Modeling Mood Variation and Covariation among Adolescent Smokers: Application of a Bivariate Location-Scale Mixed-Effects Model

Transcription

1 Modelng Mood Varaton and Covaraton among Adolescent Smokers: Applcaton of a Bvarate Locaton-Scale Mxed-Effects Model Oksana Pgach, PhD, Donald Hedeker, PhD, Robn Mermelsten, PhD Insttte for Health Research and Polcy Unversty of Illnos at Chcago May, 2013

2 Motvaton Objectves Model and Its Estmaton Data Analyss Reslts Conclsons Otlne

3 Motvaton 1. Heterogeneos wthn- and between-sbject (WS and BS) varances n longtdnal or clstered data 2. Mltple otcomes n behavoral, socal, and medcal stdes 3. Ecologcal Momentary Assessment (EMA) data collecton prodces many observatons per sbject

4 Objectve Specfy a jont model for two contnos otcomes wth heterogeneos WS and BS varances Two otcomes are modeled by mxed-effects regresson models wth random ntercepts BS varance s modeled as heterogeneos between sbjects WS varance s modeled as heterogeneos wth random scale effects BS and WS covarances are modeled wth ther own set of covarates

5 Model n Matrx Form (1) ( 2) Y X β Z ε j (1) ( 2) j j exp ( V ), k 1,2 2 ( k) T ( k) (12) T (12) 2 ( k) T ( k) ( k) exp ( Wj γ, k 1 V ( W ) γ ( 12) T (12) j ),2 model for the means model for BS varances model for BS covarance model for WS varances model for WS covarance ω ~ N 0, G ; jobservaton ; (1) (1) (1) 1,,,ω ( ω ) (2) (2) (2) n, (1) (1) (1) 2 ~ N 0, Σ ε sbject

6 Model - Means General bvarate mxed-effects model wth random ntercepts (1) (1) (1) (1) (1) Y 1 0 X 0 β n ε (2) (2) (2) (2) (2) Y X β n ε X n - desgn matrx p p - vector of fxed effect parameters - ndvdal random effect, k=1,2 ω (1) (1) (1) j G ~ N 0, Σj ( ω ) ~ N 0, ;,, (2) (2) (2) j

7 Model - WS varance-covarance Σ j ( ω ) 2 (1) (1) ( 2) j j j 2 (1) ( 2) ( 2) j j j Varance-covarance matrx of (j) th error vector W (12) j j (12), W, j (1) ( 2) j j 2 T ( k) exp ( Wj ) γ, k 1,2 ( W ) γ (12) T (12) j - vector of covarates for WS varances and covarance - vector of parameters for WS varances and covarance - vector of random scale effects

8 Model - WS varance-covarance Snce random scale has Normal dstrbton ( k) 2 N k and WS varance s modeled as log-lnear model j ~ (0; ), 1,2 2 ( k) T ( k) ( k) Wj γ k exp ( ), 1, 2 Then WS varance has log-normal dstrbton k T k ( ) lgn Wj γ ( ) ~o ( ),, k 1, 2 2 ( ) ( ) 2 k j k

9 Model BS varance-covarance Random locaton-scale effects: (1) (2) (1) (2) ~ N 0, G ; G 2 2 (1) (1) ( 2) (1) (1) (1) ( 2) (1) ( 2) ( 2) ( 2) (1) ( 2) ( 2) 2 2 (1) (1) ( 2) (1) (1) (1) ( 2) (1) ( 2) ( 2) ( 2) (1) ( 2) ( 2) (1) ( 2) exp ( V ), k 1,2 2 ( k) T ( k) V T (12) (12) V, V (12), (12) -vector of covarates for BS varances and covarance - vector of parameters for BS varances and covarance

