Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this paper, we investigate two alternative solutions: Test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: As one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.
Many real datasets contain values missing not at random (MNAR). In this scenario, investigators often perform list-wise deletion, or delete samples with any missing values, before applying causal discovery algorithms. List-wise deletion is a sound and general strategy when paired with algorithms such as FCI and RFCI, but the deletion procedure also eliminates otherwise good samples that contain only a few missing values. In this report, we show that we can more efficiently utilize the observed values with test-wise deletion while still maintaining algorithmic soundness. Here, test-wise deletio…
Case-cohort studies are conducted within cohort studies, wherein collection of exposure data is limited to a subset of the cohort, leading to a large proportion of missing data by design. Standard analysis uses inverse probability weighting (IPW) to address this intended missing data, but little research has been conducted into how best to perform analysis when there is also unintended missingness. Multiple imputation (MI) has become a default standard for handling unintended missingness, but when used in combination with IPW, the imputation model needs to take account of the weighting to ensu…
We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process. The combination of the observed data model and causal assumptions allows us to identify any type of causal effect - differences, ratios, or quantile effects, either marginally or for subpopulations of interest. The proposed BNP model is well-suited for causal inference problems, as it does not require parametric assumptions about the distribution of confoun…
High-dimensional multiple imputation (HDMI) for partially observed confounders including natural language processing-derived auxiliary covariates
Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；Duke University School of Medicine（杜克大学医学院）；US Food and Drug Administration（美国食品药品监督管理局）；Harvard Medical School and Harvard Pilgrim Health Care Institute（哈佛医学院与哈佛朝圣者医疗保健研究所）；Harvard Pilgrim Health Care Institute（哈佛朝圣者医疗保健研究所）
The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, estimation of causal effects requires additional assumptions and techniques, the implementations of which have varied across disciplines. This paper reviews current methods, and it identifies and contrasts the treatment effects that each one …
Multiple imputation provides us with efficient estimators in model-based methods for handling missing data under the true model. It is also well-understood that design-based estimators are robust methods that do not require accurately modeling the missing data; however, they can be inefficient. In any applied setting, it is difficult to know whether a missing data model may be good enough to win the bias-efficiency trade-off. Raking of weights is one approach that relies on constructing an auxiliary variable from data observed on the full cohort, which is then used to adjust the weights for th…
Objective: Researchers often use model-based multiple imputation to handle missing at random data to minimize bias while making the best use of all available data. However, there are sometimes constraints within the data that make model-based imputation difficult and may result in implausible values. In these contexts, we describe how to use random hot deck imputation to allow for plausible multiple imputation in longitudinal studies. Study Design and Setting: We illustrate random hot deck multiple imputation using The Childhood Health, Activity, and Motor Performance School Study Denmark (CHA…
When fitting a generalized linear model -- such as a linear regression, a logistic regression, or a hierarchical linear model -- analysts often wonder how to handle missing values of the dependent variable Y. If missing values have been filled in using multiple imputation, the usual advice is to use the imputed Y values in analysis. We show, however, that using imputed Ys can add needless noise to the estimates. Better estimates can usually be obtained using a modified strategy that we call multiple imputation, then deletion (MID). Under MID, all cases are used for imputation, but following im…
Comparing Imputation Methods for Clinical Prediction Model Development under Complex Missingness Scenarios: A Simulation Study Using Real-World Cardiac Data
Multiple imputation (MI) has become one of the main procedures used to treat missing data, but the guidelines from the methodological literature are not easily transferred to multilevel research. For models including random slopes, proper MI can be difficult, especially when the covariate values are partially missing. In the present article, we discuss applications of MI in multilevel random-coefficient models, theoretical challenges posed by slope variation, and the current limitations of standard MI software. Our findings from three simulation studies suggest that (a) MI is able to recover m…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model-based approach using the marginal density for the observed values, assuming a finite mixture model of multivariate $t$ distributions. We compare our approximate algorithm to the corresponding full expectation-maximization (EM) approach that considers the missing valu…
Handling Overlapping Asymmetric Datasets -- A Twice Penalized P-Spline Approach
Newcastle University（纽卡斯尔大学）；School of Computing（计算机学院）；School of Mathematics, Statistics and Physics（数学、统计与物理学院）；Translational & Clinical Research Institute（转化与临床研究院）
In the context of missing data, the identifiability or "recoverability" of the average causal effect (ACE) depends on causal and missingness assumptions. The latter can be depicted by adding variable-specific missingness indicators to causal diagrams, creating "missingness-directed acyclic graphs" (m-DAGs). Previous research described ten canonical m-DAGs, representing typical multivariable missingness mechanisms in epidemiological studies, and determined the recoverability of the ACE in the absence of effect modification. We extend the research by determining the recoverability of the ACE in …
The case-cohort study design bypasses resource constraints by collecting certain expensive covariates for only a small subset of the full cohort. Weighted Cox regression is the most widely used approach for analysing case-cohort data within the Cox model, but is inefficient. Alternative approaches based on multiple imputation and nonparametric maximum likelihood suffer from incompatibility and computational issues respectively. We introduce a novel Bayesian framework for case-cohort Cox regression that avoids the aforementioned problems. Users can include auxiliary variables to help predict th…
Assessing treatment effects in observational data with missing confounders: A comparative study of practical doubly-robust and traditional missing data methods
Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；University of Washington（华盛顿大学）；TL Revolution, LLC（TL革命有限责任公司）；Vanderbilt University（范德堡大学）；University of California at Berkeley（加州大学伯克利分校）；University of Auckland（奥克兰大学）；US Food and Drug Administration（美国食品药品监督管理局）
In longitudinal data a response variable is measured over time, or under different conditions, for a cohort of individuals. In many situations all intended measurements are not available which results in missing values. If the missing value is never followed by an observed measurement, this leads to dropout pattern. The missing values could be in the response variable, the covariates or in both. The missingness mechanism is termed non-random when the probability of missingness depends on the missing value and may be on the observed values. In this case the missing values should be considered i…
