Data envelopment analysis with missing data: a multiple imputation approach

Problem: Patients may withdraw from longitudinal clinical trials for many reasons. Methods for handling the problem presented by missing data of patients who withdraw before reaching the time point of the primary measurement include carrying the last observation forward (LOCF), data as observed analysis (DAO), mixed model approaches, and pattern mixture models. Method: We evaluate a multiple imputation (MI) approach that has the flexibility to adjust inferences about the treatment effect for the withdrawn patients relative to currently used alternatives. Sensitivity analyses are performed under a collection of scenarios that include many circumstances that may arise in practice, including different assumptions about treatment effects post-withdrawal and about the missing data mechanism. Simulations are used to compare the results of analyses based on the MI approach with those based on the LOCF, DAO, and the mixed model approaches. Results: The LOCF and DAO approaches cannot be recommended as strategies for handling missing responses, at least for these scenarios, because they provide biased estimates of treatment effects and biased tests of the null hypothesis of no treatment effect. Application of the various approaches to the analysis of clinical data from a longitudinal trial confirms the underestimation of the variability when the LOCF approach is used. *Dr. Paul Gallo served as Acting Editor for this manuscript.

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.

An important evolution in the missing data arena has been the recognition of need for clarity in objectives. The objectives of primary focus in clinical trials can often be categorized as assessing efficacy or effectiveness. The present investigation illustrated a structured framework for choosing estimands and estimators when testing investigational drugs to treat the symptoms of chronic illnesses. Key issues were discussed and illustrated using a reanalysis of the confirmatory trials from a new drug application in depression. The primary analysis used a likelihood-based approach to assess efficacy: mean change to the planned endpoint of the trial assuming patients stayed on drug. Secondarily, effectiveness was assessed using a multiple imputation approach. The imputation model-derived solely from the placebo group-was used to impute missing values for both the drug and placebo groups. Therefore, this so-called placebo multiple imputation (a.k.a. controlled imputation) approach assumed patients had reduced benefit from the drug after discontinuing it. Results from the example data provided clear evidence of efficacy for the experimental drug and characterized its effectiveness. Data after discontinuation of study medication were not required for these analyses. Given the idiosyncratic nature of drug development, no estimand or approach is universally appropriate. However, the general practice of pairing efficacy and effectiveness estimands may often be useful in understanding the overall risks and benefits of a drug. Controlled imputation approaches, such as placebo multiple imputation, can be a flexible and transparent framework for formulating primary analyses of effectiveness estimands and sensitivity analyses for efficacy estimands.

Purpose– The purpose of this paper is to measure the efficiencies of parallel subsystems with shared inputs/outputs. Each subsystem has not only a set of common inputs and outputs, but also some dedicated inputs and outputs as well as some shared inputs and outputs. A more general data envelopment analysis (DEA) approach is proposed to deal with this efficiency evaluation issue. Based on the proposed approach, mechanisms for shared inputs/outputs distribution and efficiency decomposition among sub-units are presented.Design/methodology/approach– To evaluate the efficiency of the parallel systems, this paper proposes a centralized DEA approach by assuming that the same input/output factor in a decision-making unit (DMU) has the same multiplier for all its sub-units. Furthermore, different proportions of shared inputs/outputs are imposed on sub-units within different DMUs in evaluating each DMU’s efficiency. The proposed approach is applied to evaluate the operational efficiencies of 18 railway firms in China.Findings– By using the proposed DEA approach, the efficiencies of the whole DMU and its sub-units can be measured at the same time, and the optimal allocation strategy of shared inputs/outputs can also be obtained. The proposed model is more reasonable and robust for measuring the operational performance of parallel systems with shared inputs and outputs. The efficiency of railway system in China is relatively low, and its inefficiency is largely caused by lower freight transportation performance. Great disparities among firms can be found in the passenger transportation efficiency and freight transportation efficiency.Research limitations/implications– This study develops the DEA model under the assumption of constant returns to scale, which can be directly extended to a situation with variable returns to scale.Practical implications– In this paper, the proposed approach is a more effective way to evaluate the efficiencies of parallel systems with shared inputs/outputs. With respect to the application, to improve the overall efficiency of China’s railway system, more efforts should be taken to improve its operational performance of freight transportation. Furthermore, firms’ disparities should also be considered when making these related policies.Originality/value– The proposed approach can evaluate the whole DMU and its sub-units at the same time. Considering simultaneously the common/dedicated/shared inputs/outputs, the proposed approach is more general than the existing approaches in the literature. In the described approach, the same type of input or output is assumed to have the same weight for all sub-units within one DMU. More importantly, the proposed model imposes different proportions of shared inputs/outputs on different DMUs’ sub-units when measuring the efficiency for each DMU.

