cmest is used to implement six causal mediation analysis approaches including
the regression-based approach by Valeri et al. (2013) and VanderWeele
et al. (2014), the weighting-based approach by VanderWeele et al. (2014),
the inverse odd-ratio weighting approach by Tchetgen Tchetgen (2013),
the natural effect model by Vansteelandt et al. (2012), the marginal structural
model by VanderWeele et al. (2017), and the g-formula approach by Robins (1986).
cmest( data = NULL, model = "rb", full = TRUE, casecontrol = FALSE, yrare = NULL, yprevalence = NULL, estimation = "imputation", inference = "bootstrap", outcome = NULL, event = NULL, exposure = NULL, mediator = NULL, EMint = NULL, basec = NULL, postc = NULL, yreg = NULL, mreg = NULL, wmnomreg = NULL, wmdenomreg = NULL, ereg = NULL, postcreg = NULL, astar = 0, a = 1, mval = NULL, yval = NULL, basecval = NULL, nboot = 200, boot.ci.type = "per", nRep = 5, multimp = FALSE, args_mice = NULL ) # S3 method for cmest print(x, ...) # S3 method for cmest summary(object, ...) # S3 method for summary.cmest print(x, digits = 4, ...)
| data | dataset |
|---|---|
| model | causal mediation analysis approach. |
| full | a logical value. If |
| casecontrol | a logical value. |
| yrare | a logical value (used when |
| yprevalence | the prevalence of the case (used when |
| estimation | method for estimating causal effects. |
| inference | method for estimating standard errors of causal effects. |
| outcome | variable name of the outcome. |
| event | variable name of the event (used when |
| exposure | variable name of the exposure. |
| mediator | a vector of variable name(s) of the mediator(s). |
| EMint | a logical value indicating the existence of exposure-mediator interaction in
|
| basec | a vector of variable name(s) of the exposure-outcome confounder(s), exposure-mediator confounder(s) and mediator-outcome confounder(s) not affected by the exposure |
| postc | a vector of variable name(s) of the mediator-outcome confounder(s) affected by the exposure following the temporal order |
| yreg | outcome regression model. See |
| mreg | a list specifying a regression model for each variable in |
| wmnomreg | a list specifying a regression model for calculating the nominators of
weights with respect to each variable in |
| wmdenomreg | a list specifying a regression model for calculating the denominators of
weights with respect to each variable in |
| ereg | exposure regression model for calculating weights with respect to the exposure (used
when |
| postcreg | a list specifying a regression model for each variable in |
| astar | the control value for the exposure. Default is |
| a | the active value for the exposure. Default is |
| mval | a list specifying a value for each variable in |
| yval | the value of the outcome at which causal effects on the risk/odds ratio scale are estimated (used when the outcome is categorical). |
| basecval | a list specifying a conditional value for each variable in |
| nboot | the number of boots applied (used when |
| boot.ci.type | the type of bootstrap confidence interval. If |
| nRep | number of replications or hypothetical values of the exposure to sample for
each observation unit (used when |
| multimp | a logical value (used when |
| args_mice | a list of additional arguments passed to the mice function. See mice for details. |
| x | an object of class |
| object | an object of class |
| digits | minimal number of significant digits. See print.default. |
An object of class cmest is returned:
the function call,
the dataset,
a list of methods used which may include model, full,
casecontrol, yprevalence, yrare, estimation, inference,
nboot, boot.ci.type and nRep,
a list of variables used which may include outcome, event,
exposure, mediator, EMint, basec and postc,
a list of regressions input,
a list of arguments used for multiple imputation,
reference values used which may include a, astar, mval,
yval and basecval,
a list of regressions output. If multimp is TRUE,
reg.output contains regressions fitted by each of the imputed dataset,
point estimates of causal effects,
standard errors of causal effects,
the lower limits of 95% confidence intervals of causal effects,
the higher limits of 95% confidence intervals of causal effects,
p-values of causal effects,
Regressions
Each regression in yreg, mreg, wmnomreg, wmdenomreg,
ereg and postcreg can be specified by a user-defined regression
object or the character name of the regression.
The Character Name of A Regression
linear: linear regression fitted by glm with family = gaussian()
logistic: logistic regression fitted by glm with family = logit()
loglinear: log linear regression fitted by glm with
family = poisson() for a binary response
poisson: poisson regression fitted by glm with
family = poisson() for a count response
quasipoisson: quasipoisson regression fitted by glm with
family = quasipoisson()
negbin: negative binomial regression fitted by glm.nb
multinomial: multinomial regression fitted by multinom
ordinal: ordered logistic regression fitted by polr
coxph: cox proportional hazard model fitted by coxph
aft_exp: accelerated failure time model fitted by survreg
with dist = "exponential"
aft_weibull: accelerated failure time model fitted by survreg
with dist = "weibull"
coxph, aft_exp and aft_weibull are currently not implemented for
mreg, wmnomreg, wmdenomreg, ereg and postcreg.
