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G-computation-based transportability analysis

Core Clinical Sciences

transportGC.Rmd
#> 
#> Attaching package: 'TransportHealth'
#> The following object is masked from 'package:base':
#> 
#>     trunc

Introduction

In this vignette, we demonstrate how to use TransportHealth for g-computation-based transportability analysis for instances where individual participant-level data (IPD) is available in both the original study and target sample, but they are not mergable.

Brief introduction to g-computation

In transportability and generalizability analysis, g-computation proceeds largely the same as for confounding adjustment.

Firstly, a model of the outcome in terms of the treatment, covariates and effect modifiers is fitted using the source data. Then, this model is used to calculate fitted values of the outcome when treatment is set to control or treatment for all observations in the target data; in particular, observed covariate and effect modifier values in the target data are used to calculate the fitted values. Finally, treatment effects are calculated using these fitted values to obtain an unbiased estimate of the treatment effect in the target population.

Example

Suppose we are interested in estimating the causal effect of a medication on systolic blood pressure in a target population, but we were only able to conduct an observational study using samples from the study population. To obtain unbiased causal effect estimates using the study sample, we account for the following covariates: sex, body fat percentage, and stress level.

We know that the effectiveness of the medication depends on two effect modifiers: 1) stress level, and 2) whether patients are taking another medication.

Note that the covariates adjusted for in the study data can also be effect modifiers.

Coded variables

  • Medication - med1

    • 1 for treated
    • 0 for untreated

  • Systolic blood pressure (SBP) - sysBloodPressure (continuous)

  • Sex - sex

    • 1 for male
    • 0 for female

  • Body fat percentage - percentBodyFat (continuous)

  • Stress level - stress

    • 1 for stressed
    • 0 for normal

  • Medication 2 - med2

    • 1 for treated
    • 0 for untreated

Analyses

First, for the implementation of g-computation in TransportHealthR specifically, the data from the study and target population should be in separate data frames in the R environment. The study data should contain response, treatment, covariate and effect modifier information, while the target data should contain only covariate and effect modifier information.

Suppose that we have the study and target data separately as follows.

names(testData)
#> [1] "studyData"  "targetData"
print("Study data:")
#> [1] "Study data:"
head(testData$studyData)
#>   sysBloodPressure med1 sex stress med2 percentBodyFat
#> 1         109.4347    1   1      0    0       16.84868
#> 2         115.9803    0   1      1    0       14.48698
#> 3         112.7886    0   1      0    0       15.53636
#> 4         107.6026    1   1      0    0       13.76442
#> 5         120.6845    0   0      1    0       30.08657
#> 6         113.4424    0   1      0    0       16.23256
print("Target data:")
#> [1] "Target data:"
head(testData$targetData)
#>   sex stress med2 percentBodyFat
#> 1   0      1    0       26.12896
#> 2   1      1    0       12.04972
#> 3   1      1    0       12.55972
#> 4   0      0    1       27.07130
#> 5   1      1    0       11.85846
#> 6   0      1    0       27.64520

We can now perform transportability analysis using g-computation with the transportGCPreparedModel and transportGC functions.

transportGCPreparedModel(outcomeModel,
                         treatment,
                         family,
                         studyData,
                         wipe)

transportGC(effectType,
            preparedModel,
            targetData)

Arguments for the transportGCPreparedModel and transportGC functions

The transportGCPreparedModel function requires the following arguments:

  • outcomeModel: A formula expressing the outcome model to be fit

  • treatment: The name of the variable indicating treatment

  • family: The type of outcome model to be fit.

This can be any of the families that are used in glm, one of "coxph","survreg" or "polr". The "coxph" and "survreg" options are for survival analysis and will use default options of these methods from the survival package. The "polr" option is for ordinal outcomes, and the link function can be specified by the method argument, which uses the logistic link by default.

  • studyData: The source data

  • wipe: A boolean indicating whether to erase the source data in the resulting transportGCPreparedModel object

The transportGC function requires the following arguments:

  • effectType: A string indicating the type of effect to calculate, such as "meanDiff" for mean difference, `“rr”`` for relative risk, and so on.

