Nonparametric quantile regression with missing data using local estimating equations

We consider nonparametric regression of a scalar outcome on a covariate when the outcome is missing at random (MAR) given the covariate and other observed auxiliary variables. We propose a class of augmented inverse probability weighted (AIPW) kernel estimating equations for nonparametric regression under MAR. We show that AIPW kernel estimators are consistent when the probability that the outcome is observed, that is, the selection probability, is either known by design or estimated under a correctly specified model. In addition, we show that a specific AIPW kernel estimator in our class that employs the fitted values from a model for the conditional mean of the outcome given covariates and auxiliaries is double-robust, that is, it remains consistent if this model is correctly specified even if the selection probabilities are modeled or specified incorrectly. Furthermore, when both models happen to be right, this double-robust estimator attains the smallest possible asymptotic variance of all AIPW kernel estimators and maximally extracts the information in the auxiliary variables. We also describe a simple correction to the AIPW kernel estimating equations that while preserving double-robustness it ensures efficiency improvement over nonaugmented IPW estimation when the selection model is correctly specified regardless of the validity of the second model used in the augmentation term. We perform simulations to evaluate the finite sample performance of the proposed estimators, and apply the methods to the analysis of the AIDS Costs and Services Utilization Survey data. Technical proofs are available online.

A doubly robust estimation framework to quantify potential bias in linked crash-EMS-trauma data with multi-cohort overlap.

We develop a novel doubly-robust (DR) imputation framework for longitudinal studies with monotone dropout, motivated by the informative dropout that is common in FDA-regulated trials for Alzheimer's disease. In this approach, the missing data are first imputed using a doubly-robust augmented inverse probability weighting (AIPW) estimator, then the imputed completed data are substituted into a full-data estimating equation, and the estimate is obtained using standard software. The imputed completed data may be inspected and compared to the observed data, and standard model diagnostics are available. The same imputed completed data can be used for several different estimands, such as subgroup analyses in a clinical trial, allowing for reduced computation and increased consistency across analyses. We present two specific DR imputation estimators, AIPW-I and AIPW-S, study their theoretical properties, and investigate their performance by simulation. AIPW-S has substantially reduced computational burden compared to many other DR estimators, at the cost of some loss of efficiency and the requirement of stronger assumptions. Simulation studies support the theoretical properties and good performance of the DR imputation framework. Importantly, we demonstrate their ability to address time-varying covariates, such as a time by treatment interaction. We illustrate using data from a large randomized Phase III trial investigating the effect of donepezil in Alzheimer's disease, from the Alzheimer's Disease Cooperative Study (ADCS) group.

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.

Principled methods with which to appropriately analyze missing data have long existed; however, broad implementation of these methods remains challenging. In this and 2 companion papers (Am J Epidemiol. 2018;187(3):576-584 and Am J Epidemiol. 2018;187(3):585-591), we discuss issues pertaining to missing data in the epidemiologic literature. We provide details regarding missing-data mechanisms and nomenclature and encourage the conduct of principled analyses through a detailed comparison of multiple imputation and inverse probability weighting. Data from the Collaborative Perinatal Project, a multisite US study conducted from 1959 to 1974, are used to create a masked data-analytical challenge with missing data induced by known mechanisms. We illustrate the deleterious effects of missing data with naive methods and show how principled methods can sometimes mitigate such effects. For example, when data were missing at random, naive methods showed a spurious protective effect of smoking on the risk of spontaneous abortion (odds ratio (OR) = 0.43, 95% confidence interval (CI): 0.19, 0.93), while implementation of principled methods multiple imputation (OR = 1.30, 95% CI: 0.95, 1.77) or augmented inverse probability weighting (OR = 1.40, 95% CI: 1.00, 1.97) provided estimates closer to the "true" full-data effect (OR = 1.31, 95% CI: 1.05, 1.64). We call for greater acknowledgement of and attention to missing data and for the broad use of principled missing-data methods in epidemiologic research.

After a short introduction of the model, the missing mechanism and the method of inference some imputation procedures are introduced with special focus on the simulation experiment. Within this experiment, the simple additive model y = f(x) + e is assumed to have missing values in the independent variable according to MCAR. Besides the well-known complete case analysis, mean imputation plus random noise, a single imputation and two ways of nearest neighbor imputation are used. These methods are compared within a simulation experiment based on the average mean square error, variances and biases of \hat{f}(x) at the knots.

A review on missing values for main challenges and methods

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A shape change in the random effects distribution is considered by directly modeling the effect of the missing data process on the evolution of the latent structure. To estimate the resulting model, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. The proposal is illustrated via simulations and then applied on a dataset concerning skin cancers. Comparisons with other well-established methods are provided as well.

Missing data are uncollected data but meaningful for the statistical analysis due to clinical relevancy of the data for properly specified estimands in clinical trials. Meanwhile the efforts to prevent or minimize missing data are commonly applied in clinical trials, in practice, missing data still occurs. Choosing a statistical method for imputation that deals with missing data targeting specified estimands provides the more reliable estimates of treatment effects. We considered longitudinal clinical settings that have different degrees of missing data and treatment effects, and simulated different missing mechanisms using data from randomized, double-blind, placebo-controlled phase 3 confirmatory clinical trials of approved drugs. We compared four commonly used statistical methods to deal with missing data in clinical trials. We find that, when the data are missing not at random (MNAR) with higher missing rates, mixed model for repeated measurements (MMRM) method overestimates treatment difference. Pattern-mixture model estimates were seen to be more conservative in our studies than MMRM given MNAR assumptions, which are more realistic with missing datain clinical trials. We emphasize the importance of prevention of missing data and specifying the estimand based on trial objectives beforehand. The specified proper estimand and the proper statistical method might be key features to value the clinical trial results despite missing data.

