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CausalInference
Causal Inference
Imke Mayer, Pan Zhao, Noah Greifer, Nick Huntington-Klein, Julie Josse
2023-08-04

Overview

Causal inference can be seen as a subfield of statistical analysis. It is used in various fields such as econometrics, epidemiology, educational sciences, etc. With causal inference one addresses questions about effects of a treatment, intervention, or policy on some target over a given sample or population. Under certain identifiability and model assumptions, causal inference can be carried out by fitting simple regression models or combining several regression models in a specific way as will be sketched out later. For observational data, additional untestable assumptions have to be made to (non-parametrically) identify causal effects.

There are no basic R functions that are direct implementations of standard causal inference designs, but many methods - more or less complex - are implemented in different packages on CRAN, which we structure into main topics:

Certain causal inference methods originated in specific fields such as econometrics or clinical trials and remain most popular therein. In certain cases, we therefore refer to other task views covering these methods in more depth. More generally, in this task view we focus on causal analyses with observational data.

If you think that we missed some important packages in this list, please contact the maintainers.

[Methods for randomized controlled trial (RCT) and other experimental data]{#rct}

  • Construction of experimental designs is implemented in r pkg("blocksdesign") (blocks for general factorial treatment designs), r pkg("BCHM") (Bayesian cluster hierarchical model design for multiple subgroup basket trials), r pkg("Boptbd") (Bayesian optimal block designs under linear mixed effects model), r pkg("seqDesign") (sequential design of randomized two-stage treatment efficacy trials with time-to-event endpoints). Many other tools and packages exist for designing experiments and clinical trials, we refer to the r view("ExperimentalDesign") and r view("ClinicalTrials") CRAN Task Views.
  • Tests based on pairwise comparisons are provided in r pkg("BuyseTest").
  • Regression models where the causal estimand is defined as a coefficient of a regression model are implemented in the packages r pkg("allestimates").
  • Analysis methods for RCTs are provided in r pkg("experiment") (various statistical methods), r pkg("eefAnalytics") (Frequentist and Bayesian multilevel models), r pkg("ipcwswitch") (IPW adapted to treatment switch in an RCT), r pkg("idem") (with death and missingness).
  • Posterior analysis tools are implemented in r pkg("cjoint") (conjoint analysis for survey experiments).
  • Design and analysis of two-stage preference trials is implemented in r pkg("preference").
  • In case of non-compliance, r pkg("rpsftm") uses g-estimation to estimate the causal effect of a treatment in a two-armed randomised control trial where non-compliance exists and is measured, under an assumption of an accelerated failure time model and no unmeasured confounders.
  • A time series causal inference model for RCT under spillover effect is implemented in r pkg("SPORTSCausal").
  • Design and analysis of clinical non-inferiority or superiority trials with active and placebo control is implemented in r pkg("ThreeArmedTrials").

[Average treatment effect estimation and other univariate treatment effect estimates]{#ate}