  • preparedModel: A transportGCPreparedModel object returned by the transportGCPreparedModel function

  • targetData: The target data

Specification of transportability analysis

Recall that: - sysBloodPressure is the response

  • med1 is the treatment

  • sex, percentBodyFat, and stress are covariates to be controlled in the original study

  • med2 (other medication) and stress are effect modifiers of interest.

First, we fit a regression model of the outcome in terms of the covariates and effect modifiers, making sure to include interaction terms of the effect modifiers. We need to wrap the results using the transportGCPreparedModel function to be able to use the transportGC function, as follows. Note that we only provide the study data to this function.

preparedModel <- TransportHealth::transportGCPreparedModel(sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress + med1:med2, # Formula for outcome model
                                          treatment = "med1", # Name of treatment variable
                                          family = gaussian, # Type of model
                                          studyData = testData$studyData, # Study data
                                          wipe = F # Wipe study data from model?
                                          )

To estimate the average treatment effect of using the medication on systolic blood pressure in the target population, we can use the transportGC function as follows. Note that we only provide the target data to this function.

result <- TransportHealth::transportGC("meanDiff", # Type of effect estimate (mean difference, relative risk, etc)
                      preparedModel, # transportGCPreparedModel object
                      testData$targetData # Target data
                      )

Producing statistical results

To show the results of the analysis, use summary like you would for lm when fitting a linear model. Using summary will print out the names of the treatment and response variables, the transported treatment effect, its estimated standard error, and a summary of the fitted outcome model. Note that scientific conclusions should only be drawn from the transported effect estimate.

summary(result)
#> Response: sysBloodPressure
#> Treatment: med1
#> Effect type: meanDiff
#> ATE estimate: -1.4575638820277
#> Standard error: 0.125829267599943
#> Fitted outcome model:
#> 
#> Call:
#> stats::glm(formula = outcomeModel, family = family, data = studyData, 
#>     model = !wipe)
#> 
#> Coefficients:
#>                Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)     99.9742     0.4449  224.70   <2e-16 ***
#> med11           -4.9526     0.0844  -58.66   <2e-16 ***
#> sex1             5.0582     0.2136   23.68   <2e-16 ***
#> stress1          4.9920     0.0838   59.59   <2e-16 ***
#> percentBodyFat   0.4996     0.0157   31.80   <2e-16 ***
#> med11:stress1    6.9820     0.1299   53.74   <2e-16 ***
#> med10:med21     -0.3776     0.1342   -2.81    0.005 ** 
#> med11:med21     -5.1624     0.1514  -34.09   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for gaussian family taken to be 0.9692829)
#> 
#>     Null deviance: 22462.80  on 999  degrees of freedom
#> Residual deviance:   961.53  on 992  degrees of freedom
#> AIC: 2817
#> 
#> Number of Fisher Scoring iterations: 2

The workflow is constructed in this way to accommodate situations where the source data and target data cannot be merged due to privacy concerns. Owners of the source data can apply the transportGCPreparedModel function to the source data with wipe = T to erase the source data from the transportGCPreparedModel object and send this object to the owners of the target data in an .rds file. Then the owners of the target data can extract the object to conduct g-computation using transportGC. See below for a comparison of transportGCPreparedModel objects with wipe = T and wipe = F.

