kaz-yos/regmedint

R implementation of effect measure modification-extended regression-based closed-formula causal mediation analysis

regmedint

This is an extension of the regression-based causal mediation analysis first proposed by Valeri and VanderWeele (2013) and Valeri and VanderWeele (2015). The current version supports including effect measure modification by covariates (treatment-covariate and mediator-covariate product terms in mediator and outcome regression models). It also accommodates the original ‘SAS’ macro (can be found at Dr. VanderWeele’s Tools and Tutorials) and PROC CAUSALMED procedure in ‘SAS’ when there is no effect measure modification. Linear and logistic models are supported for the mediator model. Linear, logistic, loglinear, Poisson, negative binomial, Cox, and accelerated failure time (exponential and Weibull) models are supported for the outcome model.

To cite this software, please use: regmedint (v1.0.0; Yoshida, Li, & Mathur, 2021)

Implemented models

The following grid of models are implemented. yreg refers to the outcome model and mreg refers to the mediator model.

yreg \\ mreg	linear	logistic
linear	✔️	✔️
logistic1	✔️	✔️
loglinear	✔️2	✔️2
poisson	✔️	✔️
negbin	✔️	✔️
survCox1	✔️	✔️
survAFT exp	✔️	✔️
survAFT weibull	✔️	✔️

¹ Approximation depends on the rare event assumptions.

² Implemented as a modified Poisson model (log link with robust variance) as in Z2004.

See the corresponding vignettes (Articles on the package website) for how to perform bootstrapping and multiple imputation.

Installation

For the developmental version on Github, use the following commands to install the package.

# install.packages("devtools") # If you do not have devtools already.
devtools::install_github("kaz-yos/regmedint")

## 
##      checking for file ‘/private/var/folders/5m/w191nn3d52bc91mq5_jjgw880000gn/T/RtmpTDYzP5/remotesf00c1976f8fd/kaz-yos-regmedint-43d42e2/DESCRIPTION’ ...  ✔  checking for file ‘/private/var/folders/5m/w191nn3d52bc91mq5_jjgw880000gn/T/RtmpTDYzP5/remotesf00c1976f8fd/kaz-yos-regmedint-43d42e2/DESCRIPTION’
##   ─  preparing ‘regmedint’:
##      checking DESCRIPTION meta-information ...  ✔  checking DESCRIPTION meta-information
##   ─  checking for LF line-endings in source and make files and shell scripts
##   ─  checking for empty or unneeded directories
##      Removed empty directory ‘regmedint/man/figures’
##   ─  building ‘regmedint_1.0.0.tar.gz’
##      
## 

The CRAN version can be installed as follows.

install.packages("regmedint")

Data Example

We use VV2015 dataset for demonstration.

library(regmedint)
data(vv2015)

regmedint() to fit models

The regmedint function is the user interface for constructing a result object of class regmedint. The interface is similar to the original SAS macro. For survival outcomes, the indicator variable is an event indicator (1 for event, 0 for censoring). c_cond vector is required be specified. This vector is the vector of covariate values at which the conditional effects are evaluated at.

1. When there is no effect measure modification by covariates, emm_ac_mreg = NULL, emm_ac_yreg = NULL, emm_mc_yreg = NULL.

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 0.000000043
## 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.

1. When there is effect measure modification by covariates, emm_ac_mreg, emm_ac_yreg and emm_mc_yreg can take a sub-vector of covariates in cvar.

regmedint_obj2 <- 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_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 + 
##     x:c + m:c, data = data, dist = "weibull")
##               Value Std. Error     z         p
## (Intercept) -0.9959     0.2071 -4.81 0.0000015
## 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.

summary() to examine extended results

The summary method gives the summary for mreg, yreg, and mediation analysis results. The exponentiate option will add the exponentiated estimate and confidence limits if the outcome model is not a linear model. The pure natural direct effect (pnde) is what is typically called the natural direct effect (NDE). The total natural indirect effect (tnie) is the corresponding natural indirect effect (NIE).

summary(regmedint_obj2, exponentiate = TRUE)

