Identification of Local Causal Effects with Missing Outcome Values and an Instrument for Non Response

Even in randomized experiments the identification of causal effects is often threatened by the presence of missing outcome values, with missingness possibly being non ignorable. We provide sufficient conditions under which the availability of a binary instrument for non response allows us to non parametrically point identify average causal effects in some latent subgroups of units, named Principal Strata, defined by their non response behavior in all possible combinations of treatment and instrument. Examples are provided as possible scenarios where our assumptions may be plausible.     

Refusal to Answer Specific Questions in a Survey: A Case Study

It is well known that non ignorable item non response may occur when the cause of the non response is the value of the latent variable of interest. In these cases, a refusal by a respondent to answer specific questions in a survey should be treated sometimes as a non ignorable item non response. The Rasch-Rasch model (RRM) is a new two-dimensional item response theory model for addressing non ignorable non response. This article demonstrates the use of the RRM on data from an Italian survey focused on assessment of healthcare workers’ knowledge about sudden infant death syndrome (that is, a context in which non response is presumed to be more likely among individuals with a low level of competence). We compare the performance of the RRM with other models within the Rasch model family that assume the unidimensionality of the latent trait. We conclude that this assumption should be considered unreliable for the data at hand, whereas the RRM provides a better fit of the data.     

Model-based inference for categorical survey data subject to non-ignorable non-response

We consider non-response models for a single categorical response with categorical covariates whose values are always observed. We present Bayesian methods for ignorable models and a particular non-ignorable model, and we argue that standard methods of model comparison are inappropriate for comparing ignorable and non-ignorable models. Uncertainty about ignorability of non-response is incorporated by introducing parameters describing the extent of non-ignorability into a pattern mixture specification and integrating over the prior uncertainty associated with these parameters. Our approach is illustrated using polling data from the 1992 British general election panel survey. We suggest sample size adjustments for surveys when non-ignorable non-response is expected.     

Perfect value and outlier detection in logistic binary choice models

Tins paper discussed some diagnostic tools for logistics binary choice models using techniques based on perfect values. The concept of perfect value fit is defined for logistic models in an analogous approach used when dealing with non ignorable non-iespouse in contingency tables. Performance ol outlier diagnostics based on perfect values is illustrated on a set of data on incidents in pre-Challenger launches.     

Inference for proportional hazard model with propensity score

Since the publication of the seminal paper by Cox (1972), proportional hazard model has become very popular in regression analysis for right censored data. In observational studies, treatment assignment may depend on observed covariates. If these confounding variables are not accounted for properly, the inference based on the Cox proportional hazard model may perform poorly. As shown in Rosenbaum and Rubin (1983), under the strongly ignorable treatment assignment assumption, conditioning on the propensity score yields valid causal effect estimates. Therefore we incorporate the propensity score into the Cox model for causal inference with survival data. We derive the asymptotic property of the maximum partial likelihood estimator when the model is correctly specified. Simulation results show that our method performs quite well for observational data. The approach is applied to a real dataset on the time of readmission of trauma patients. We also derive the asymptotic property of the maximum partial likelihood estimator with a robust variance estimator, when the model is incorrectly specified.     

Strategies for composite estimands in confirmatory clinical trials: Examples from trials in nasal polyps and steroid reduction

The draft addendum to the ICH E9 regulatory guideline asks for explicit definition of the treatment effect to be estimated in clinical trials. The draft guideline also introduces the concept of intercurrent events to describe events that occur post‐randomisation that may affect efficacy assessment. Composite estimands allow incorporation of intercurrent events in the definition of the endpoint. A common example of an intercurrent event is discontinuation of randomised treatment and use of a composite strategy would assess treatment effect based on a variable that combines the outcome variable of interest with discontinuation of randomised treatment. Use of a composite estimand may avoid the need for imputation which would be required by a treatment policy estimand. The draft guideline gives the example of a binary approach for specifying a composite estimand. When the variable is measured on a non‐binary scale, other options are available where the intercurrent event is given an extreme unfavourable value, for example comparison of median values or analysis based on categories of response. This paper reviews approaches to deriving a composite estimand and contrasts the use of this estimand to the treatment policy estimand. The benefits of using each strategy are discussed and examples of the use of the different approaches are given for a clinical trial in nasal polyposis and a steroid reduction trial in severe asthma.     