preparedModelNoWipe <- TransportHealth::transportGCPreparedModel(sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress + med1:med2,
                                          treatment = "med1",
                                          family = gaussian,
                                          studyData = testData$studyData,
                                          wipe = F)
write("Components of outcomeModel with wipe = F:", stdout())
#> Components of outcomeModel with wipe = F:
str(preparedModelNoWipe$outcomeModel)
#> List of 30
#>  $ coefficients     : Named num [1:8] 99.97 -4.95 5.06 4.99 0.5 ...
#>   ..- attr(*, "names")= chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ residuals        : Named num [1:1000] 0.93743 -1.28172 -0.00575 0.64614 0.68715 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ fitted.values    : Named num [1:1000] 108 117 113 107 120 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ effects          : Named num [1:1000] -3605.9 -41.9 12.6 120.7 -31.8 ...
#>   ..- attr(*, "names")= chr [1:1000] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ R                : num [1:8, 1:8] -31.6 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>   .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ rank             : int 8
#>  $ qr               :List of 5
#>   ..$ qr   : num [1:1000, 1:8] -31.6228 0.0316 0.0316 0.0316 0.0316 ...
#>   .. ..- attr(*, "dimnames")=List of 2
#>   .. .. ..$ : chr [1:1000] "1" "2" "3" "4" ...
#>   .. .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>   ..$ rank : int 8
#>   ..$ qraux: num [1:8] 1.03 1.03 1.03 1.03 1.03 ...
#>   ..$ pivot: int [1:8] 1 2 3 4 5 6 7 8
#>   ..$ tol  : num 1e-11
#>   ..- attr(*, "class")= chr "qr"
#>  $ family           :List of 12
#>   ..$ family    : chr "gaussian"
#>   ..$ link      : chr "identity"
#>   ..$ linkfun   :function (mu)  
#>   ..$ linkinv   :function (eta)  
#>   ..$ variance  :function (mu)  
#>   ..$ dev.resids:function (y, mu, wt)  
#>   ..$ aic       :function (y, n, mu, wt, dev)  
#>   ..$ mu.eta    :function (eta)  
#>   ..$ initialize:  expression({  n <- rep.int(1, nobs)  if (is.null(etastart) && is.null(start) && is.null(mustart) && ((family$link| __truncated__
#>   ..$ validmu   :function (mu)  
#>   ..$ valideta  :function (eta)  
#>   ..$ dispersion: num NA
#>   ..- attr(*, "class")= chr "family"
#>  $ linear.predictors: Named num [1:1000] 108 117 113 107 120 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ deviance         : num 962
#>  $ aic              : num 2817
#>  $ null.deviance    : num 22463
#>  $ iter             : int 2
#>  $ weights          : Named num [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ prior.weights    : Named num [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ df.residual      : int 992
#>  $ df.null          : int 999
#>  $ y                : Named num [1:1000] 109 116 113 108 121 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ converged        : logi TRUE
#>  $ boundary         : logi FALSE
#>  $ model            :'data.frame':   1000 obs. of  6 variables:
#>   ..$ sysBloodPressure: num [1:1000] 109 116 113 108 121 ...
#>   ..$ med1            : Factor w/ 2 levels "0","1": 2 1 1 2 1 1 1 2 1 2 ...
#>   ..$ sex             : Factor w/ 2 levels "0","1": 2 2 2 2 1 2 1 2 1 1 ...
#>   ..$ stress          : Factor w/ 2 levels "0","1": 1 2 1 1 2 1 2 2 1 2 ...
#>   ..$ percentBodyFat  : num [1:1000] 16.8 14.5 15.5 13.8 30.1 ...
#>   ..$ med2            : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "terms")=Classes 'terms', 'formula'  language sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress +      med1:med2
#>   .. .. ..- attr(*, "variables")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. .. ..- attr(*, "factors")= int [1:6, 1:6] 0 1 0 0 0 0 0 0 1 0 ...
#>   .. .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. .. ..$ : chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>   .. .. .. .. ..$ : chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. .. ..- attr(*, "term.labels")= chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. .. ..- attr(*, "order")= int [1:6] 1 1 1 1 2 2
#>   .. .. ..- attr(*, "intercept")= int 1
#>   .. .. ..- attr(*, "response")= int 1
#>   .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
#>   .. .. ..- attr(*, "predvars")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. .. ..- attr(*, "dataClasses")= Named chr [1:6] "numeric" "factor" "factor" "factor" ...
#>   .. .. .. ..- attr(*, "names")= chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>  $ call             : language stats::glm(formula = outcomeModel, family = family, data = studyData, model = !wipe)
#>  $ formula          :Class 'formula'  language sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress +      med1:med2
#>   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
#>  $ terms            :Classes 'terms', 'formula'  language sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress +      med1:med2
#>   .. ..- attr(*, "variables")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. ..- attr(*, "factors")= int [1:6, 1:6] 0 1 0 0 0 0 0 0 1 0 ...
#>   .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. ..$ : chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>   .. .. .. ..$ : chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. ..- attr(*, "term.labels")= chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. ..- attr(*, "order")= int [1:6] 1 1 1 1 2 2
#>   .. ..- attr(*, "intercept")= int 1
#>   .. ..- attr(*, "response")= int 1
