In this document, we demonstrate including effect measure
modification (EMM) terms in the mediator or the outcome models. The
dataset used in this document is still vv2015.
In the first model fit, we do not include any EMM term.
regmedint_obj1 <- regmedint(data = vv2015,
## Variables
yvar = "y",
avar = "x",
mvar = "m",
cvar = c("c"),
eventvar = "event",
## Values at which effects are evaluated
a0 = 0,
a1 = 1,
m_cde = 1,
c_cond = 3,
## Model types
mreg = "logistic",
yreg = "survAFT_weibull",
## Additional specification
interaction = TRUE,
casecontrol = FALSE)
summary(regmedint_obj1)## ### Mediator model
##
## Call:
## glm(formula = m ~ x + c, family = binomial(link = "logit"), data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.3545 0.3252 -1.090 0.276
## x 0.3842 0.4165 0.922 0.356
## c 0.2694 0.2058 1.309 0.191
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 138.59 on 99 degrees of freedom
## Residual deviance: 136.08 on 97 degrees of freedom
## AIC: 142.08
##
## Number of Fisher Scoring iterations: 4
##
## ### Outcome model
##
## Call:
## survival::survreg(formula = Surv(y, event) ~ x + m + x:m + c,
## data = data, dist = "weibull")
## Value Std. Error z p
## (Intercept) -1.0424 0.1903 -5.48 4.3e-08
## x 0.4408 0.3008 1.47 0.14
## m 0.0905 0.2683 0.34 0.74
## c -0.0669 0.0915 -0.73 0.46
## x:m 0.1003 0.4207 0.24 0.81
## Log(scale) -0.0347 0.0810 -0.43 0.67
##
## Scale= 0.966
##
## Weibull distribution
## Loglik(model)= -11.4 Loglik(intercept only)= -14.5
## Chisq= 6.31 on 4 degrees of freedom, p= 0.18
## Number of Newton-Raphson Iterations: 5
## n= 100
##
## ### Mediation analysis
## est se Z p lower upper
## cde 0.541070807 0.29422958 1.8389409 0.06592388 -0.03560858 1.11775019
## pnde 0.505391952 0.21797147 2.3186151 0.02041591 0.07817572 0.93260819
## tnie 0.015988820 0.03171597 0.5041252 0.61417338 -0.04617334 0.07815098
## tnde 0.513662425 0.22946248 2.2385465 0.02518544 0.06392423 0.96340062
## pnie 0.007718348 0.02398457 0.3218047 0.74760066 -0.03929055 0.05472725
## te 0.521380773 0.22427066 2.3247837 0.02008353 0.08181835 0.96094319
## pm 0.039039346 0.07444080 0.5244348 0.59997616 -0.10686194 0.18494063
##
## Evaluated at:
## avar: x
## a1 (intervened value of avar) = 1
## a0 (reference value of avar) = 0
## mvar: m
## m_cde (intervend value of mvar for cde) = 1
## cvar: c
## c_cond (covariate vector value) = 3
##
## Note that effect estimates can vary over m_cde and c_cond values when interaction = TRUE.Now suppose the covariate \(C\)
modifies the treatment effect on the mediator. We add
emm_ac_mreg = c("c") in regmedint(). Although
there is only one covariate in our dataset, emm_ac_mreg can
take a vector of multiple covariates. Please note that the covariates in
emm_ac_mreg should be a subset of the covariates specified
in cvar, i.e. if a covariate is an effect measure modifier
included in emm_ac_mreg, it must be included in
cvar, otherwise an error message will be printed.