Estimating low pay transition probabilities accounting for endogenous selection mechanisms

Summary.  We propose a model of transitions into and out of low paid employment that accounts for non-ignorable panel dropout, employment retention and base year low pay status ('initial conditions'). The model is fitted to data for men from the British Household Panel Survey. Initial conditions and employment retention are found to be non-ignorable selection processes. Whether panel dropout is found to be ignorable depends on how item non-response on pay is treated. Notwithstanding these results, we also find that models incorporating a simpler approach to accounting for non-ignorable selections provide estimates of covariate effects that differ very little from the estimates from the general model.     

Logistic regression analysis of non‐randomized response data collected by the parallel model in sensitive surveys

To study the relationship between a sensitive binary response variable and a set of non‐sensitive covariates, this paper develops a hidden logistic regression to analyse non‐randomized response data collected via the parallel model originally proposed by Tian (2014). This is the first paper to employ the logistic regression analysis in the field of non‐randomized response techniques. Both the Newton–Raphson algorithm and a monotone quadratic lower bound algorithm are developed to derive the maximum likelihood estimates of the parameters of interest. In particular, the proposed logistic parallel model can be used to study the association between a sensitive binary variable and another non‐sensitive binary variable via the measure of odds ratio. Simulations are performed and a study on people's sexual practice data in the United States is used to illustrate the proposed methods.     

Bayesian predictive inference of a finite population proportion under selection bias

We show how to infer about a finite population proportion using data from a possibly biased sample. In the absence of any selection bias or survey weights, a simple ignorable selection model, which assumes that the binary responses are independent and identically distributed Bernoulli random variables, is not unreasonable. However, this ignorable selection model is inappropriate when there is a selection bias in the sample. We assume that the survey weights (or their reciprocals which we call ‘selection’ probabilities) are available, but there is no simple relation between the binary responses and the selection probabilities. To capture the selection bias, we assume that there is some correlation between the binary responses and the selection probabilities (e.g., there may be a somewhat higher/lower proportion of positive responses among the sampled units than among the nonsampled units). We use a Bayesian nonignorable selection model to accommodate the selection mechanism. We use Markov chain Monte Carlo methods to fit the nonignorable selection model. We illustrate our method using numerical examples obtained from NHIS 1995 data.     

PARAMETRIC FRACTIONAL IMPUTATION FOR NON‐IGNORABLE CATEGORICAL MISSING DATA WITH FOLLOW‐UP

Incomplete data subject to non‐ignorable non‐response are often encountered in practice and have a non‐identifiability problem. A follow‐up sample is randomly selected from the set of non‐respondents to avoid the non‐identifiability problem and get complete responses. Glynn, Laird, & Rubin analyzed non‐ignorable missing data with a follow‐up sample under a pattern mixture model. In this article, maximum likelihood estimation of parameters of the categorical missing data is considered with a follow‐up sample under a selection model. To estimate the parameters with non‐ignorable missing data, the EM algorithm with weighting, proposed by Ibrahim, is used. That is, in the E‐step, the weighted mean is calculated using the fractional weights for imputed data. Variances are estimated using the approximated jacknife method. Simulation results are presented to compare the proposed method with previously presented methods.     

Optimizing a control plan using a structural equation model with an application to statistical process analysis

In the case where non-experimental data are available from an industrial process and a directed graph for how various factors affect a response variable is known based on a substantive understanding of the process, we consider a problem in which a control plan involving multiple treatment variables is conducted in order to bring a response variable close to a target value with variation reduction. Using statistical causal analysis with linear (recursive and non-recursive) structural equation models, we configure an optimal control plan involving multiple treatment variables through causal parameters. Based on the formulation, we clarify the causal mechanism for how the variance of a response variable changes when the control plan is conducted. The results enable us to evaluate the effect of a control plan on the variance of a response variable from non-experimental data and provide a new application of linear structural equation models to engineering science.     

