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.
library(regmedint)
library(tidyverse)
## Prepare dataset
data(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)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5143 -1.1765 0.9177 1.1133 1.4602
##
## 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)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5689 -1.1585 0.8925 1.1242 1.4342
##
## 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)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5689 -1.1585 0.8925 1.1242 1.4342
##
## 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)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5689 -1.1585 0.8925 1.1242 1.4342
##
## 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.