This document provides an overview of generalized linear mixed models (GLMMs) for medical research: - GLMMs combine generalized linear models, which handle non-normal data distributions using link functions, and linear mixed models, which incorporate random effects. - When reporting GLMM analyses, it is important to adequately describe the statistical methods, research design, causal inference approach, model validation, and software/functions used. Previous reviews found much room for improvement in GLMM reporting quality. - Guidelines for standardized GLMM reporting in medical journals could help ensure the validity of conclusions by documenting the analysis methods generating the results.

1. 市 川 周 平
国⽴⼤学法⼈ 三重⼤学⼤学院 医学系研究科
地域医療学講座 助教
(介⼊研究での)
線形混合モデルの書き⽅
REQUIRE-23
2015/12/19 (⼟) 14:30-17:40
東京医科⻭科⼤学 1号館⻄7階 ⼝腔保健学科第3講義室

2. お品書き
 GLMMの概要
 GLMMの記載事項
 GLMMでの例数設計
 参考⽂献
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 4

3.  仮説検定
 ⽴てた仮説が正しいかどうかを検証
 統計的⼿法
 t検定, F検定
 分散分析 (ANOVA), 共分散分析 (ANCOVA)
 カイ⼆乗検定とその亜種 (OR, CMH, etc...)
 尤度⽐検定
 ノンパラメトリック検定
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 5
仮説検定とモデル推計

4.  モデル推計
 アウトカムを表現する数理モデルを設計
→ 現象をより良く表現できるモデルを探索
 統計的⼿法
 回帰分析 (単/重回帰, ポアソン, ロジスティック)
 線形混合モデル
 ⼀般化線形モデル
 ⼀般化線形混合モデル
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 6
仮説検定とモデル推計

5. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 7
Progress in Statistical Modeling
Linear Model
LM
Linear Model
LM
Generalized Linear Model
GLM
Generalized Linear Mixed
Model
GLMM
Hierarchical Bayes Model
HBM
according to Kubo (2012)

6. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 8
Linear Models (LM)
Y = α + βX + ε

7. Linear Models (LM)
50
100
150
200
0 500 1000 1500
Numberofcrime
sales of icecream (n)
残差 (residual)残差 (residual)
予測モデルで
説明できない誤差 (yi – Y)
回帰直線
(regression line)
回帰直線
(regression line)
2015/11/6 2015年度 統計学 / 基礎統計学 第14回 9

8.  ⼀般線形モデル (General Linear Model)
 t検定
 ANOVA/ANCOVA
 単/重回帰分析
 GLMの特殊な形
 正規性、等分散性、線形性、独⽴性
 LMMの特殊な形
 混合効果を含まない
 推定：最尤推定 (実質的には最⼩⼆乗推定)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 10
Linear Models (LM)

9. For simple analyses where the response variables are normal, all
treatments have equal sample sizes (i.e. the design is balanced)
and all random effects are nested effects, classical ANOVA
methods based on computing differences of sums of squares
give the same answers as ML approaches.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 11
Linear Models (LM)
Bolker et al. Trends Ecol Evol 2008. doi:10.116/j.tree.2008.10.008

10. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 12
Generalized Linear Models (GLM)
link(Y) = α + βX + ε

11.  ⼀般化線形モデル
 重回帰/単回帰分析
 ポアソン回帰
 ロジステック回帰
 正規分布以外の分布に拡張したLM
 Yにリンク関数をかませる
 前提から正規性、等分散性、線形性がはずれる
 前提：独⽴性
 推定：最尤推定
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 13
Generalized Linear Models (GLM)

12. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 14
Linear Mixed Models (LMM)
Y = (β0+bj) + (β1+bj)X + ε

13.  線形混合モデル
 マルチレベル分析
 ⼀般化推計⽅程式 (GEE)
 混合効果を含めたLM
 前提から独⽴性がはずれる
 前提：正規性、等分散性、線形性
 推定：最尤推定
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 15
Linear Mixed Models (LMM)

14. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 16
Generalized Linear Mixed Model
link(Y)
= (β0+bj) + (β1+bj)X + ε

15.  ⼀般化線形混合モデル (GLMM)
 混合効果を含むGLM
 ⾮正規分布に拡張したLMM
 別名
 階層的⼀般化線形モデル (HGLM)
 マルチレベル⼀般化線形モデル (MGLM)
 推定：いろいろ
 最尤推定
 マルコフ連鎖モンテカルロ法 (MCMC)
etc...
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 17
Generalized Linear Mixed Model