  • Regression models where the causal estimand is a regression parameter are implemented in lm() and glm() from stats, as well as in a number of more specialized packages such as r pkg("fixest", priority = "core"), r pkg("estimatr"), r pkg("CausalGAM") (using generalized additive models), r pkg("sampleSelection") (two-step and maximum likelihood estimation of Heckman-type sample selection models), r pkg("BCEE") (Bayesian causal effect estimation for binary or continuous treatment and outcomes), r pkg("borrowr") (Bayesian PATE estimation for multiple exchangeable data sources), r pkg("causaldrf") (average causal dose response functions), r pkg("hdm") (efficient estimators with uniformly valid confidence intervals, it assumes approximately sparse models for high-dimensional settings). Estimation in fixed effects designs is possible through r pkg("fixest") (linear and generalized linear fixed effects models and combined with instrumental variables), r pkg("plm") (for panel data), and r pkg("alpaca") (for high-dimensional k-way fixed effects).
  • G-computation and other conditional outcome regression based methods are supported in the packages r pkg("gfoRmula") (also for time-varying treatment and confounding), r pkg("EffectLiteR") (based on structural equation modeling), r pkg("endoSwitch") (maximum likelihood estimation of endogenous switching regression models), and r pkg("riskRegression", priority = "core") (for survival outcomes with or without competing risks). For parametric models, g-computation is the same as estimating average marginal effects, which can be achieved using r pkg("margins"), r pkg("marginaleffects"), r pkg("modelbased"), and r pkg("stdReg").
  • Matching methods are implemented in r pkg("MatchIt", priority = "core"), which provides wrappers for a number of popular methods including propensity score matching and subclassification, (coarsened) exact matching, full matching, and cardinality matching; more specialized matching methods are implemented in some of the packages below, some of which MatchIt depends on. r pkg("MatchThem") provides a wrapper for MatchIt with multiply-imputed data. r pkg("Matching", priority = "core") performs nearest neighbor and genetic matching and implements Abadie and Imbens-style matching imputation estimators. r pkg("optmatch") performs optimal matching using network flows; several other packages rely on the same infrastructure, including r pkg("DiPs") (near-fine matching with directional penalties), r pkg("matchMulti") (optimal matching for clustered data), r pkg("rcbalance") and r pkg("rcbsubset") (optimal matching for refined balance), r pkg("approxmatch") (near-optimal matching for multi-category treatments), and r pkg("match2C") (optimal matching using two criteria). Other packages include r pkg("cem") (coarsened exact matching), r pkg("designmatch") (optimization-based matching using mixed integer programming), r pkg("stratamatch") (matching and stratification in large datasets), r pkg("FLAME") (almost-matching-exactly via learned weighted Hamming distance), r pkg("PanelMatch") (matching with time-series cross-sectional data), and r pkg("CausalGPS") (generalized propensity score matching for continuous treatments).
  • Inverse propensity weighting (IPW, also known as inverse probability of treatment weighting, IPTW) methods are implemented in r pkg("WeightIt", priority = "core"), which provides implementations and wrappers for several popular weighting methods for binary, multi-category, continuous, and longitudinal treatments. r pkg("MatchThem") provides a wrapper for WeightIt with multiply-imputed data. r pkg("PSweight", priority = "core") offers propensity score weighting and uncertainty estimation using M-estimation. r pkg("clusteredinterference") and r pkg("inferference") offer weighting methods in the context of interference. Several packages offer specialized methods of estimating balancing weights for various treatment types, which may or may not involve a propensity score: r pkg("CBPS") (generalized method of moments-based propensity score estimation for binary, multi-category, continuous, and longitudinal treatments), r pkg("twang") and r pkg("twangContinuous") (propensity score weighting using gradient boosting machines for binary, multi-category, continuous, and longitudinal treatments), r pkg("sbw") and r pkg("optweight") (optimization-based weights using quadratic programming), and r pkg("ebal") (entropy balancing). r pkg("mvGPS") estimates weights for multivariate treatments using WeightIt's infrastructure. Matching-adjusted indirect comparison, a relative of propensity score weighting when unit-level data is only available for some groups, is available in r pkg("maic"), r pkg("maicChecks"), and r pkg("optweight") (using the optweight.svy() function).
  • Doubly robust methods involve both a treatment and outcome model. Augmented IPW (AIPW) is implemented in r pkg("AIPW"), r pkg("PSweight"), r pkg("DoubleML"), r pkg("grf") (functions causal_forest followed by average_causal_effect), and r pkg("causalweight"). Targeted maximum likelihood estimation (TMLE, also known as targeted minimum loss-based estimation) is available in r pkg("drtmle"), r pkg("tmle", priority = "core"), r pkg("ctmle") (for TMLE with variable selection), r pkg("ltmle") (for longitudinal data), and r pkg("AIPW").
  • Difference in differences methods are implemented in r pkg("DRDID") (doubly robust estimators with two choices for nuisance function estimation), r pkg("bacondecomp") (using the Goodman-Bacon decomposition to allow for variation in treatment timing), r pkg("did") (for cases with more than two periods and with variation in treatment timing), r pkg("fixest") (Sun & Abraham estimator), and in r pkg("qte").
  • Quantile treatment effects can be estimated using the r pkg("qte"), r pkg("Counterfactual") and r pkg("grf") packages.
  • Odds ratio estimation and power calculation for the Trend in Trend model is implemented in r pkg("TrendInTrend").
  • Synthetic control methods are implemented in r pkg("Synth") (using a group method for comparative case studies),r pkg("microsynth") (for micro- and meso-level data), and r pkg("gsynth") (extension to multiple treated units and variable treatment periods). r pkg("tidysynth") offers an easy-to-use syntax for using synthetic control methods. r pkg("scpi") implements multiple synthetic control estimators using lasso, ridge, simplex, and linear constraints, and constructs prediction intervals.
  • Instrumental variable methods are implemented in r pkg("ivreg"), r pkg("ivmodel"), r pkg("bpbounds") (nonparametric bounds on ATE), r pkg("grf"), r pkg("fixest"), r pkg("estimatr"), and r pkg("DoubleML") (function DoubleMLIIVM). r pkg("ivmte") provides a choice-theoretic interpretation to IV models using Marginal Treatment Effects to extrapolate from the compliers to estimate treatment effects for other subpopulations. r pkg("LARF") uses Local Average Response Functions for IV estimation of treatment effects with binary endogenous treatment and instrument. r pkg("icsw") implements inverse compliance score weighting for estimating average treatment effects with an instrumental variable. r pkg("ivdesc") gives descriptive statistics for the complier, never-taker and always-taker subpopulations. More details and a longer list of packages for IV methods can be found in r view("Econometrics", "Instrumental variables") in the r view("Econometrics") task view.
  • Mediation analysis can be performed with r pkg("cfma") (functional mediation analysis), r pkg("cit") (likelihood-based tests), r pkg("MultisiteMediation") (multisite trials), r pkg("DirectEffects") (controlled direct effect when fixing a potential mediator to a specific value), r pkg("medflex") (natural effect models). r pkg("causalweight") and r pkg("twangMediation") implement weighted estimators for mediation. r pkg("mediation", priority = "core") and r pkg("cfdecomp") implement identification, inference and r pkg("mediation") additionally also provides sensitivity analysis for causal mediation effects. r pkg("paths") uses an imputation approach to estimate path-specific causal effects along with a set of bias formulas for conducting sensitivity analysis. r pkg("regmedint") implements regression-based analysis with a treatment-mediator interaction term. r pkg("gma") performs Granger mediation analysis for time series. r pkg("bmem") provides several different methods for mediation analysis in the case of missing data (listwise/pairwise deletion, multiple imputation, two stage maximum likelihood) and power analysis for mediation analysis.
  • Under interference, causal effect estimation can be achieved using r pkg("inferference") by inverse-probability weighted (IPW) estimators, r pkg("netchain") on collective outcomes by chain graph models approximating the projection of the full longitudinal data onto the observed data.
  • Diagnostics and visualization for Multiplicative Interaction Models are implemented in r pkg("interflex").
  • r pkg("InvariantCausalPrediction") provides confidence intervals for causal effects, using data collected in different experimental or environmental conditions (with hidden variables), extensions to nonlinear models are implemented in r pkg("nonlinearICP").
  • Regression discontinuity design (RDD) methods are implemented in r pkg("rdrobust") (offering robust confidence interval construction and bandwidth selection). A more detailed curated list of packages for RDD methods can be found in r view("Econometrics", "Regression discontinuity design") in the r view("Econometrics") task view.