Sensitivity to censored‐at‐random assumption in the analysis of time‐to‐event endpoints

Over the past years, significant progress has been made in developing statistically rigorous methods to implement clinically interpretable sensitivity analyses for assumptions about the missingness mechanism in clinical trials for continuous and (to a lesser extent) for binary or categorical endpoints. Studies with time‐to‐event outcomes have received much less attention. However, such studies can be similarly challenged with respect to the robustness and integrity of primary analysis conclusions when a substantial number of subjects withdraw from treatment prematurely prior to experiencing an event of interest. We discuss how the methods that are widely used for primary analyses of time‐to‐event outcomes could be extended in a clinically meaningful and interpretable way to stress‐test the assumption of ignorable censoring. We focus on a ‘tipping point’ approach, the objective of which is to postulate sensitivity parameters with a clear clinical interpretation and to identify a setting of these parameters unfavorable enough towards the experimental treatment to nullify a conclusion that was favorable to that treatment. Robustness of primary analysis results can then be assessed based on clinical plausibility of the scenario represented by the tipping point. We study several approaches for conducting such analyses based on multiple imputation using parametric, semi‐parametric, and non‐parametric imputation models and evaluate their operating characteristics via simulation. We argue that these methods are valuable tools for sensitivity analyses of time‐to‐event data and conclude that the method based on piecewise exponential imputation model of survival has some advantages over other methods studied here. Copyright © 2016 John Wiley & Sons, Ltd.     

Monte Carlo methods for nonparametric survival model determination

In the causal analysis of survival data a time-based response is related to a set of explanatory variables. Definition of the relation between the time and the covariates may become a difficult task, particularly in the preliminary stage, when the information is limited. Through a nonparametric approach, we propose to estimate the survival function allowing to evaluate the relative importance of each potential explanatory variable, in a simple and explanatory fashion. To achieve this aim, each of the explanatory variables is used to partition the observed survival times. The observations are assumed to be partially exchangeable according to such partition. We then consider, conditionally on each partition, a hierarchical nonparametric Bayesian model on the hazard functions. We define and compare different prior distribution for the hazard functions.     

Estimating the causal effects in randomized trials for survival data with a cure fraction and non compliance

We consider causal inference in randomized studies for survival data with a cure fraction and all-or-none treatment non compliance. To describe the causal effects, we consider the complier average causal effect (CACE) and the complier effect on survival probability beyond time t (CESP), where CACE and CESP are defined as the difference of cure rate and non cured subjects’ survival probability between treatment and control groups within the complier class. These estimands depend on the distributions of survival times in treatment and control groups. Given covariates and latent compliance type, we model these distributions with transformation promotion time cure model whose parameters are estimated by maximum likelihood. Both the infinite dimensional parameter in the model and the mixture structure of the problem create some computational difficulties which are overcome by an expectation-maximization (EM) algorithm. We show the estimators are consistent and asymptotically normal. Some simulation studies are conducted to assess the finite-sample performance of the proposed approach. We also illustrate our method by analyzing a real data from the Healthy Insurance Plan of Greater New York.     

基于协变量平衡加权的平均处理效应的稳健有效估计

倾向性得分是估计平均处理效应的重要工具。但在观察性研究中,通常会由于协变量在处理组与对照组分布的不平衡性而导致极端倾向性得分的出现,即存在十分接近于0或1的倾向性得分,这使得因果推断的强可忽略假设接近于违背,进而导致平均处理效应的估计出现较大的偏差与方差。Li等(2018a)提出了协变量平衡加权法,在无混杂性假设下通过实现协变量分布的加权平衡,解决了极端倾向性得分带来的影响。本文在此基础上,提出了基于协变量平衡加权法的稳健且有效的估计方法,并通过引入超级学习算法提升了模型在实证应用中的稳健性;更进一步,将前一方法推广至理论上不依赖于结果回归模型和倾向性得分模型假设的基于协变量平衡加权的稳健有效估计。蒙特卡洛模拟表明,本文提出的两种方法在结果回归模型和倾向性得分模型均存在误设时仍具有极小的偏差和方差。实证部分将两种方法应用于右心导管插入术数据,发现右心导管插入术大约会增加患者6. 3%死亡率。     