## ### 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 0.0000015
## 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 exp(est) exp(lower) exp(upper)
## cde  0.60705735 0.52594922 1.1542128 0.2484129 -0.4237842 1.6378989 1.835024  0.6545651   5.144349
## pnde 0.57902523 0.51447701 1.1254638 0.2603926 -0.4293312 1.5873816 1.784298  0.6509443   4.890926
## tnie 0.05333600 0.10591830 0.5035579 0.6145721 -0.1542601 0.2609321 1.054784  0.8570491   1.298139
## tnde 0.58889505 0.51488644 1.1437377 0.2527324 -0.4202638 1.5980539 1.801996  0.6568735   4.943403
## pnie 0.04346618 0.09107534 0.4772552 0.6331804 -0.1350382 0.2219706 1.044425  0.8736825   1.248535
## te   0.63236123 0.52776615 1.1981845 0.2308452 -0.4020414 1.6667639 1.882049  0.6689530   5.295005
## pm   0.11082259 0.20960355 0.5287248 0.5969964 -0.2999928 0.5216380       NA         NA         NA
## 
## 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.

Use coef to extract the mediation analysis results only.

coef(summary(regmedint_obj2, exponentiate = TRUE))

##             est         se         Z         p      lower     upper exp(est) exp(lower) exp(upper)
## cde  0.60705735 0.52594922 1.1542128 0.2484129 -0.4237842 1.6378989 1.835024  0.6545651   5.144349
## pnde 0.57902523 0.51447701 1.1254638 0.2603926 -0.4293312 1.5873816 1.784298  0.6509443   4.890926
## tnie 0.05333600 0.10591830 0.5035579 0.6145721 -0.1542601 0.2609321 1.054784  0.8570491   1.298139
## tnde 0.58889505 0.51488644 1.1437377 0.2527324 -0.4202638 1.5980539 1.801996  0.6568735   4.943403
## pnie 0.04346618 0.09107534 0.4772552 0.6331804 -0.1350382 0.2219706 1.044425  0.8736825   1.248535
## te   0.63236123 0.52776615 1.1981845 0.2308452 -0.4020414 1.6667639 1.882049  0.6689530   5.295005
## pm   0.11082259 0.20960355 0.5287248 0.5969964 -0.2999928 0.5216380       NA         NA         NA

Note that the estimates can be re-evaluated at different m_cde and c_cond without re-fitting the underlyng models.

coef(summary(regmedint_obj2, exponentiate = TRUE, m_cde = 0, c_cond = 5))

##             est        se         Z         p      lower     upper exp(est) exp(lower) exp(upper)
## cde  0.58192722 1.0143233 0.5737098 0.5661642 -1.4061100 2.5699644 1.789484  0.2450949  13.065360
## pnde 0.65642157 0.9349234 0.7021127 0.4826089 -1.1759946 2.4888377 1.927881  0.3085120  12.047265
## tnie 0.07541287 0.1873908 0.4024363 0.6873630 -0.2918664 0.4426921 1.078329  0.7468683   1.556893
## tnde 0.66420100 0.9330958 0.7118251 0.4765731 -1.1646332 2.4930352 1.942937  0.3120371  12.097940
## pnie 0.06763343 0.1720653 0.3930683 0.6942690 -0.2696084 0.4048753 1.069973  0.7636785   1.499116
## te   0.73183444 0.9597352 0.7625379 0.4457390 -1.1492119 2.6128808 2.078891  0.3168864  13.638283
## pm   0.13996739 0.3295286 0.4247503 0.6710187 -0.5058969 0.7858316       NA         NA         NA

Formulas

See here for the following formulas.

Effect formulas in the supplementary document

yreg \\ mreg	linear	logistic
linear	Formulas (1) - (5)	Formulas (11) - (15)
logistic	Formulas (21) - (25)	Formulas (31) - (35)
loglinear	Formulas (21) - (25)	Formulas (31) - (35)
poisson	Formulas (21) - (25)	Formulas (31) - (35)
negbin	Formulas (21) - (25)	Formulas (31) - (35)
survCox	Formulas (21) - (25)	Formulas (31) - (35)
survAFT exp	Formulas (21) - (25)	Formulas (31) - (35)
survAFT weibull	Formulas (21) - (25)	Formulas (31) - (35)