Data envelopment analysis (DEA) is a tool for measuring the relative efficiency of decision-making units (DMUs) that perform similar tasks. One of the uses of the DEA is the establishment of benchmarks for inefficient DMUs. These benchmarks play the role of target for inefficient DMUs. However, traditional DEA (TDEA) models fail to rank the efficient DMUs, and as a result, they cannot determine a benchmark for the inefficient DMUs. To overcome this shortcoming, this paper proposes virtual network DEA (NDEA) approach. The proposed method not only ranks the whole inefficient and efficient DMUs but also establishes a virtual benchmark called ideal DMU. The case study demonstrates the applicability of the proposed model.

BackgroundMissing data are a common problem in prospective studies with a long follow-up, and the volume, pattern and reasons for missing data may be relevant when estimating the cost of illness. We aimed to evaluate the effects of different methods for dealing with missing longitudinal cost data and for costing caregiver time on total societal costs in Alzheimer’s disease (AD).MethodsGERAS is an 18-month observational study of costs associated with AD. Total societal costs included patient health and social care costs, and caregiver health and informal care costs. Missing data were classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Simulation datasets were generated from baseline data with 10–40 % missing total cost data for each missing data mechanism. Datasets were also simulated to reflect the missing cost data pattern at 18 months using MAR and MNAR assumptions. Naïve and multiple imputation (MI) methods were applied to each dataset and results compared with complete GERAS 18-month cost data. Opportunity and replacement cost approaches were used for caregiver time, which was costed with and without supervision included and with time for working caregivers only being costed.ResultsTotal costs were available for 99.4 % of 1497 patients at baseline. For MCAR datasets, naïve methods performed as well as MI methods. For MAR, MI methods performed better than naïve methods. All imputation approaches were poor for MNAR data. For all approaches, percentage bias increased with missing data volume. For datasets reflecting 18-month patterns, a combination of imputation methods provided more accurate cost estimates (e.g. bias: −1 % vs −6 % for single MI method), although different approaches to costing caregiver time had a greater impact on estimated costs (29–43 % increase over base case estimate).ConclusionsMethods used to impute missing cost data in AD will impact on accuracy of cost estimates although varying approaches to costing informal caregiver time has the greatest impact on total costs. Tailoring imputation methods to the reason for missing data will further our understanding of the best analytical approach for studies involving cost outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0188-1) contains supplementary material, which is available to authorized users.

In many applications of data envelopment analysis (DEA) approach, there is often a fixed cost or resource which is imposed on all decision making units (DMUs). One nature question then is: how can this cost or resource be assigned in a reasonable way to various DMUs? In this paper, we present a new DEA-based method for obtaining this cost or resource allocation. To illustrate our methods, numerical results for an example from the literature are presented.

BackgroundMultiple imputation is frequently used to deal with missing data in healthcare research. Although it is known that the outcome should be included in the imputation model when imputing missing covariate values, it is not known whether it should be imputed. Similarly no clear recommendations exist on: the utility of incorporating a secondary outcome, if available, in the imputation model; the level of protection offered when data are missing not-at-random; the implications of the dataset size and missingness levels.MethodsWe used realistic assumptions to generate thousands of datasets across a broad spectrum of contexts: three mechanisms of missingness (completely at random; at random; not at random); varying extents of missingness (20–80% missing data); and different sample sizes (1,000 or 10,000 cases). For each context we quantified the performance of a complete case analysis and seven multiple imputation methods which deleted cases with missing outcome before imputation, after imputation or not at all; included or did not include the outcome in the imputation models; and included or did not include a secondary outcome in the imputation models. Methods were compared on mean absolute error, bias, coverage and power over 1,000 datasets for each scenario.ResultsOverall, there was very little to separate multiple imputation methods which included the outcome in the imputation model. Even when missingness was quite extensive, all multiple imputation approaches performed well. Incorporating a secondary outcome, moderately correlated with the outcome of interest, made very little difference. The dataset size and the extent of missingness affected performance, as expected. Multiple imputation methods protected less well against missingness not at random, but did offer some protection.ConclusionsAs long as the outcome is included in the imputation model, there are very small performance differences between the possible multiple imputation approaches: no outcome imputation, imputation or imputation and deletion. All informative covariates, even with very high levels of missingness, should be included in the multiple imputation model. Multiple imputation offers some protection against a simple missing not at random mechanism.

Efficiency evaluations with context-dependent and measure-specific data envelopment approaches: An application in a World Bank supported project

BackgroundMissing data due to attrition are rampant in substance abuse clinical trials. However, missing data are often ignored in the presentation of substance abuse clinical trials. This paper demonstrates missing data methods which may be used for hypothesis testing.MethodsMethods involving stratifying and weighting individuals based on missing data pattern are shown to produce tests that are robust to missing data mechanisms in terms of Type I error and power. In this article, we describe several methods of combining data that may be used for testing hypotheses of the treatment effect. Furthermore, illustrations of each test's Type I error and power under different missing data percentages and mechanisms are quantified using a Monte-Carlo simulation study.ResultsType I error rates were similar for each method, while powers depended on missing data assumptions. Specifically, power was greatest for the weighted, compared to un-weighted methods, especially for greater missing data percentages.ConclusionResults of this study as well as extant literature demonstrate the need for standards of design and analysis specific to substance abuse clinical trials. Given the known substantial attrition rates and concern for the missing data mechanism in substance abuse clinical trials, investigators need to incorporate missing data methods a priori. That is, missing data methods should be specified at the outset of the study and not after the data have been collected.