Identification of the Direction of a Causal Effect by Instrumental Variables

This article provides a strategy to identify the existence and direction of a causal effect in a generalized nonparametric and nonseparable model identified by instrumental variables. The causal effect concerns how the outcome depends on the endogenous treatment variable. The outcome variable, treatment variable, other explanatory variables, and the instrumental variable can be essentially any combination of continuous, discrete, or “other” variables. In particular, it is not necessary to have any continuous variables, none of the variables need to have large support, and the instrument can be binary even if the corresponding endogenous treatment variable and/or outcome is continuous. The outcome can be mismeasured or interval-measured, and the endogenous treatment variable need not even be observed. The identification results are constructive, and can be empirically implemented using standard estimation results.     

Partial identification of average treatment effects on the treated through difference-in-differences

ABSTRACT

The difference-in-differences (DID) method is widely used as a tool for identifying causal effects of treatments in program evaluation. When panel data sets are available, it is well-known that the average treatment effect on the treated (ATT) is point-identified under the DID setup. If a panel data set is not available, repeated cross sections (pretreatment and posttreatment) may be used, but may not point-identify the ATT. This paper systematically studies the identification of the ATT under the DID setup when posttreatment treatment status is unknown for the pretreatment sample. This is done through a novel application of an extension of a continuous version of the classical monotone rearrangement inequality which allows for general copula bounds. The identifying power of an instrumental variable and of a ‘matched subsample’ is also explored. Finally, we illustrate our approach by estimating the effect of the Americans with Disabilities Act of 1991 on employment outcomes of the disabled.     

Maximum likelihood estimation of bivariate logistic models for incomplete responses with indicators of ignorable and non-ignorable missingness

Summary. Missing observations are a common problem that complicate the analysis of clustered data. In the Connecticut child surveys of childhood psychopathology, it was possible to identify reasons why outcomes were not observed. Of note, some of these causes of missingness may be assumed to be ignorable , whereas others may be non-ignorable . We consider logistic regression models for incomplete bivariate binary outcomes and propose mixture models that permit estimation assuming that there are two distinct types of missingness mechanisms: one that is ignorable; the other non-ignorable. A feature of the mixture modelling approach is that additional analyses to assess the sensitivity to assumptions about the missingness are relatively straightforward to incorporate. The methods were developed for analysing data from the Connecticut child surveys, where there are missing informant reports of child psychopathology and different reasons for missingness can be distinguished.     

Symmetric pattern models: a latent variable approach to item non-response in attitude scales

This paper proposes a new approach to the treatment of item non-response in attitude scales. It combines the ideas of latent variable identification with the issues of non-response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non-response. We present a symmetric pattern methodology for handling item non-response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a 'dependent' variable) and is pattern based in that the pattern of responses and non-responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.     

Effects of correlation and missing data on sample size estimation in longitudinal clinical trials

In longitudinal clinical trials, a common objective is to compare the rates of changes in an outcome variable between two treatment groups. Generalized estimating equation (GEE) has been widely used to examine if the rates of changes are significantly different between treatment groups due to its robustness to misspecification of the true correlation structure and randomly missing data. The sample size formula for repeated outcomes is based on the assumption of missing completely at random and a large sample approximation. A simulation study is conducted to investigate the performance of GEE sample size formula with small sample sizes, damped exponential family of correlation structure and non‐ignorable missing data. Copyright © 2008 John Wiley & Sons, Ltd.