 Electrocardiogram signal analysis is very difficult to classify cardiac arrhythmia using machine learning methods. The ECG datasets normally come with multiple missing values. The reason for the missing values is the faults or distortion. When performing data mining, missing value imputation is the biggest task for data preprocessing. This problem could arise due to incomplete medical datasets if the incomplete missing values and cases were removed from the original database. To produce a good quality dataset for better analyzing the clinical trials, the suitable missing value imputation method is used. In this paper, we explore the different machine-learning techniques for the computed missing value in the electrocardiogram dataset. To estimate the missing imputation values, the collected data contains feature dimensions with their attributes. The experiments to compute the missing values in the dataset are carried out by using the four feature selection methods and imputation methods. The implemented results are shown by combined features using IG (information gain), GA (genetic algorithm) and the different machine learning classifiers such as NB (naïve bayes), KNN (K-nearest neighbor), MLP (Multilayer perception), and RF (Random forest). The GA (genetic algorithm) and IG (information gain) are the best suitable methods for obtaining the results on lower dimensional datasets with RMSE (Root mean square error. It efficiently calculates the best results for missing values. These four classifiers are used to analyze the impact of imputation methods. The best results for missing rate 10% to 40% are obtained by NB that is 0.657, 0.6541, 0.66, 0.657, and 0.657, as computed by RMSE (Root mean Square error). It means that error will efficiently reduced by naïve bayes classifier.

BackgroundTraditional approaches to identify missing mechanisms are usually based on the hypothesis test and confronted with both theoretical and practical challenges. It has been proved that the Bayesian network is powerful in integrating, analyzing and visualizing information, and some previous researches have verified the promising features of Bayesian network to deal with the aforementioned challenges in missing mechanism identification. Based on the above reasons, this paper explores the application of Bayesian network to the identification of missing mechanisms for the first time, and proposes a new method, the Bayesian network-based missing mechanism identification (BN-MMI) method, to identify missing mechanism in medical research.MethodsThe procedure of BN-MMI method consists three easy-to-implement steps: estimating the missing data structure by the Bayesian network; assessing the credibility of the estimated missing data structure; and identifying the missing mechanism from the estimated missing data structure. The BN-MMI method is verified by simulation research and empirical research.ResultsThe simulation study verified the validity, consistency and robustness of BN-MMI method, and indicated its outperformance in contrast to the traditional logistic regression method. In addition, the empirical study illustrated the applicability of BN-MMI method in the real world by an example of medical record data.ConclusionsIt was confirmed that the BN-MMI method itself, together with human knowledge and expertise, could identify the missing mechanisms according to the probabilistic dependence/independence relations among variables of interest. At the same time, our research shed light upon the potential application of BN-MMI method to a broader range of missing data issues in medical studies.

Focus of presentation Missing data are ubiquitous in medical research. Although there is increasing guidance on how to handle missing data, practice is changing slowly and misapprehensions abound, particularly in observational research. We present a practical framework for handling and reporting the analysis of incomplete data in observational studies, which we illustrate using a case study from the Avon Longitudinal Study of Parents and Children. Findings The framework consists of three steps: 1) Develop an analysis plan specifying the analysis model and how missing data are going to be addressed. Important considerations are whether a complete records analysis is likely to be valid, whether multiple imputation or an alternative approach is likely to offer benefits, and whether a sensitivity analysis regarding the missingness mechanism is required. 2) Explore the data, checking the methods outlined in the analysis plan are appropriate, and conduct the pre-planned analysis. 3) Report the results, including a description of the missing data, details on how missing data were addressed, and the results from all analyses, interpreted in light of the missing data and clinical relevance. Conclusions/Implications This framework encourages researchers to think carefully about their missing data and be transparent about the potential effect on the study results. This will increase confidence in the reliability and reproducibility of results from published papers. Key messages Researchers need to develop a plan for missing data prior to conducting their analysis, and be transparent about how they handled the missing data and its potential effect when reporting their results.

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

The 'AIPW' package implements the augmented inverse probability weighting, a doubly robust estimator, for average causal effect estimation with user-defined stacked machine learning algorithms. To cite the 'AIPW' package, please use: "Yongqi Zhong, Edward H. Kennedy, Lisa M. Bodnar, Ashley I. Naimi (2021). AIPW: An R Package for Augmented Inverse Probability Weighted Estimation of Average Causal Effects. American Journal of Epidemiology. &lt;<a href="https://doi.org/10.1093%2Faje%2Fkwab207" target="_top">doi:10.1093/aje/kwab207</a>&gt;". Visit: &lt;<a href="https://yqzhong7.github.io/AIPW/" target="_top">https://yqzhong7.github.io/AIPW/</a>&gt; for more information.

Pooled analysis of the MANTICO2 and MONET randomized controlled trials comparing drug efficacy for early treatment of COVID-19 during Omicron waves