Standard error formulas in the supplementary document

yreg \\ mreg	linear	logistic
linear	Formulas (6) - (10)	Formulas (16) - (20)
logistic	Formulas (26) - (30)	Formulas (36) - (40)
loglinear	Formulas (26) - (30)	Formulas (36) - (40)
poisson	Formulas (26) - (30)	Formulas (36) - (40)
negbin	Formulas (26) - (30)	Formulas (36) - (40)
survCox	Formulas (26) - (30)	Formulas (36) - (40)
survAFT exp	Formulas (26) - (30)	Formulas (36) - (40)
survAFT weibull	Formulas (26) - (30)	Formulas (36) - (40)

Note: The point estimate and standard error formulas (multivariate delta method) were derived based on the following references.

• V2015: VanderWeele (2015) Explanation in Causal Inference.
• VV2013A: Valeri & VanderWeele (2013) Appendix
• VV2015A: Valeri & VanderWeele (2015) Appendix

Effect formulas are based on the following propositions

yreg \\ mreg	linear	logistic
linear	V2015 p466 Proposition 2.3	V2015 p471 Proposition 2.5
logistic	V2015 p468 Proposition 2.4	V2015 p473 Proposition 2.6
loglinear	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
poisson	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
negbin	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
survCox	V2015 p496 Proposition 4.4 (Use 2.4)	V2015 p499 Proposition 4.6 (Use 2.6)
survAFT exp	V2015 p494 Proposition 4.1 (Use 2.4)	V2015 p495 Proposition 4.3 (Use 2.6)
survAFT weibull	V2015 p494 Proposition 4.1 (Use 2.4)	V2015 p495 Proposition 4.3 (Use 2.6)

Standard error formulas are based on the following propositions

yreg \\ mreg	linear	logistic
linear	V2015 p466 Proposition 2.3	V2015 p471 Proposition 2.5
logistic	V2015 p468 Proposition 2.4	V2015 p473 Proposition 2.6
loglinear	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
poisson	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
negbin	VV2013A p8 Use Proposition 2.4	VV2013A p8 Use Proposition 2.6
survCox	V2015 p496 Use Proposition 2.4	V2015 p499 Use Proposition 2.6
survAFT exp	V2015 p494 Use Proposition 2.4	V2015 p495 Use Proposition 2.6
survAFT weibull	V2015 p494 Use Proposition 2.4	V2015 p495 Use Proposition 2.6

Similar or related projects for counterfactual-based causal mediation analysis

R

• mediation (simulation-based): https://CRAN.R-project.org/package=mediation
• medflex (natural effect model): https://CRAN.R-project.org/package=medflex
• intmed (interventional analogue): https://CRAN.R-project.org/package=intmed
• CMAverse (regression-based approach, weighting-based approach, inverse odd-ratio weighting, natural effect model, marginal structural model, g-formula approach): https://bs1125.github.io/CMAverse/
• mediator (regression-based): https://github.com/GerkeLab/mediator
• causalMediation (regression-based): https://github.com/harvard-P01/causalMediation

Other statistical environment

• SAS macro (original regression-based) https://www.hsph.harvard.edu/tyler-vanderweele/tools-and-tutorials/
• SAS PROC CAUSALMED (regression-based) https://support.sas.com/rnd/app/stat/procedures/causalmed.html

References

• V2015: VanderWeele (2015) Explanation in Causal Inference.
• VV2013: Valeri & VanderWeele (2013) Psych Method. 18:137.
• VV2015: Valeri & VanderWeele (2015) Epidemiology. 26:e23.
• Z2004: Zou (2004) Am J Epidemiol 159:702.

regmedint's Issues

Seeking your advice on conducting a sensitivity analysis for a causal mediation analysis where both the mediator and outcome are binary.

How to conduct a sensitivity analysis for a causal mediation analysis where both the mediator and outcome are binary.

continuous treatment variable: How to define treatment and control values

Dear regmedint team,

Thank you very much for providing this valuable package.

I have a continuous treatment variable, namely BMI. How should I define the treatment and control values? For example, in the study (https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2777980), how should I set the values of a0 and a1 for HR for a 5-unit change? If a1=5 and a0=0, or a1=25 and a0=20, the results change. In addition, most studies did not report the values of a1 and a0, only showing the effect size. Are there specific rules for determining these a1 and a0 values?