16.  ⼀般化線形混合モデル (GLMM)
 混合効果を含むGLM
 ⾮正規分布に拡張したLMM
Generalized linear mixed models (GLMMs) combine the
properties of two statistical frameworks that are widely used in
EE, linear mixed model (which incorporate random effects) and
generalized linear models (which handle nonnormal data by
using link functions and exponential family [e.g. normal, Poisson
or binomial] distributions)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 18
Generalized Linear Mixed Model
Bolker et al. Trends Ecol Evol 2008. doi:10.116/j.tree.2008.10.008

17. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 19
Relationships in Statistical Modeling
LM
Linear Model
LM
Linear Model
GLM
Generalized Linear
Model
GLM
Generalized Linear
Model
LMM
Linear Mixed
Model
LMM
Linear Mixed
Model
GLMM
Generalized Linear
Mixed Model
GLMM
Generalized Linear
Mixed Model
⾮正規分布
⾮線形
混合効果
混合効果
⾮正規分布
⾮線形
最尤推定
最尤推定
ベイズ推定, etc

18. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 20
医学研究でのGLMM
PLoS One 2014; 9: e112653.

19. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 21
反復測定
0
5
10
15
20
25
30
pre 2m 3m 5m 8m
BDIScore
TAU BtheB
測定点T個測定点T個
ベースライン1つベースライン1つ
Psych Med 2003; 33: 217-227.

20.  個体差を考慮したモデルを構築できる
 ベースライン : 切⽚モデル
 反応傾向 : 傾きモデル
 その両⽅ : 切⽚ + 傾きモデル
 ⽋測に強くなる
 ⽋測が⽣じても、【測定データが少なくとも⼀
つは存在する】可能性が⼤きくなる
⇒⽐較的弱いMAR (missing at random) 仮定の下
で⽋測を無視して解析できる
 サンプルサイズを低減できる? (仮説)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 22
介⼊研究でGLMMを⾏うメリット

21. お品書き
 GLMMの概要
 GLMMの記載事項
 GLMMでの例数設計
 参考⽂献
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 23

22.  Casals M, Girabent-Farres M, Carrasco JL.
 Methodological quality of reporting of
generalized linear mixed models in clinical
medicine (2000-2012): A systematic review.
 PLoS ONE 2014; 9: e112653.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 24
GLMMの適正報告

23.  研究デザインに関わる事項
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 25
GLMMの報告事項と報告率
報告事項* 報告数 (N=108)
1. データの形式
縦断研究かどうか 99 (91.7%)
反復測定かどうか 97 (89.8%)
階層データかどうか 108 (100%)
2. 分析の⽬的 108 (100%)
3. 研究デザイン 78 (72.2%)
PLoS One 2014; 9: e112653. *: ⾮報告例に不明確な情報を含む

24.  因果推論に関わる事項
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 26
GLMMの報告事項と報告率
報告事項 報告数 (N=108)
4. 固定効果の検定⽅法 5 (4.63%)
5. ランダム効果の検定⽅法 3 (2.78%)
6. ランダム効果の分散の推定 10 (9.26%)
7. 解析に⽤いたソフトウェア 98 (90.7%)
8. 解析に⽤いた関数とマクロ 42 (38.9%)
9. 推定⽅法 21 (19.4%)
10. 従属変数の分布 95 (88.0%)
PLoS One 2014; 9: e112653.

25.  モデルの検証に関する事項
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 27
GLMMの報告事項と報告率
報告事項 報告数 (N=108)†
11. 過分散の有無 10 (9.26%)
12. 過分散を測定したか 1 (0.93%)
13. 過分散への対処案の提案 8 (7.41%)
14. 変数選択の⽅法と基準 38 (35.2%)
15. モデルの適合性 17 (15.7%)
16. モデルの検証結果 7 (6.48%)
PLoS One 2014; 9: e112653.

