# Chapter 14 Prendre en compte l’interaction

## 14.1 Avec le sport

exp1 <- cmest(
data = base3,                    # base
model = "gformula",             # approach, defaut is rb (regression-based)
# if postc is not empty only gformula or msm
estimation = "imputation",      # method of estimation. "imputation" is conterfactual estimation
inference = "bootstrap",        # method for se and CI
nboot = 100,                    # defaut is 200
EMint = TRUE,                  # interaction exposure mediator

multimp = TRUE,                 # imputation multiple des DM
m = 10,

outcome = "t8_SBP",
exposure = "t0_baby_sex",
mediator = c("t4_act_sport"),
basec = c("t0_mother_scol_crt",
"t0_fathers_csp_defav"),# confusion baseline
postc = c("t4_litteraciepbm",
"t4_numeraciepbm",
"t4_O_level",
"t4_married",
"t4_act_friend",
"t4_religious"),    # confusion intermédiaire

yreg = "linear",              # outcome regression model

a = "Homme",                    # "active" value of exposure
astar = "Femme",                # "control" value of exposure

mreg = list("logistic"),          # regression model for each mediator
mval = list("Non"),   # ref for M
postcreg = list("logistic",
"logistic",
"logistic",
"logistic",
"logistic",
"logistic",
"logistic",
"logistic")                 # ref for M
) ;    set.seed(28062022)
 type effect ci.low ci.high cde 14.78 11.34 19.56 rpnde 13.49 10.97 17.48 rtnde 11.90 9.94 15.58 rpnie -1.25 -3.53 -0.55 rtnie -2.84 -5.36 -1.58 te 10.66 8.23 13.67 rintref -1.28 -2.80 0.09 rintmed -1.59 -3.51 0.13 cde(prop) 1.39 1.16 1.73 rintref(prop) -0.12 -0.24 0.01 rintmed(prop) -0.15 -0.33 0.01 rpnie(prop) -0.12 -0.35 -0.05 rpm -0.27 -0.55 -0.14 rint -0.27 -0.58 0.03 rpe -0.39 -0.73 -0.16

On peut décrire plusieurs effets :

• l’effet direct (qui ne passe pas par l’activité physique) “moyen” d’être né homme est CDE = +14.78mmHg (95CI = [11.34 to 19.56]
• il y a interaction avec le sport de : Int_Ref = -1.28mmHg (95CI = [-2.8 to 0.09]. Le fait de faire du sport change l’effet direct (chemins non en lien avec le sport) chez les hommes par rapport aux femmes.
• la proportion médiée “moyenne” est PM = -26.78% (95CI = [-55.15% to -14.29%]
• L’effet du n’est pas le meme entre les hommes et les femmes : chez les hommes le fait de faire du sport diminue la TAS de Int_MEd = -1.59mmHg (95CI = [-3.51 to 0.13] de plus que chez les hommes.

## 14.2 Avec la lecture

exp1 <- cmest(
data = base3,                    # base
model = "gformula",             # approach, defaut is rb (regression-based)
# if postc is not empty only gformula or msm
estimation = "imputation",      # method of estimation. "imputation" is conterfactual estimation
inference = "bootstrap",        # method for se and CI
nboot = 100,                    # defaut is 200
EMint = TRUE,                  # interaction exposure mediator

multimp = TRUE,                 # imputation multiple des DM
m = 10,

outcome = "t8_SBP",
exposure = "t0_baby_sex",
basec = c("t0_mother_scol_crt",
"t0_fathers_csp_defav"),# confusion baseline
postc = c("t4_litteraciepbm",
"t4_O_level",
"t4_married"),    # confusion intermédiaire

yreg = "linear",              # outcome regression model

a = "Homme",                    # "active" value of exposure
astar = "Femme",                # "control" value of exposure

mreg = list("logistic"),          # regression model for each mediator
mval = list("Oui"),   # ref for M
postcreg = list("logistic",
"logistic",
"logistic",
"logistic")                 # ref for M
) ;    set.seed(28062022)`
 type effect ci.low ci.high cde 9.49 6.70 12.84 rpnde 9.97 7.78 12.91 rtnde 10.36 8.07 13.26 rpnie 0.34 -0.32 1.04 rtnie 0.73 -0.05 1.80 te 10.70 8.50 13.77 rintref 0.48 -0.38 1.86 rintmed 0.39 -0.25 1.25 cde(prop) 0.89 0.68 1.04 rintref(prop) 0.05 -0.05 0.18 rintmed(prop) 0.04 -0.03 0.12 rpnie(prop) 0.03 -0.04 0.10 rpm 0.07 -0.00 0.16 rint 0.08 -0.07 0.29 rpe 0.11 -0.04 0.32

On peut décrire plusieurs effets :

• l’effet direct (qui ne passe pas par l’activité de lecture) “moyen” d’être né homme est CDE = +9.49mmHg (95CI = [6.7 to 12.84]
• il ne semble pas y avoir d’interaction avec la lecture de : Int_Ref = +0.48mmHg (95CI = [-0.38 to 1.86].
• la proportion médiée “moyenne” est PM = 6.84% (95CI = [-0.31 to 15.87]
• l’effet de la lecture semble a peu près similaire chez les hommes et les femmes Int_Med = +0.39mmHg (95CI = [-0.25 to 1.25]