In the example provided, a1=1 and a0=0 for a continuous variable. However, when I attempt to set different values for a1 and a0, the results change.

Best regards,
Haibin Li

Seems like p-values for the pm has changed in the past half a year

Hello,
Thank you for the package, it seemed to be one of the very few (only?) options for survival outcomes in R.
I wonder if something happened between Dec21/jan22 and now Aug22?
I am re-running analyses from that time and all the results from redmedint function are the same but the confidence interval for partial mediation (much wider now). Both for logistic mreg and yreg, and for survCox yreg.

Interpretation of the mediation analysis

Thanks for writing this R package!
I just found the abbreviations in the mediation analysis output is bit of confusing (pnde, cnie, etc.). Could you give an interpretation of these names? Or if you could direct me to any references for interpreting them?

Thank you!

Using time in and time out in survCox

Dear developer,

I want to use age at recruitment and age at disease as the input of 'yvar' in regmedint. I believe it is different from using a single survival time (it compares the patients with the same age). I wonder how to achieve that? The mediator is continuous so it is linear + survCox.

How to build a Hierarchical Cox Regression Model

Dear regmedint team,
Thank you very much for this package，it's very useful. And I wonder that how to build a Hierarchical Cox Regression Model, because i want to konw effect of risk factors in different tissues. But there is no arguement to define a Hierarchical Cox Regression Model. I hope that you can help me out.
Thanks

weights

Dear regmedint team,

First of all, thank you very much for this valuable package.

I wonder if there is any possibility to add "weights" as an argument in the function of regmedint. If that is not possible at this moment, is there is any indirect way to add them? I did my best to get the function "calc_myreg_mreg_linear_yreg_linear" working (because I know how to add weights in lm or survreg), but unfortunately, even after adding all the relevant functions related to the package (ie, here from the documentation in github), I was not able to see results (I was able to run it, but I was not able to see the outcomes. I hope that you can help me out.

Thanks in advance.
Kind regards,
Ali Al Mubarak

Questions on the "c_cond" argument for dummy variables

Hi, I have read the documents presented on your website, and I found that the argument "c_cond" was required. I have read the manual of Prof. Vanderweele's macro and found that it could use, by default, the average level of covariates to estimate PNDE and TNIE. I want to use similar method to complete my estimations but I don't know how to deal with the dummy variables generated from the categorical variables. How can I give the "average" level of dummy variables, or will there be an option in the future to omit the c_cond like the original macro? I'm looking forward to your suggestions.
Thanks for your help and you excellent great work!

Categorical exposure using regmedint

Hi, using regmedint is it possible to compute the effects comparing two levels of a categorical exposure variable which has more than two categories? Thanks.

multiple mediators

Hi,

Is it possible to implement multiple sequential mediators (E --> M1 --> M2 --> Y) in this package? I am receiving this error when trying to include multiple mediators:

Error: length(mvar) not equal to 1

If it is not possible - do the authors have any recommendations for regression-based analysis of multiple mediators?

If not possible for regression-based, then for the inverse probability weight method used in page 123-125 for multiple mediators of the vanderweele book, are confounders included for the exposure and outcome models those that are identified on the exposure-outcome association (not considering mediator-outcome confounders?)

Thanks,

Sahra

How to install and library the developmental version on Github

Dear regmedint team,

Thank you very much for this valuable package.

I was glad that an updated version of regmedint package supported including effect measure modification by covariates. However, since the version was not released on CRAN, I need to use the developmental version on Github. However, when I ran the code as follows:
devtools :: install_github( "einsley1993/regmedint",force = TRUE)
library(regmedint)

There were errors showing "package or namespace load failed for ‘regmedint’ in get(method, envir = home):
lazy-load database '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/regmedint/R/regmedint.rdb' is corrupt
此外: Warning message:
In get(method, envir = home) : internal error -3 in R_decompress1"

Therefore, I wonder how could I install the developmental version on Github supporting "EMM_AC_Mmodel, EMM_AC_Ymodel and EMM_MC"?

Thank you in advance. I look forward to your reply.