regmedint_obj2 <- regmedint(data = vv2015,
## Variables
yvar = "y",
avar = "x",
mvar = "m",
cvar = c("c"),
emm_ac_mreg = c("c"),
emm_ac_yreg = NULL,
emm_mc_yreg = NULL,
eventvar = "event",
## Values at which effects are evaluated
a0 = 0,
a1 = 1,
m_cde = 1,
c_cond = 3,
## Model types
mreg = "logistic",
yreg = "survAFT_weibull",
## Additional specification
interaction = TRUE,
casecontrol = FALSE)
summary(regmedint_obj2)## ### Mediator model
##
## Call:
## glm(formula = m ~ x + c + x:c, family = binomial(link = "logit"),
## data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.32727 0.34979 -0.936 0.349
## x 0.30431 0.56789 0.536 0.592
## c 0.24085 0.24688 0.976 0.329
## x:c 0.09216 0.44624 0.207 0.836
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 138.59 on 99 degrees of freedom
## Residual deviance: 136.04 on 96 degrees of freedom
## AIC: 144.04
##
## Number of Fisher Scoring iterations: 4
##
## ### Outcome model
##
## Call:
## survival::survreg(formula = Surv(y, event) ~ x + m + x:m + c,
## data = data, dist = "weibull")
## Value Std. Error z p
## (Intercept) -1.0424 0.1903 -5.48 4.3e-08
## x 0.4408 0.3008 1.47 0.14
## m 0.0905 0.2683 0.34 0.74
## c -0.0669 0.0915 -0.73 0.46
## x:m 0.1003 0.4207 0.24 0.81
## Log(scale) -0.0347 0.0810 -0.43 0.67
##
## Scale= 0.966
##
## Weibull distribution
## Loglik(model)= -11.4 Loglik(intercept only)= -14.5
## Chisq= 6.31 on 4 degrees of freedom, p= 0.18
## Number of Newton-Raphson Iterations: 5
## n= 100
##
## ### Mediation analysis
## est se Z p lower upper
## cde 0.54107081 0.29422958 1.8389409 0.06592388 -0.03560858 1.11775019
## pnde 0.50404000 0.21666437 2.3263632 0.01999919 0.07938564 0.92869435
## tnie 0.02377050 0.05679639 0.4185213 0.67556602 -0.08754838 0.13508937
## tnde 0.51632801 0.23444392 2.2023519 0.02764046 0.05682637 0.97582965
## pnie 0.01148248 0.03882957 0.2957149 0.76744784 -0.06462208 0.08758704
## te 0.52781049 0.22811645 2.3137765 0.02067998 0.08071046 0.97491053
## pm 0.05727853 0.13042523 0.4391676 0.66054011 -0.19835021 0.31290728
##
## Evaluated at:
## avar: x
## a1 (intervened value of avar) = 1
## a0 (reference value of avar) = 0
## mvar: m
## m_cde (intervend value of mvar for cde) = 1
## cvar: c
## c_cond (covariate vector value) = 3
##
## Note that effect estimates can vary over m_cde and c_cond values when interaction = TRUE.Now suppose in addition to the EMM on mediator, the covariate \(C\) also modifies the treatment effect on
the outcome We add emm_ac_yreg = c("c") in
regmedint(). Please note that the covariates in
emm_ac_yreg should be a subset of the covariates specified
in cvar, i.e. if a covariate is an effect measure modifier
included in emm_ac_yreg, it must be included in
cvar, otherwise an error message will be printed.
regmedint_obj3 <- regmedint(data = vv2015,
## Variables
yvar = "y",
avar = "x",
mvar = "m",
cvar = c("c"),
emm_ac_mreg = c("c"),
emm_ac_yreg = c("c"),
emm_mc_yreg = NULL,
eventvar = "event",
## Values at which effects are evaluated
a0 = 0,
a1 = 1,
m_cde = 1,
c_cond = 3,
## Model types
mreg = "logistic",
yreg = "survAFT_weibull",
## Additional specification
interaction = TRUE,
casecontrol = FALSE)
summary(regmedint_obj3)## ### Mediator model
##
## Call:
## glm(formula = m ~ x + c + x:c, family = binomial(link = "logit"),
## data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.32727 0.34979 -0.936 0.349
## x 0.30431 0.56789 0.536 0.592
## c 0.24085 0.24688 0.976 0.329
## x:c 0.09216 0.44624 0.207 0.836
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 138.59 on 99 degrees of freedom
## Residual deviance: 136.04 on 96 degrees of freedom
## AIC: 144.04
##
## Number of Fisher Scoring iterations: 4
##
## ### Outcome model
##
## Call:
## survival::survreg(formula = Surv(y, event) ~ x + m + x:m + c +
## x:c, data = data, dist = "weibull")
## Value Std. Error z p
## (Intercept) -1.04148 0.19261 -5.41 6.4e-08
## x 0.43626 0.33092 1.32 0.19
## m 0.09138 0.26954 0.34 0.73
## c -0.06844 0.10315 -0.66 0.51
## x:m 0.09681 0.43437 0.22 0.82
## x:c 0.00725 0.22300 0.03 0.97
## Log(scale) -0.03473 0.08104 -0.43 0.67
##
## Scale= 0.966
##
## Weibull distribution
## Loglik(model)= -11.4 Loglik(intercept only)= -14.5
## Chisq= 6.31 on 5 degrees of freedom, p= 0.28
## Number of Newton-Raphson Iterations: 5
## n= 100
##
## ### Mediation analysis
## est se Z p lower upper
## cde 0.55481498 0.51519657 1.0768996 0.2815251 -0.45495174 1.56458171
## pnde 0.51905802 0.51048271 1.0167984 0.3092493 -0.48146970 1.51958574
## tnie 0.02345019 0.05730239 0.4092359 0.6823666 -0.08886042 0.13576081
## tnde 0.53092081 0.50659327 1.0480218 0.2946285 -0.46198375 1.52382537
## pnie 0.01158740 0.03904582 0.2967641 0.7666466 -0.06494101 0.08811581
## te 0.54250821 0.50656000 1.0709654 0.2841850 -0.45033114 1.53534756
## pm 0.05535403 0.13968838 0.3962680 0.6919074 -0.21843016 0.32913822
##
## Evaluated at:
## avar: x
## a1 (intervened value of avar) = 1
## a0 (reference value of avar) = 0
## mvar: m
## m_cde (intervend value of mvar for cde) = 1
## cvar: c
## c_cond (covariate vector value) = 3
##
## Note that effect estimates can vary over m_cde and c_cond values when interaction = TRUE.Now suppose in addition to the EMM of treatment effect, the covariate
\(C\) also modifies the mediator effect
on the outcome. We add emm_mc_yreg = c("c") in
regmedint(). Please note that the covariates in
emm_mc_yreg should be a subset of the covariates specified
in cvar, i.e. if a covariate is an effect measure modifier
included in emm_mc_yreg, it must be included in
cvar, otherwise an error message will be printed.