In addition, r pkg("causalsens"), r pkg("OVtool"), r pkg("dstat"), r pkg("sensemakr") and r pkg("EValue") provide functions for sensitivity analyses (for unmeasured confounding, selection bias, measurement error), and r pkg("ui") implements functions to derive uncertainty intervals and conduct sensitivity analysis for missing data and unobserved confounding. r pkg("cobalt", priority = "core") and r pkg("tableone") generate balance tables and plots before and after covariate balancing, and r pkg("confoundr") implements covariate-balance diagnostics for time-varying confounding. r pkg("WhatIf") offers methods to assess overlap and extrapolation.

[Heterogeneous treatment effect estimation]{#hte}

Some of the above mentioned packages can also be used for heterogeneous treatment effect (HTE) estimation.

  • Bayesian approaches for individual causal effect estimation are available in r pkg("bartCause") (based on Bayesian Additive Regression Trees).
  • Fisherian approaches for an omnibus test of heterogeneity and decomposition of overall treatment effect heterogeneity into a systematic component explained by covariates and an idiosyncratic component is implemented in r pkg("hettx").
  • Efficacious treatment or population subset selection exploiting treatment effect heterogeneity is implemented in r pkg("FindIt") and r pkg("grf"). This latter package supports missing covariate values using the Missing Incorporated in Attributes approach. Additionally the package r pkg("subdetect") provides a test for the existence of a subgroup with enhanced treatment effect.
  • Other approaches for personalized causal predictions are provided by r pkg("EffectTreat") (exploiting correlation-based expressions), and for randomized data by r pkg("evalITR") (it additionally allows for defining budget constraints) and by r pkg("SortedEffects") (estimation and inference methods for sorted causal effects and classification analysis).
  • r pkg("stepp") provides diagnostic plots to explore treatment-covariate interactions for survival or generalized linear models, applicable for continuous, binomial and count data arising from two or more treatment arms of a clinical trial.