26.  Our review also indicated that there is room for
improvement in quality when basic characteristics
about the GLMMs are reported in medical journals.
 It is important to adequately describe the
statistical methods used in the analysis.
 the validity of the conclusion is linked to the adequacy
of the methods used to generate the results.
 Standardized guidelines to report GLMM
characteristics in medicine could be beneficial, ......
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 28
Casals, et al. 2015の結論

27. 1. RQを明確にする
2. データの分布を確認し、リンク関数を選ぶ
3. ランダム効果の構造を特定する
4. パラメータの推定法を選ぶ
5. モデルを構築し、⽐較・検証する
 尤度⽐検定
 情報量基準 (AIC, BIC)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 30
LMM, GLMMでのモデリング

28. 1. RQを明確にする
2. データの分布を確認し、リンク関数を選ぶ
3. ランダム効果の構造を特定する
4. パラメータの推定法を選ぶ
5. 事前に定めた主解析・副解析を実施する
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 31
介⼊研究でのLMM, GLMM

29. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 32
介⼊研究でのGLMMの報告事項
報告事項
1. データの形式
3. 研究解析デザイン
7, 8. 解析に⽤いたソフトウェア, 関数, マクロ
9. 推定⽅法
10. 従属変数の分布
11-13. 過分散の取り扱い
based on PLoS One 2014; 9: e112653.

30.  階層性の有無
 多施設共同研究
 クラスターRCT
 fixedや共変量として取り扱うほどじゃないけど
影響が想定される因⼦
 反復測定の有無
 縦断研究かどうか
 介⼊研究なら基本的にあるはず
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 33
1. データの形式

31. Two-level and 3-level models utilized assessment occasions as
level 1 measurement units (ie, the baseline, postintervention,
and 3 follow-up assessment of unprotected vaginal and anal
intercourse), and participants as level 2 units. In the 3-level
models, the level 1 measurement units were assessment
occasions, which were nested within the level 2 units, study
participants, which, in turn, were nested within the level 3 units,
the 26 specific intervention groups (ie, the distinct coping or
support groups).
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 34
1. データの形式
J Acquir Immune Defic Syndr 2008; 47: 506-513.

32. The 3-level models were used to rule out differential group-level
effects (eg, therapist, group dynamics), which could confound
comparisons between study conditions. Because results did not
differ between 2- and 3-level models and there was no
significant group level effect, only 2-level models are reported.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 35
1. データの形式
J Acquir Immune Defic Syndr 2008; 47: 506-513.

33. To consult the models, we used the number of ADR reports as
the dependent variable, with individual observations (per month
per physician) as level 1, physicians as level 2, and spatial
clusters (as indicator variable) as level3; random-effects were
considered, both among physicians and among spatial
clusters.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 36
1. データの形式
JAMA 2006; 296: 1086-1093.

34.  切⽚モデル
Y = (β0+b0j) + β1*Group + β2*Time + β3*Group*Time + e
 傾きモデル
Y = β0 + β1*Group + (β1+b0j)*Time + β3*Group*Time + e
 切⽚ + 傾きモデル
Y = (β0+b0j) + β1*Group + (β1+b0j)*Time + β3*Group*Time + e
 Ancovaモデル
Y = bj(Ancova) + β0 + β1*Group + β2*Time + β3*Group*Time + e
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 37
3. 解析デザイン

35. We derived those estimates specifying a random intercept-
random slope generalized linear mixed model (GLMM) with a
logit link function and binomial family.
Generalized linear mixed models with random intercepts were
used to estimate the overall independent effects of participation
in physical activity on quality of life and to estimate the
independent interindividual (differences between participants)
and intraindividual (within-participant changes) effects of
physical activity on quality of life.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 38
3. 解析デザイン
Am J Respir Crit Care Med 2013; 187: 439-445.
J Clin Oncol 2008; 26: 4480-4487.

36.  ソフトウェア (90.7%) と⽐較して、関数・
マクロ (38.9%) は報告されない。
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 39
7. 解析環境
Bolker et al. Trends Ecol Evol 2008. doi:10.116/j.tree.2008.10.008
based on PLoS One 2014; 9: e112653.

37. To examine changes in the frequency of unprotected anal and
vaginal intercourse by intervention condition, generalized linear
mixed models (GLMMs) were employed, using the SAS macro
PROC GLIMMIX (SAS Institute, Inc., Cary, NC).
Analyses were performed using S-Plus 6.2 (Insightful Corp,
Seattle, Wash).
All data were double entered into a database and statistical
analyses were performed using Stata 12.1 (Stata Corp Lp,
College Station, TX) and R 2.15.0.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 40
7. 解析環境
J Acquir Immune Defic Syndr 2008; 47: 506-513.
JAMA 2006; 296: 1086-1093.
Am J Respir Crit Care Med 2013; 187: 439-445.