regmedint_obj4 <- regmedint(data = vv2015,
## Variables
yvar = "y",
avar = "x",
mvar = "m",
cvar = c("c"),
emm_ac_mreg = c("c"),
emm_ac_yreg = c("c"),
emm_mc_yreg = c("c"),
eventvar = "event",
## Values at which effects are evaluated
a0 = 0,
a1 = 1,
m_cde = 1,
c_cond = 3,
## Model types
mreg = "logistic",
yreg = "survAFT_weibull",
## Additional specification
interaction = TRUE,
casecontrol = FALSE)
summary(regmedint_obj4)## ### Mediator model
##
## Call:
## glm(formula = m ~ x + c + x:c, family = binomial(link = "logit"),
## data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.32727 0.34979 -0.936 0.349
## x 0.30431 0.56789 0.536 0.592
## c 0.24085 0.24688 0.976 0.329
## x:c 0.09216 0.44624 0.207 0.836
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 138.59 on 99 degrees of freedom
## Residual deviance: 136.04 on 96 degrees of freedom
## AIC: 144.04
##
## Number of Fisher Scoring iterations: 4
##
## ### Outcome model
##
## Call:
## survival::survreg(formula = Surv(y, event) ~ x + m + x:m + c +
## x:c + m:c, data = data, dist = "weibull")
## Value Std. Error z p
## (Intercept) -0.9959 0.2071 -4.81 1.5e-06
## x 0.4185 0.3354 1.25 0.21
## m -0.0216 0.3112 -0.07 0.94
## c -0.1339 0.1405 -0.95 0.34
## x:m 0.0905 0.4265 0.21 0.83
## x:c 0.0327 0.2242 0.15 0.88
## m:c 0.1275 0.1861 0.69 0.49
## Log(scale) -0.0406 0.0814 -0.50 0.62
##
## Scale= 0.96
##
## Weibull distribution
## Loglik(model)= -11.1 Loglik(intercept only)= -14.5
## Chisq= 6.78 on 6 degrees of freedom, p= 0.34
## Number of Newton-Raphson Iterations: 5
## n= 100
##
## ### Mediation analysis
## est se Z p lower upper
## cde 0.60705735 0.52594922 1.1542128 0.2484129 -0.4237842 1.6378989
## pnde 0.57902523 0.51447701 1.1254638 0.2603926 -0.4293312 1.5873816
## tnie 0.05333600 0.10591830 0.5035579 0.6145721 -0.1542601 0.2609321
## tnde 0.58889505 0.51488644 1.1437377 0.2527324 -0.4202638 1.5980539
## pnie 0.04346618 0.09107534 0.4772552 0.6331804 -0.1350382 0.2219706
## te 0.63236123 0.52776615 1.1981845 0.2308452 -0.4020414 1.6667639
## pm 0.11082259 0.20960355 0.5287248 0.5969964 -0.2999928 0.5216380
##
## Evaluated at:
## avar: x
## a1 (intervened value of avar) = 1
## a0 (reference value of avar) = 0
## mvar: m
## m_cde (intervend value of mvar for cde) = 1
## cvar: c
## c_cond (covariate vector value) = 3
##
## Note that effect estimates can vary over m_cde and c_cond values when interaction = TRUE.