 3.70 3.70 0.85 0.84 0.84
# > ---
# > Number of simulations: 2000 | alpha: 0.05
# > Time points (n1): 11
# > Subjects per cluster (n2 x n3): 40 (treatment)
# > 40 (control)
# > Total number of subjects: 80
# > ---
# > At least one of the models applied a data transformation during simulation,
# > summaries that depend on the true parameter values will no longer be correct,
# > see 'help(summary.plcp_sim)'また、特定のモデルを見ることができます。2-LVL LMMの結果は次のとおりです。
summary( res , model = " LMM " )
# > Model: LMM
# >
# > Random effects
# >
# > parameter M_est theta est_rel_bias prop_zero is_NA
# > subject_intercept 99.00 100.0 -0.00560 0 0
# > subject_slope 2.00 2.0 -0.00310 0 0
# > error 100.00 100.0 0.00086 0 0
# > cor_subject -0.39 -0.4 -0.03200 0 0
# >
# > Fixed effects
# >
# > parameter M_est theta M_se SD_est Power Power_bw Power_satt
# > (Intercept) 0.0048 0.0 1.30 1.30 0.050 . .
# > time 0.0011 0.0 0.25 0.25 0.054 . .
# > time:treatment -1.1000 -1.1 0.32 0.32 0.930 0.93 .
# > ---
# > Number of simulations: 2000 | alpha: 0.05
# > Time points (n1): 11
# > Subjects per cluster (n2 x n3): 40 (treatment)
# > 40 (control)
# > Total number of subjects: 80
# > ---
# > At least one of the models applied a data transformation during simulation,
# > summaries that depend on the true parameter values will no longer be correct,
# > see 'help(summary.plcp_sim)' パッケージの基本的な機能は、R.に慣れていないユーザーを対象とした光沢のあるWebアプリケーションにも実装されています。
library( powerlmm )
shiny_powerlmm()