38.  LMM
 ML, FIML : Full Information Maximum Likelihood
 REML : REstricted Maximum Likelihood
 GLMM
 PQL : Pseudo- and penalized QuasiLlikelihood
 Laplace approximations
 GHQ : Gauss-Hermite quadrature
 MCMC : Markov chain Monte Carlo
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 41
9. 推定⽅法

39. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 42
9. 推定⽅法
⼿法 特徴
PQL  ランダム効果のSDが⼤きい場合、推定
結果にバイアスが乗る
 尤度を⽤いる⼿法が使えない
Laplace  真の尤度を近似
→ 尤度を⽤いた⼿法が使える
GHQ  Laplace近似より正確だけど重い
 mixedは3つくらいまで
MCMC  推定結果を事前確率とするベイズ推定
を数千〜数万回反復
 Bayesian flavorと技術的な困難
重さ
正確さ
重さ
正確さ
低低
⾼⾼ Bolker et al. Trends Ecol Evol 2008. doi:10.116/j.tree.2008.10.008

40. Generalized linear mixed model, using penalized quasilikelihood,
were applied to the statistical analysis.
We reported restricted maximum likelihood (REML) estimates, as
they provided better estimates of variance components.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 43
9. 推定⽅法
JAMA 2006; 296: 1086-1093.
Int J Cancer 2015; 137: 448-462.

41.  分布の種類
 normal
 Poisson
 binomial
 ゼロが重たい分布
 zero-inflated model
 hurdle model
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 44
10. 従属変数の分布

42. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 46
10. 従属変数の分布
 Zero-inflated model
Am J Drug Alcohol Abuse 2011; 37: 367-375.
真のゼロと偽のゼロを
⼆項分布で識別
真のゼロと偽のゼロを
⼆項分布で識別

43. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 48
10. 従属変数の分布
 Hurdle model
Am J Drug Alcohol Abuse 2011; 37: 367-375.
ゼロを超えたかどうかを
⼆項分布で識別
ゼロを超えたかどうかを
⼆項分布で識別

44. Because the dependent variable was a count outcome, a Poisson
generalized linear mixed model was used.
A mixed effects with (random effect for subject) logistic
regression model was used to compare the proportion of
positive responders for CFP-10 and ESAT-6, between the
treatment arms. The quantitative responses were zero inflated
and severely over dispersed. To allow this, a mixed effects
Tweedie (compound Poisson) model was fitted using the R
package cplm.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 49
10. 従属変数の分布
Am J Repir Crit Care Med 2013; 187: 439-445.
JAMA 2006; 296: 1086-1093.

45.  過分散 (over/under-dispersion) とは
 過⼤分散: 分散が期待値より⼤きくなること
 過⼩分散: 分散が期待値より⼩さくなること
ex: Poisson分布
 平均 = SDとなる分布。
→SDが平均値から⼤きくずれれば、over/under-
dispersionを疑う
⇒分布あるいは推定⽅法の⾒直し
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 50
11-13. 過分散の取り扱い

46. The quantitative responses were zero inflated and severely over
dispersed. To allow this, a mixed effects Tweedie (compound
Poisson) model was fitted using the R package cplm.
Because the Poisson assumption (that the mean and variance of
the dependent variable are equal) was not met in our data, the
models were adjusted taking the overdispersion parameter into
account.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 51
11-13. 過分散の取り扱い
Am J Repir Crit Care Med 2013; 187: 439-445.
JAMA 2006; 296: 1086-1093.

47. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 52
介⼊研究でのGLMMの報告事項
報告事項
1. データの形式
3. 研究解析デザイン
7, 8. 解析に⽤いたソフトウェア, 関数, マクロ
9. 推定⽅法
10. 従属変数の分布
11-13. 過分散の取り扱い
based on PLoS One 2014; 9: e112653.

48. Four important characteristics to consider when specifying
analyses for longitudinal clinical trials include: (1) the
mechanism(s) giving rise to the missing data; (2) the
correlations between repeated measures on each patient; (3) the
time trends; and (4) the statistical distribution that best
describes the looklihood of various outcomes.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 53
Mallinckrodt CH.
Mallinckrodt CH. Preventing and Treating Missing Data in Longitudinal Clinical Trials. 2013.