#>   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
#>   .. ..- attr(*, "predvars")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. ..- attr(*, "dataClasses")= Named chr [1:6] "numeric" "factor" "factor" "factor" ...
#>   .. .. ..- attr(*, "names")= chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>  $ data             :'data.frame':   1000 obs. of  6 variables:
#>   ..$ sysBloodPressure: num [1:1000] 109 116 113 108 121 ...
#>   ..$ med1            : Factor w/ 2 levels "0","1": 2 1 1 2 1 1 1 2 1 2 ...
#>   ..$ sex             : Factor w/ 2 levels "0","1": 2 2 2 2 1 2 1 2 1 1 ...
#>   ..$ stress          : Factor w/ 2 levels "0","1": 1 2 1 1 2 1 2 2 1 2 ...
#>   ..$ med2            : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
#>   ..$ percentBodyFat  : num [1:1000] 16.8 14.5 15.5 13.8 30.1 ...
#>  $ offset           : NULL
#>  $ control          :List of 3
#>   ..$ epsilon: num 1e-08
#>   ..$ maxit  : num 25
#>   ..$ trace  : logi FALSE
#>  $ method           : chr "glm.fit"
#>  $ contrasts        :List of 4
#>   ..$ med1  : chr "contr.treatment"
#>   ..$ sex   : chr "contr.treatment"
#>   ..$ stress: chr "contr.treatment"
#>   ..$ med2  : chr "contr.treatment"
#>  $ xlevels          :List of 4
#>   ..$ med1  : chr [1:2] "0" "1"
#>   ..$ sex   : chr [1:2] "0" "1"
#>   ..$ stress: chr [1:2] "0" "1"
#>   ..$ med2  : chr [1:2] "0" "1"
#>  - attr(*, "class")= chr [1:2] "glm" "lm"
preparedModelWipe <- TransportHealth::transportGCPreparedModel(sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress + med1:med2,
                                          treatment = "med1",
                                          family = gaussian,
                                          studyData = testData$studyData,
                                          wipe = T)
write("\n", stdout())
write("Components of outcomeModel with wipe = T:", stdout())
#> Components of outcomeModel with wipe = T:
str(preparedModelWipe$outcomeModel)
#> List of 21
#>  $ coefficients : Named num [1:8] 99.97 -4.95 5.06 4.99 0.5 ...
#>   ..- attr(*, "names")= chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ effects      : Named num [1:1000] -3605.9 -41.9 12.6 120.7 -31.8 ...
#>   ..- attr(*, "names")= chr [1:1000] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ R            : num [1:8, 1:8] -31.6 0 0 0 0 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>   .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>  $ rank         : int 8
#>  $ qr           :List of 5
#>   ..$ qr   : num [1:1000, 1:8] -31.6228 0.0316 0.0316 0.0316 0.0316 ...
#>   .. ..- attr(*, "dimnames")=List of 2
#>   .. .. ..$ : chr [1:1000] "1" "2" "3" "4" ...
#>   .. .. ..$ : chr [1:8] "(Intercept)" "med11" "sex1" "stress1" ...
#>   ..$ rank : int 8
#>   ..$ qraux: num [1:8] 1.03 1.03 1.03 1.03 1.03 ...
#>   ..$ pivot: int [1:8] 1 2 3 4 5 6 7 8
#>   ..$ tol  : num 1e-11
#>   ..- attr(*, "class")= chr "qr"
#>  $ family       :List of 12
#>   ..$ family    : chr "gaussian"
#>   ..$ link      : chr "identity"
#>   ..$ linkfun   :function (mu)  
#>   ..$ linkinv   :function (eta)  
#>   ..$ variance  :function (mu)  
#>   ..$ dev.resids:function (y, mu, wt)  
#>   ..$ aic       :function (y, n, mu, wt, dev)  
#>   ..$ mu.eta    :function (eta)  
#>   ..$ initialize:  expression({  n <- rep.int(1, nobs)  if (is.null(etastart) && is.null(start) && is.null(mustart) && ((family$link| __truncated__
#>   ..$ validmu   :function (mu)  
#>   ..$ valideta  :function (eta)  
#>   ..$ dispersion: num NA
#>   ..- attr(*, "class")= chr "family"
#>  $ deviance     : num 962
#>  $ aic          : num 2817
#>  $ null.deviance: num 22463
#>  $ iter         : int 2
#>  $ prior.weights: Named num [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
#>  $ df.residual  : int 992
#>  $ df.null      : int 999
#>  $ converged    : logi TRUE
#>  $ boundary     : logi FALSE
#>  $ call         : language stats::glm(formula = outcomeModel, family = family, data = studyData, model = !wipe)
#>  $ formula      :Class 'formula'  language sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress +      med1:med2
#>   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
#>  $ terms        :Classes 'terms', 'formula'  language sysBloodPressure ~ med1 + sex + stress + percentBodyFat + med1:stress +      med1:med2
#>   .. ..- attr(*, "variables")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. ..- attr(*, "factors")= int [1:6, 1:6] 0 1 0 0 0 0 0 0 1 0 ...
#>   .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. ..$ : chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>   .. .. .. ..$ : chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. ..- attr(*, "term.labels")= chr [1:6] "med1" "sex" "stress" "percentBodyFat" ...
#>   .. ..- attr(*, "order")= int [1:6] 1 1 1 1 2 2
#>   .. ..- attr(*, "intercept")= int 1
#>   .. ..- attr(*, "response")= int 1
#>   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
#>   .. ..- attr(*, "predvars")= language list(sysBloodPressure, med1, sex, stress, percentBodyFat, med2)
#>   .. ..- attr(*, "dataClasses")= Named chr [1:6] "numeric" "factor" "factor" "factor" ...
#>   .. .. ..- attr(*, "names")= chr [1:6] "sysBloodPressure" "med1" "sex" "stress" ...
#>  $ control      :List of 3
#>   ..$ epsilon: num 1e-08
#>   ..$ maxit  : num 25
#>   ..$ trace  : logi FALSE
#>  $ method       : chr "glm.fit"
#>  $ contrasts    :List of 4
#>   ..$ med1  : chr "contr.treatment"
#>   ..$ sex   : chr "contr.treatment"
#>   ..$ stress: chr "contr.treatment"
#>   ..$ med2  : chr "contr.treatment"
#>  - attr(*, "class")= chr [1:2] "glm" "lm"

