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In this paper, we consider methods for generating draws of a binary random variable whose expectation conditional on covariates follows a logistic regression model with known covariate coefficients. We examine approximations for finding a "balancing intercept," that is, a value for the intercept of the logistic model that leads to a desired marginal expectation for the binary random variable. We show that a recently proposed analytical approximation can produce inaccurate results, especially when targeting more extreme marginal expectations or when the linear predictor of the regression model has high variance. We then formulate the balancing intercept as a solution to an integral equation, implement a numerical approximation for solving the equation based on Monte Carlo methods, and show that the approximation works well in practice. Our approach to the basic problem of the balancing intercept provides an example of a broadly applicable strategy for formulating and solving problems that arise in the design of simulation studies used to evaluate or teach epidemiologic methods. [ABSTRACT FROM AUTHOR]

An increasing number of recent studies have suggested that doubly robust estimators with cross-fitting should be used when estimating causal effects with machine learning methods. However, not all existing programs that implement doubly robust estimators support machine learning methods and cross-fitting, or provide estimates on multiplicative scales. To address these needs, we developed AIPW , a software package implementing augmented inverse probability weighting (AIPW) estimation of average causal effects in R (R Foundation for Statistical Computing, Vienna, Austria). Key features of the AIPW package include cross-fitting and flexible covariate adjustment for observational studies and randomized controlled trials (RCTs). In this paper, we use a simulated RCT to illustrate implementation of the AIPW estimator. We also perform a simulation study to evaluate the performance of the AIPW package compared with other doubly robust implementations, including CausalGAM , npcausal , tmle , and tmle3. Our simulation showed that the AIPW package yields performance comparable to that of other programs. Furthermore, we also found that cross-fitting substantively decreases the bias and improves the confidence interval coverage for doubly robust estimators fitted with machine learning algorithms. Our findings suggest that the AIPW package can be a useful tool for estimating average causal effects with machine learning methods in RCTs and observational studies. [ABSTRACT FROM AUTHOR]