[Policy learning and dynamic treatment regimes]{#policy}

  • Estimation of an optimal dynamic treatment regime (DTR) is implemented in r pkg("DynTxRegime") (Q-Learning, Interactive Q-Learning, weighted learning, and value-search methods based on Augmented Inverse Probability Weighted Estimators and Inverse Probability Weighted Estimators); methods based on marginal quantile, marginal mean, and mean absolute difference are implemented in r pkg("quantoptr") as well as doubly-robust methods for quantile-optimal treatment regime). r pkg("lmtp") also provides doubly-robust causal effect estimates for modified treatment policies, dynamic treatment regimes (and static interventions). r pkg("DTRreg") proposes different methods such as G-estimation, dynamic weighted OLS and Q-learning, as well as several variance estimation approaches, it can handle survival outcomes and continuous treatment variables. r pkg("QTOCen") provides methods for estimation of mean- and quantile-optimal treatment regimes from censored data. r pkg("ITRLearn") implements maximin-projection learning for recommending a meaningful and reliable individualized treatment regime, and also Q-learning and A-learning for estimating the group-wise contrast function. r pkg("simml") and r pkg("simsl") offer Single-Index Models with Multiple-Links for, respectively, experimental and observational data. r pkg("personalized") implements methods for estimation of individualized treatment rules from observational and randomized data with options for variable-selection and gradient boosting based estimation, and for outcome model augmentation (for continuous, binary, count, and time-to-event outcomes).
  • Estimation of DTR with variable selection is proposed by r pkg("ITRLearn") implements maximin-projection learning for recommending a meaningful and reliable individualized treatment regime, and also Q-learning and A-learning for estimating the group-wise contrast function. r pkg("ITRSelect") implements sequential advantage selection and penalized A-learning for selecting important variables in optimal individualized (dynamic) treatment regime in both single-stage or multi-stage studies. r pkg("OTRselect") implements a penalized regression method that can simultaneously estimate the optimal treatment strategy and identify important variables for either censored or uncensored continuous response. r pkg("DTRlearn2") offers Q-learning and outcome-weighted learning methods with variable selection via penalization.
  • For sequential, multiple assignment, randomized trials (SMART), r pkg("smartsizer") provides a set of tools for determining the necessary sample size in order to identify the optimal DTR; r pkg("DTRlearn2") also implements estimators for general K-stage DTRs from SMARTs.

[Structural equation models (SEM), do-calculus causal discovery]{#dag}

  • Identifiability is addressed by r pkg("causaleffect") and r pkg("dosearch") providing algorithms to decide whether a causal effect is identifiable (non-parametric identifiability) and by r pkg("CausalQueries") that calculates arbitrary estimands for a given causal model. r pkg("SEMID") implements SEM-based routines to check identifiability or non-identifiability of linear SEMs. r pkg("causaloptim") provides tight bounds for a user defined DAG, query and constraints using a symbolic linear optimizer.
  • Causal structure learning is possible with functions from r pkg("pcalg", priority = "core"): PC, for observational data without hidden variables, FCI and RFCI, for observational data with hidden variables, and GIES, for a mix of observational and interventional data without hidden variables; r pkg("pcalg") also allows to do causal inference using graphical models (the IDA algorithm, the Generalized Backdoor Criterion - GBC, the Generalized Adjustment Criterion - GAC). Incorporating background knowledge is also possible. Many algorithms and methods for general and specific graphical models exist, we refer to the r view("GraphicalModels") and r view("Psychometrics") CRAN Task Views for a comprehensive overview.
  • Estimation of causal effects is possible in r pkg("CIEE") using estimating equations derived from a DAG and in r pkg("InvariantCausalPrediction") using adjustment sets derived from conditional independence tests that leverage causal invariances across environments.
  • Causal networks estimation is implemented in r pkg("CompareCausalNetworks").
  • r pkg("generalCorr") computes generalized correlations, partial correlations and plausible causal paths.

In addition, r pkg("dagitty", priority = "core") provides methods to define different types of graphical models (cpdags, pdag, ect.) and to identify adjustment sets (a web-based graphical environment is also available: DAGitty).

[Specific types of data]{#data}

  • Longitudinal data / time series and censored data: Causal effect estimation for time series is implemented in r pkg("CausalImpact") (using a Bayesian approach) and r pkg("CausalMBSTS") (for multivariate responses).
  • GWAS and SNPs: r pkg("CKAT") implements kernel based methods to jointly test genetic main effect and gene-treatment interaction effects for a set of SNPs.
  • Example data sets to run frequent example problems from causal inference textbooks are accessible through the r pkg("causaldata") package.
  • Weighted, two-mode, and longitudinal networks analysis is implemented in r pkg("tnet")

[Specific application fields]{#applications}

  • Behavior change sciences use specialized analyses and visualization tools implemented in r pkg("behaviorchange").
  • Evaluation of biomarkers and estimation of treatment-biomarker effects can be done using tools from r pkg("bhm") (for biomarker-treatment effects).
  • Qualitative Comparative Analysis type methods are implemented in r pkg("cna").
  • Mendelian randomization methods used to examine causal effects related to certain genes are implemented in r pkg("MendelianRandomization"), r pkg("mr.raps") (two-sample Mendelian randomization with summary statistics by using Robust Adjusted Profile Score), r pkg("MRPC") (PC algorithm with the principle of Mendelian Randomization).
  • Causal inference approaches in genetic systems exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes: functions to simultaneously infer causal graphs and genetic architecture (acyclic and cyclic) are implemented in r pkg("qtlnet").
  • r pkg("tools4uplift") uplift modeling aims at predicting the causal effect of an action such as a marketing campaign on a particular individual.
  • Coincidence analysis through configurational comparative methods is provided by r pkg("cna").

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