Note that this workflow does not enable the calculation of the correct variance estimators using bootstrap (which is the approach transportGC uses) when wipe = T to support privacy needs. One work around is that the owners of the source data can resample the source data and provide transportGCPreparedModel objects for each resample of the source data, and the owners of the target data can independently resample the target data and apply transportGC using each transportGCPreparedModel object to each resampled target dataset to obtain bootstrap samples of the MSM coefficient estimates.

To obtain a coefficient plot of estimates, use the plot function.

plot(result)

One can assess the appropriateness of the outcome model by performing usual diagnostic techniques on the outcome model. For example, we can look at the residual plot of the outcome model.

plot(preparedModel$outcomeModel, which = 1)

In our example, the residual plot of the outcome model is patternless, indicating that it is appropriate. Note that this step should be done by owners of the study data when the study and target data cannot be merged, as residuals are also erased in the transportGCPreparedModel object when wipe = T.

Like inverse odds of participation weighting (IOPW), the validity of g-computation depends on untestable causal inference assumptions, including stable unit treatment value (SUTVA), conditional exchangeability, positivity and consistency (Ling et al. 2023; Degtiar and Rose 2023). Unlike IOPW, g-computation does not have readily available diagnostics to evaluate if these assumptions are likely to hold or not. For conditional exchangeability, we suggest conducting sensitivity analyses with respect to unmeasured confounding, but this is beyond on the scope of the package. For positivity, a simple method would be to examine marginal distributions of covariates and effect modifiers in the study and target data and compare them: the distributions should overlap between the study and target data, but they do not need to be identical.

References

Degtiar, I, and S Rose. 2023. “A Review of Generalizability and Transportability.” Annual Review of Statistics and Its Application 10: 501–24. https://doi.org/https://doi.org/10.1146/annurev-statistics-042522-103837.
Ling, AY, R Jreich, ME Montez-Rath, P Carita, KJ Chandross, L Lucats, Z Meng, B Sebastien, K Kappahn, and M Desai. 2023. “An Overview of Current Methods for Real-World Applications to Generalize or Transport Clinical Trial Findings to Target Populations of Interest.” Epidemiology 34: 627–36. https://doi.org/10.1097/EDE.0000000000001633.