49.  縦断研究では、患者 (被験者) 内相関を考慮
する
 推定結果の効率性と精度が向上する
 ⽋測がある場合、妥当な推定結果を得るために、
共分散に基づいてモデルを修正する
 相関構造への配慮
 共変量のパターンを制限しない
 共変量のパターンを特定の構造を基に制限する
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 54
ex. 従属変数の相関構造
Applied Longitudinal Analysis (2nd ed). 2011.

50. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 58
ex. 従属変数の相関構造
Unstructured
Compound
Symmetry
Auto-
regressive
データ構造
N：⼤
測定回数：少
測定回数と⽐較して
Nが⼩さい
データの種類 - 客観指標 主観指標
相関の原因 -
患者固有の
要素
経時変化
Mallinckrodt CH. Preventing and Treating Missing Data in Longitudinal Clinical Trials. 2013.

51. Separate mixed-effects models were fit for each of those
outcomes, which were measured repeatedly at baseline, 6
months, and 12 months. Main effects of treatment group and
time, as well as the treatment group x time interaction effect
were examined in the mixed-effect models using the
unstructured dependence structure.
We used baseline scores as a dependent variable, the cluster was
represented by random effect, and the within patient covariance
structure was unstructured.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 59
ex. 従属変数の相関構造
JAMA 2010; 304: 1795-1802.
BMJ 2014; 349: g5392.

52.  事前に定める主解析は柔軟にしておく
 相関構造の事前想定が⼤雑把だと収束しない
The final analysis of the trial will be carried out on an intention-
to-treat basis. The freedom of the clusters to fill in the precise
implementation of the intervention will probably relate to the
(cost)-effectiveness of the intervention and, therefore, the
clustering of patients in GP practices should be taken into
consideration in the analysis. Therefore, the results will be
investigated with respect to the differences in intensity between
and within clusters over time using multi-level analysis.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 60
ex. 従属変数の相関構造
BMC Pulm Med 2013; 13: 17, the protocol paper for BMJ 2014; 349: g5392.
Mallinckrodt CH. Preventing and Treating Missing Data in Longitudinal Clinical Trials. 2013.

53. お品書き
 GLMMの概要
 GLMMの記載事項
 GLMMでの例数設計
 参考⽂献
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 61

54. 丹後俊郎. 継時的繰り返し測定デザイン. 東京; 朝倉書店: 2015.
190-209.
Tango T. On the repeated measures designs and sample sizes
for randomized controlled trial. Biostatistics 2015; pil: kxv. [e-
pub, ahead of print]
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 64
詳しくは以下を参照

55. 2015/12/19 REQUIRE23 Generalized Linear Mixed Model 65
1:Tモデル
0
5
10
15
20
25
30
pre 2m 3m 5m 8m
BDIScore
TAU BtheB
測定点T個測定点T個
ベースライン1つベースライン1つ
Psych Med 2003; 33: 217-227.

56.  あ
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 66
S:Tデザイン
測定点T個測定点T個
ベースラインS個ベースラインS個
NEJM 1998; 338: 861-6.

57.  個体差を考慮したモデルを構築できる
 ベースライン : 切⽚モデル
 反応傾向 : 傾きモデル
 その両⽅ : 切⽚ + 傾きモデル
 ⽋測に強くなる
 ⽋測が⽣じても、【測定データが少なくとも⼀
つは存在する】可能性が⼤きくなる
⇒⽐較的弱いMAR (missing at random) 仮定の下
で⽋測を無視して解析できる
 サンプルサイズを低減できる? (仮説)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 69
介⼊研究でGLMMを⾏うメリット

58.  個体差を考慮したモデルを構築できる
 ベースライン : 切⽚モデル
 反応傾向 : 傾きモデル
 その両⽅ : 切⽚ + 傾きモデル
 ⽋測に強くなる
 ⽋測が⽣じても、【測定データが少なくとも⼀
つは存在する】可能性が⼤きくなる
⇒⽐較的弱いMAR (missing at random) 仮定の下
で⽋測を無視して解析できる
 サンプルサイズを低減できる? (仮説)
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 72
介⼊研究でGLMMを⾏うメリット
GLMMのメリットGLMMのメリット
1:Tモデルのメリット1:Tモデルのメリット
S:TモデルのメリットS:Tモデルのメリット

59. Figuerias A, Herdeiro MT, Polonia J, Gestal-Otero JJ.
An educational intervention to improve physician
reporting of adverse drug reactions.
JAMA 2006; 296: 1086-193.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 78
S:Tモデルの解析

60. To consult the models, we used the number of ADR reports as
the dependent variable, with individual observations (per month
per physician) as level 1, physicians as level 2, ...... To measure
the intervention effect, a dichotomous indicator variable was
created. This variable (period) assumed a value of 0 for baseline
period and a value of 1 for months between the start of the
intervention and the end of the follow-up. The intervention
effect was evaluated on the basis of the interaction between the
group (1 for intervention group, 0 for control group) and period
variables.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 79
S:Tモデルの解析
JAMA 2006; 296: 1086-1093.

