Buckley–James Type Estimator for Censored Data with Covariates Missing by Design

Abstract. The Buckley–James estimator (BJE) is a well‐known estimator for linear regression models with censored data. Ritov has generalized the BJE to a semiparametric setting and demonstrated that his class of Buckley–James type estimators is asymptotically equivalent to the class of rank‐based estimators proposed by Tsiatis. In this article, we revisit such relationship in censored data with covariates missing by design. By exploring a similar relationship between our proposed class of Buckley–James type estimating functions to the class of rank‐based estimating functions recently generalized by Nan, Kalbfleisch and Yu, we establish asymptotic properties of our proposed estimators. We also conduct numerical studies to compare asymptotic efficiencies from various estimators.     

Computations of predictors/estimators under a linear random-effects model with parameter restrictions

This paper considers the problem of simultaneously predicting/estimating unknown parameter spaces in a linear random-effects model with both parameter restrictions and missing observations. We shall establish explicit formulas for calculating the best linear unbiased predictors (BLUPs) of all unknown parameters in such a model, and derive a variety of mathematical and statistical properties of the BLUPs under general assumptions. We also discuss some matrix expressions related to the covariance matrix of the BLUP, and present various necessary and sufficient conditions for several equalities and inequalities of the covariance matrix of the BLUP to hold.     

Treatment policy estimands for recurrent event data using data collected after cessation of randomised treatment

In the past, many clinical trials have withdrawn subjects from the study when they prematurely stopped their randomised treatment and have therefore only collected ‘on‐treatment’ data. Thus, analyses addressing a treatment policy estimand have been restricted to imputing missing data under assumptions drawn from these data only. Many confirmatory trials are now continuing to collect data from subjects in a study even after they have prematurely discontinued study treatment as this event is irrelevant for the purposes of a treatment policy estimand. However, despite efforts to keep subjects in a trial, some will still choose to withdraw. Recent publications for sensitivity analyses of recurrent event data have focused on the reference‐based imputation methods commonly applied to continuous outcomes, where imputation for the missing data for one treatment arm is based on the observed outcomes in another arm. However, the existence of data from subjects who have prematurely discontinued treatment but remained in the study has now raised the opportunity to use this ‘off‐treatment’ data to impute the missing data for subjects who withdraw, potentially allowing more plausible assumptions for the missing post‐study‐withdrawal data than reference‐based approaches. In this paper, we introduce a new imputation method for recurrent event data in which the missing post‐study‐withdrawal event rate for a particular subject is assumed to reflect that observed from subjects during the off‐treatment period. The method is illustrated in a trial in chronic obstructive pulmonary disease (COPD) where the primary endpoint was the rate of exacerbations, analysed using a negative binomial model.     

Quantifying the magnitude and potential influence of missing data in campus sexual assault surveys: A systematic review of surveys, 2010–2016

Objective: To understand how missing data may influence conclusions drawn from campus sexual assault surveys. Methods: We systematically reviewed 40 surveys from 2010–2016. We constructed a pseudo-population of the total population targeted across schools, creating records proportional to the respective response rate and reported sexual assault prevalence. We simulated the effects of 9 scenarios where the sexual assault prevalence among nonresponders differed from that of responders. Results: The surveys represented a total female undergraduate population of 317,387 with only 77,966 (24.6%) survey responses. Among responders, 20.4% reported experiences of sexual assault. However, prevalence of sexual assault could theoretically range from 5.0 to 80.4% under extreme assumptions about prevalence in nonresponders. Smaller, but still significant differences were observed with less extreme assumptions. Conclusions: Missing data are widespread in campus sexual assault surveys. Conclusions drawn from these incomplete data are highly sensitive to assumptions about the sexual assault prevalence among nonresponders.     