Considerations of multiple imputation approaches for handling missing data in clinical trials

Multiple imputation (MI) is a popular method for handling missing data. In education research, it can be challenging to use MI because the data often have a clustered structure that need to be accommodated during MI. Although much research has considered applications of MI in hierarchical data, little is known about its use in cross-classified data, in which observations are clustered in multiple higher-level units simultaneously (e.g., schools and neighborhoods, transitions from primary to secondary schools). In this article, we consider several approaches to MI for cross-classified data (CC-MI), including a novel fully conditional specification approach, a joint modeling approach, and other approaches that are based on single- and two-level MI. In this context, we clarify the conditions that CC-MI methods need to fulfill to provide a suitable treatment of missing data, and we compare the approaches both from a theoretical perspective and in a simulation study. Finally, we illustrate the use of CC-MI in real data and discuss the implications of our findings for research practice.

High‐dimensional datasets have become increasingly prominent in fields such as medicine, biology, and the social sciences. These datasets often contain missing values, which can significantly compromise the reliability and validity of analytical results. This review examines simulation studies in the literature that address the issue of missing data in high‐dimensional settings. It compares the effectiveness and applicability of multiple imputation (MI) methods, discussing their strengths and weaknesses. The review also explores the challenges encountered by MI techniques in high‐dimensional data and outlines directions for future research. Its primary aim is to guide researchers and practitioners in selecting appropriate MI methods to manage missing data issues in their own datasets. The reviewed simulation studies assess the performance of various MI approaches under different missing data mechanisms and data structures, highlighting their potential advantages and limitations in real‐world applications. In conclusion, MI methods for high‐dimensional data represent a dynamic and rapidly evolving area of research. While existing approaches offer substantial capabilities, there remains a pressing need for continual innovation and rigorous inquiry to develop MI solutions that are theoretically sound, practically feasible, and capable of producing more accurate, reliable, and efficient results. This article is categorized under: Statistical Models > Simulation Models Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Models > Model Selection

Data Envelopment Analysis (DEA) is a data-oriented performance evaluation method that has a very satisfactory performance when there are multiple inputs and outputs presented in the form of set of peer Decision Making Units (DMU). In the discussion of DEA, basically measures the efficiency of each DMU in specific performance based on DEA Efficiency Scores. In DEA, when there is a value of Non-Zero Input and Output Slacks then this often means inefficiency. This scalar measures directly with the input surplus and the output of the short decision of the decision making unit (DMU). Universitas Malikussaleh as one of the State Universities in Indonesia, it is necessary to follow the regulations of the Ministry of Research, Technology and Higher Education of the Republic of Indonesia (KEMENRISTEKDIKTI), one of which is the measurement of efficiency based on the number of lecturers research, the efficient use of resources included in the number of lecturers and employees, as well as students who can be accommodated based on efficiency measurements using DEA. This paper will measure the efficiency of each department in Malikussaleh University and if there is an inefficient department then it will be measured based on slack-based measures to advise aspects that need attention so that the department can be efficient.

In a single-cell RNA-seq (scRNA-seq) data set, a high proportion of missing values (or an excessive number of zeroes) are frequently observed. For the related follow-up tasks, such as clustering analysis and differential expression analysis, a data set without missing values is generally required. Many imputation approaches have been proposed for this purpose. Multiple imputation (MI) is a well-established approach to address possible biases in a follow-up analysis result based on one-time imputed data. There is a lack of investigation on this in the analysis of scRNA-seq data. In this study, we have investigated how to efficiently apply the MI approach to the clustering analysis and the differential expression analysis of scRNA-seq data. We proposed an MI procedure for clustering analysis and an MI procedure for differential expression analysis. To demonstrate the improvements achieved by MI in clustering analysis and differential expression analysis of scRNA-seq data, we analyzed three well-known scRNA-seq data sets. scIGANs, an scRNA-seq imputation method based on the generative adversarial networks (GANs), has been recently proposed for scRNA-seq data imputation. Multiple randomly imputed data sets can be conveniently generated by this method. We implemented our MI procedures based on scIGANs. We demonstrated that MI yielded improved performances on the clustering analysis and differential expression analysis results. Our applications to experimental scRNA-seq data illustrated the advantages of MI over one-time imputation of missing values in scRNA-seq data.