61. お品書き
 GLMMの概要
 GLMMの記載事項
 GLMMでの例数設計
 参考⽂献
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 81

62.  安藤正⼈ 2011: マルチレベル分析⼊⾨
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 82
参考図書

63.  安藤正⼈ 2011: データ解析のための統計モ
デリング⼊⾨
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 83
参考図書

64.  丹後俊郎 2015: 経時的繰り返し測定デザイ
ン
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 84
参考図書

65.  Fitzmaurice GM, Laird NM, Ware JH. Applied
Longitudinal Analysis (2nd ed).
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 85
参考図書

66.  Mallinckrodt CH. Preventing and treating
missing data in longitudinal clinical trials.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 86
参考図書

67. Casals M, Girabent-Farres M, Carrasco JL. Methodological
quality and reporting of generalized linear mixed models in
clinical medicine (2000-2012): A Systematic Review. PLoS ONE
2014; 9: e112653.
Thiele J, Markussen B. Potential of GLMM in modelling invasive
spread. CAB rev 2012; 7: 1-10.
Bolker BM, Brooks ME, Clark CJ, et al. Generalized linear mixed
models: a practical guide for ecology and evolution. Trends
ecol evol 2008; 24: 127-135.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 87
解説論⽂

68. Tango T. On the repeated measures designs and sample sizes
for randomized controlled trials. Biostatistics 2015; kxv047: 1-6.
Hu MC, Pavlicova M. Nunes EV. Zero-inflated and hurdle
models of count data with extra zeros: examples from an HIV-
RISK reduction intervention trial. Am J Drug Alcohol Abuse
2011; 37: 367-375.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 88
解説論⽂ (統計的なこと)

69. Figueiras A, Herdeiro MT, Polonia J, et al. An educational
intervention to improve physician reporting of adverse drug
reaction. A cluster-randomized controlled trial. JAMA 2006;
296: 1086-1093.
Sikkema KJ, Wilson PA, Hansen NB, et al. Effects of a coping
intervention on transmission risk behavior among people
living with HIV/AIDS and a history of childhood sexual abuse. J
Acquir Immune Defic Syndr 2008; 47: 506-513.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 89
介⼊研究の報告

70. Adetifa IM, Ota MOC, Jeffries DJ, et al. Interferon-γ ELISPOT as
biomarker of treatment efficacy in latent tuberculosis infection.
A clinical trial. Am J Respir Crit Care Med 2013; 187: 439-445.
Kruis AL, Boland MRS, Assendelft WJJ, et al. Effectiveness of
integrated disease management for primary care chronic
obstructive pulmonary disease patients: results of cluster
randomized trial. BMJ 2014; 349: g5392.
Kruis AL, Boland MRS, Shoonvelde CH, et al. RECODE: Design
and baseline results of a cluster randomized trial on cost-
effectiveness of integrated COPD management in primary care.
BMC Plum Med 2013; 13: 17.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 90
介⼊研究の報告

71. Goodpaster BH, Delany JP, Otto AD. Effects of diet and physical
activity interventions on weight loss and cardiometabolic risk
factors in severely obese adults. JAMA 2010; 304: 1795-1802.
Lynch BM, Cerin E, Owen N, et al. Prospective relationships of
physical activity with quality of life among colorectal cancer
survivors. J Clin Oncol 2008; 26: 4480-4487.
Edefonti V, Hashibe M, Parpinel M, et al. Natural vitamin C
intake and the risk of head and neck cancer: A pooled analysis
in the International Head and Neck Cancer Epidemiology
Consortium. Int J Cancer 2015; 137: 448-462.
2015/12/19 REQUIRE23 Generalized Linear Mixed Model 91
介⼊研究の報告

72. FIN
2015/12/19 REQUIRE23 Generalized Linear Mixed Model