Merging Incomplete Tertiary Datasets: The Case of 2-1-1 Information and Referral Missing Data

This study proposes a method to handle missing data when merging large tertiary datasets. Combining 25 datasets of 2-1-1 Texas Information & Referral Network’s call records to analyze unmet needs during Hurricanes Katrina and Rita highlighted a considerable bias problem due to missing data of a key variable in some of the 25 datasets. First, extensive literature about existing techniques for handling missing data was reviewed but determined not applicable for this type of missing data problem. Next, a systematic algorithm was developed to calculate missing data types and strategies in tertiary datasets. Last, this method was applied to the 2-1-1 datasets to test its effectiveness on bias due to previous missing data. Using this approach, the volume of cases available for analysis was increased approximately 30 percent, hence greatly improving validity of the findings. In terms of social service research, minimizing bias of missing data in existing tertiary data resources would help policymakers make more appropriate decisions and provide more effective and timely social support and disaster services to residents. This new method could be applied to using tertiary data with a similar dilemma and contribute to increasing potential use of available public datasets.     

Reliability of a soccer player based on the bivariate Rayleigh distribution with right censored and ignorable missing data

In this paper, we study the performance of a soccer player based on analysing an incomplete data set. To achieve this aim, we fit the bivariate Rayleigh distribution to the soccer dataset by the maximum likelihood method. In this way, the missing data and right censoring problems, that usually happen in such studies, are considered. Our aim is to inference about the performance of a soccer player by considering the stress and strength components. The first goal of the player of interest in a match is assumed as the stress component and the second goal of the match is assumed as the strength component. We propose some methods to overcome incomplete data problem and we use these methods to inference about the performance of a soccer player.     

仿EM的多变量缺失数据填补算法及其在信用评估中的应用

数据缺失会显著降低信用评估模型的准确性和可用性,尤其是多变量同时有数据缺失时。本文针对模型应用阶段的多变量数据缺失问题,提出了一种新的数据填补算法。该算法由两阶段构成：准备阶段和数据填补阶段。在准备阶段,算法基于朴素贝叶斯方法以初始数据集进行训练,对每个可能缺失的变量构建起相应的单变量预测估计模型;而数据填补阶段则借鉴了EM算法的思想,利用前期的单变量预测估计模型,对给定的多变量数据缺失样本进行交替迭代,逐步填补更新。理论证明,该算法具有单调收敛性。以人人贷数据集和UCI提供的德国和澳大利亚两个信用评估基准数据集为例,将其与众数填补法、EM填补法进行性能对比实验,结果表明本文方法的数据还原性能和填补后信用评估准确性都明显更优。这为解决信用评估时的数据多变量缺失问题提供了一种更好的处理方法。     

Review of guidelines and literature for handling missing data in longitudinal clinical trials with a case study

Missing data in clinical trials are inevitable. We highlight the ICH guidelines and CPMP points to consider on missing data. Specifically, we outline how we should consider missing data issues when designing, planning and conducting studies to minimize missing data impact. We also go beyond the coverage of the above two documents, provide a more detailed review of the basic concepts of missing data and frequently used terminologies, and examples of the typical missing data mechanism, and discuss technical details and literature for several frequently used statistical methods and associated software. Finally, we provide a case study where the principles outlined in this paper are applied to one clinical program at protocol design, data analysis plan and other stages of a clinical trial.     

Sample size calculations for time-averaged difference of longitudinal binary outcomes

In clinical trials with repeated measurements, the responses from each subject are measured multiple times during the study period. Two approaches have been widely used to assess the treatment effect, one that compares the rate of change between two groups and the other that tests the time-averaged difference (TAD). While sample size calculations based on comparing the rate of change between two groups have been reported by many investigators, the literature has paid relatively little attention to the sample size estimation for time-averaged difference (TAD) in the presence of heterogeneous correlation structure and missing data in repeated measurement studies. In this study, we investigate sample size calculation for the comparison of time-averaged responses between treatment groups in clinical trials with longitudinally observed binary outcomes. The generalized estimating equation (GEE) approach is used to derive a closed-form sample size formula, which is flexible enough to account for arbitrary missing patterns and correlation structures. In particular, we demonstrate that the proposed sample size can accommodate a mixture of missing patterns, which is frequently encountered by practitioners in clinical trials. To our knowledge, this is the first study that considers the mixture of missing patterns in sample size calculation. Our simulation shows that the nominal power and type I error are well preserved over a wide range of design parameters. Sample size calculation is illustrated through an example.