10 Model Estmaton Gven the above assmptons, the condtonal dstrbton of the otcomes random locaton and scale effects s The fll lkelhood for all sbjects n the sample s where Yω, ~ N( X β Z, ( ω )) N 1 f Y θ ( β, γ, ),, θ g(, ) T T T T gven The margnal lkelhood s obtaned by ntegratng ot all random effects from the fll lkelhood., h( Y) f Y, g(, ) The model was estmated n PROC NLMIXED, SAS v9.2

11 Data Descrpton Data sed n the analyss s part of a larger longtdnal natral hstory stdy of adolescent smokng EMA baselne data based on random prompts 461 stdents, 9 th and 10 th grades 30 prompts per stdent on average, range ,105 prompts total Otcomes: Postve Affect (PA) Negatve Affect (NA) Covarates: Smokng level, represented by a nmber of smokng events drng EMA Non-smokers to one-cgarette smokers Slope among smokers

12 Descrptve Statstcs Varable Mean Std Mn Max Postve Affect (PA) Negatve Affect (NA) Age Gender (Male) 44.9% School grade (9 th grade) 50.7% Whte 56.8% Afrcan Amercan 15.8% Latno 20.0% Asan/Pacfc 2.8% Smokng level At least one smokng event 50.8% One smokng event among smokers 24.8% Smokng epsodes on EMA among smokers

13 Bvarate locaton-scale mxed-effects model of PA and NA wth pecewse smokng predctor N sbject=461, N observatons=14,105 Postve Affect Negatve Affect Model Parameter Estmate Std Err p Estmate Std Err p Fxed Effect covarates Intercept < <.0001 Male < th grade cg smoker Amont smoked WS varance Intercept < <.0001 Male < < th grade cg smoker <.0001 Amont smoked BS varance Intercept <.0001 Male th grade cg smoker Amont smoked Random scale varance on log scale < <.0001 Exp(varance)

14 a) Mean PA b) Mean NA Estmated mean PA (a) and mean NA (b) for dfferent smokng level Sold lne - pecewse smokng; Dashed lne contnos smokng; Dotted vertcal lne break-pont n the slope of smokng effect, occrred at smokng proporton (1 cgarette) (0 cg) (2 cg) (3 cg) (5 cg) (6 cg) Smokng Proporton (Nmber of Cgarettes) (0 cg) (2 cg) (3 cg) (5 cg) (6 cg) Smokng Proporton (Nmber of Cgarettes)

15 a) WS varance n PA b) WS varance n NA Estmated WS PA and NA varance for dfferent smokng level Sold lne - pecewse smokng; Dashed lne contnos smokng; Dotted vertcal lne break-pont n the slope of smokng effect, occrred at smokng proporton (1 cgarette) (0 cg) (2 cg) (3 cg) (5 cg) (6 cg) Smokng Proporton (Nmber of Cgarettes) (0 cg) (2 cg) (3 cg) (5 cg) (6 cg) Smokng Proporton (Nmber of Cgarettes)

16 Bvarate locaton-scale mxed-effects model of PA and NA wth pecewse smokng predctor N sbject=461, N observatons=14,105 Sb-model Parameter Estmate Std Err p WS covarance Intercept <.0001 Male < th grade < cg smoker <.0001 Amont smoked <.0001 BS covarance Intercept <.0001 Male th grade cg smoker Amont smoked Random locaton () and random scale (ω) covarance ( PA) ( NA) ( PA) ( PA) <.0001 ( NA) ( PA) <.0001 ( PA) ( NA) <.0001 ( NA) ( NA)

17 Estmated WS covarance between PA and NA for dfferent smokng level Smokng Proporton (Nmber of Cgarettes) (0 cg) (2 cg) (3 cg) (5 cg) (6 cg) Legend for all fgres Pecewse smokng effect Contnos smokng effect Break-pont n smokng slope

18 Smmary A bvarate mxed-effects model was developed and appled to assess jontly postve and negatve moods as a fncton of smokng level n yoth Model specfed heterogeneos WS and BS varances WS and BS covarances were modeled n terms of covarates WS varance specfcaton had random scale effects

19 Thank yo!