The User-defined Regression Object
A user-defined regression object can be fitted by lm, glm, glm.nb,
gam, multinom, polr, coxph and
survreg. Objects fitted by coxph and survreg
are currently not supported for mreg, wmnomreg, wmdenomreg,
ereg and postcreg.
The cmest function calculates weights for regressions when weighting is required. If a
user-defined regression object is fitted with prior weights, the final weights for this
regression object are constructed by multiplying the prior weights and the weights calculated
inside the cmest function.
Causal Mediation Analysis Approaches
Let Y denote outcome, A denote exposure, M=(M_1,...,M_k)^T
denote mediator, C denote basec, L=(L_1,...,L_s)^T denote postc.
rb: the regression-based approach by Valeri et al. (2013) and
VanderWeele et al. (2014). yreg and mreg are required. If specified as
a user-defined regression object, yreg should regress Y on A,
M and C and mreg[p] should regress M_p on A and C
for p=1,...,k.
wb: the weighting-based approach by VanderWeele et al. (2014).
yreg is required. When basec is not empty, ereg is also required
and A must be categorical. If specified as a user-defined regression object,
yreg should regress Y on A, M and C and ereg
should regress A on C.
iorw: the inverse odd-ratio weighting approach by
Tchetgen Tchetgen (2013). yreg and ereg are required and
A must be categorical. If specified as a user-defined regression object,
yreg should regress Y on A and C and ereg should
regress A on M and C.
ne: the natural effect model by Vansteelandt et al. (2012).
yreg is required. If specified as a user-defined regression object, yreg
should regress Y on A, M and C. The variables in the
formula of yreg must follow the order of A, M and C, i.e.,
the first variable must point to the exposure, the variable(s) right after the
exposure must point to the mediator(s), e.g., Y ~ A + M_1 + M_2 + A*M_1 + C.
msm: the marginal structural model by VanderWeele et al. (2017).
yreg, mreg, wmnomreg and wmdenomreg are required and all
mediators must be categorical. When basec is not empty, ereg is also
required and A must be categorical. If specified as a user-defined regression
object, yreg should regress Y on A and M; mreg[p]
should regress M_p on A for p=1,...,k; wmnomreg[p] should
regress M_p on A, M_1, ..., M_{p-1} for p=1,...,k;
wmdenomreg[p] should regress M_p on A, M_1, ..., M_{p-1},
C and L for p=1,...,k; and ereg should regress A on
C.
gformula: the g-formula approach by Robins (1986).
yreg, mreg are required. postcreg is also required when postc
is not empty. If specified as a user-defined regression object, yreg should
regress Y on A, M, C and L, mreg[p] should
regress M_p on A, C and L
for p=1,...,k, postcreg[q] should regress L_q on A and C
for q=1,...,s.
When postc is not empty, only msm and gformula can be used.
When there are mediatior-mediator interactions in yreg, only wb, iorw,
ne and msm can be used.
Estimation Methods
paramfunc: closed-form parameter function estimation (only available when
model = "rb" and length(mediator) = 1). The point estimate of each causal
effect is obtained by a closed-form formula of regression coefficients. Effects conditional
on basecval are estimated.
imputation: direct counterfactual imputation estimation. The point estimate
of each causal effect is obtained by imputing counterfactuals directly.
To use paramfunc, yreg and mreg must be specified by the character name
of the regression. yreg can be chosen from linear, logistic, loglinear,
poisson, quasipoisson, negbin, coxph, aft_exp and
aft_weibull. mreg can be chosen from linear, logistic and
multinomial.
To use paramfunc with yreg = "logistic" or yreg = "coxph", the outcome must
be rare.
Inference Methods
delta: delta method (only available when estimation = "paramfunc").
The standard errors of causal effects are obtained by the delta method. The confidence
intervals of causal effects are obtained by normal distribution approximation.
bootstrap: bootstrapping. The standard errors of causal effects are
obtained by the standard deviations of bootstrapped results. The confidence intervals of
causal effects are obtained by percentiles of bootstrapped results.
Estimated Causal Effects
For a continuous outcome, the causal effects on the difference scale are estimated. For a categorical, count or survival outcome, the causal effects on the ratio scale are estimated. The interpretation of the ratio depends on the type of the outcome and it can be risk ratio for a categorical outcome, rate ratio for a count outcome, hazard ratio for a survival outcome fitted by coxph, mean survival ratio for a survival outcome fitted by survreg, etc.
Continuous Outcome
When model = "rb", "wb", "ne", "msm" or "gformula" with an empty postc and
EMint is TRUE, cde (controlled direct effect), pnde (pure natural
direct effect), tnde (total natural direct effect), pnie (pure natural indirect
effect), tnie (total natural indirect effect), te (total effect), intref
(reference interaction), intmed (mediated interaction),
cde(prop) (proportion cde), intref(prop) (proportion
intref), intmed(prop) (proportion intmed), pnie(prop)
(proportion pnie), pm (proportion mediated), int (proportion
attributable to interaction) and pe (proportion eliminated) are estimated.
When model = "rb", "wb", "ne", "msm" or "gformula" with an empty postc and
EMint is FALSE, cde, pnde, tnde, pnie, tnie,
te and pm are estimated.
When postc is not empty, pnde, tnde, pnie, tnie,
intref, intmed, intref(prop), intmed(prop), pnie(prop),
pm, int and pe are replaced by their randomized analogues rpnde,
rtnde, rpnie, rtnie, rintref, rintmed, rintref(prop),
rintmed(prop), rpnie(prop), rpm, rint and rpe.
When model = "iorw", te, pnde, tnie and pm are estimated.
Categorical, Count or Survival Outcome
When model = "rb", "wb", "ne", "msm" or "gformula" with an empty postc and
EMint is TRUE, Rcde (cde ratio), Rpnde (pnde ratio),
Rtnde (tnde ratio), Rpnie (Rpnie ratio), Rtnie (tnie ratio),
Rte (te ratio), ERcde (excess ratio due to cde), ERintref (excess
ratio due to intref), ERintmed (excess ratio due to intmed), ERpnie
(excess ratio due to pnie), ERcde(prop) (proportion ERcde),
ERintref(prop) (proportion ERintref), ERintmed(prop) (proportion ERintmed),
ERpnie(prop) (proportion ERpnie), pm, int and pe are estimated.
When model = "rb", "wb", "ne", "msm" or "gformula" with an empty postc and
EMint is FALSE, Rcde, Rpnde, Rtnde, Rpnie, tnie,
te and pm are estimated.
When model = "msm" or "gformula" with a non-empty postc, Rpnde, Rtnde,
Rpnie, Rtnie, ERintref, ERintmed, ERpnie,
ERintref(prop), ERintmed(prop), ERpnie(prop), pm, int and
pe are replaced by their randomized analogues rRpnde, rRtnde, rRpnie,
rRtnie, rERintref, rERintmed, rERpnie, rERintref(prop),
rERintmed(prop), rERpnie(prop), rpm, rint and rpe.
When model = "iorw", Rte, Rpnde, Rtnie and pm are estimated.
print(cmest): Print the results of cmest nicely
summary(cmest): Summarize the results of cmest nicely
print(summary.cmest): Print the summary of cmest nicely
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if (FALSE) { library(CMAverse) # single-mediator case with rb, no exposure-mediator interaction exp1 <- cmest(data = cma2020, model = "rb", outcome = "contY", exposure = "A", mediator = "M2", basec = c("C1", "C2"), EMint = FALSE, mreg = list("multinomial"), yreg = "linear", astar = 0, a = 1, mval = list("M2_0"), estimation = "paramfunc", inference = "delta") summary(exp1) # single-mediator case with rb exp2 <- cmest(data = cma2020, model = "rb", outcome = "contY", exposure = "A", mediator = "M2", basec = c("C1", "C2"), EMint = TRUE, mreg = list("multinomial"), yreg = "linear", astar = 0, a = 1, mval = list("M2_0"), estimation = "paramfunc", inference = "delta") summary(exp2) # multiple-mediator case with rb # 10 boots are used for illustration exp3 <- cmest(data = cma2020, model = "rb", outcome = "contY", exposure = "A", mediator = c("M1", "M2"), basec = c("C1", "C2"), EMint = TRUE, mreg = list("logistic", "multinomial"), yreg = "linear", astar = 0, a = 1, mval = list(0, "M2_0"), estimation = "imputation", inference = "bootstrap", nboot = 10, boot.ci.type = "bca") # multiple-mediator case with ne exp4 <- cmest(data = cma2020, model = "ne", outcome = "contY", EMint = TRUE, exposure = "A", mediator = c("M1", "M2"), basec = c("C1", "C2"), yreg = glm(contY ~ A + M1 + M2 + A*M1 + A*M2 + C1 + C2, family = gaussian, data = cma2020), astar = 0, a = 1, mval = list(0, "M2_0"), estimation = "imputation", inference = "bootstrap", nboot = 10) # case control study with msm exp5 <- cmest(data = cma2020, model = "msm", casecontrol = TRUE, yrare = TRUE, outcome = "binY", exposure = "A", mediator = c("M1", "M2"), EMint = TRUE, basec = c("C1", "C2"), yreg = "logistic", ereg = "logistic", mreg = list(glm(M1 ~ A, family = binomial, data = cma2020), nnet::multinom(M2 ~ A, data = cma2020, trace = FALSE)), wmnomreg = list(glm(M1 ~ A, family = binomial, data = cma2020), nnet::multinom(M2 ~ A + M1, data = cma2020, trace = FALSE)), wmdenomreg = list(glm(M1 ~ A + C1 + C2, family = binomial, data = cma2020), nnet::multinom(M2 ~ A + M1 + C1 + C2, data = cma2020, trace = FALSE)), astar = 0, a = 1, mval = list(0, "M2_0"), estimation = "imputation", inference = "bootstrap", nboot = 10) }