Imputation Procedure Research Articles

Imputation of non-ignorable nonresponses for income: analysis of a panel study on Taiwan

In this paper, the two-step generalized estimating equations (GEE) approach developed by Wang and Fitzmaurice (Biom J 2:302–318, 2006) is employed to handle income non-responses in the Panel Study of Family Dynamics survey conducted in Taiwan. In our analysis, we first construct a conditional logit model of the paid work equation by taking the missing patterns into account. We then use the estimation results to impute whether or not the nonresponses were working for pay. For those who were imputed or observed to work for pay, we adopt the two-step GEE method to estimate the income equation. Compared to simply deleting the missing cases, the two-step imputation procedure is found to improve the estimation results.

A Nomogram for Predicting Surgical Complications in Bariatric Surgery Patients

To minimize morbidity and mortality associated with surgery risks in the obese patient, algorithms offer planning operative strategy. Because these algorithms often classify patients based on inadequate category granularity, outcomes may not be predicted accurately. We reviewed patient factors and patient outcomes for those who had undergone bariatric surgical procedures to determine relationships and developed a nomogram to calculate individualized patient risk. From the American College of Surgeons National Security Quality Improvement Program database, we identified 32,426 bariatric surgery patients meeting NIH criteria and treated between 2005 and 2008. We defined a composite binary outcome of 30-day postoperative morbidity and mortality. A predictive model based on preoperative variables was developed using multivariable logistic regression; a multiple imputation procedure allowed inclusions of observations with missing data. Model performance was assessed using the C-statistic. A calibration plot graphically assessed the agreement between predicted and observed probabilities in regard to 30-day morbidity/mortality. The nomogram model was constructed for maximal predictive accuracy. The estimated C-statistic [95% confidence interval] for the predictive nomogram was 0.629 [0.614, 0.645], indicative of slight to moderate discriminative ability beyond that of chance alone, and the greatest impacts on the estimated probability of morbidity/mortality were determined to be age, body mass index, serum albumin, and functional status. By accurately predicting 30-day morbidity and mortality, this nomogram may prove useful in patient preoperative counseling on postoperative complication risk. Our results additionally indicate that neither age nor presence of obesity-related comorbidities should exclude patients from bariatric surgery consideration.

Multiple imputation of missing dual‐energy X‐ray absorptiometry data in the National Health and Nutrition Examination Survey

In 1999, dual-energy x-ray absorptiometry (DXA) scans were added to the National Health and Nutrition Examination Survey (NHANES) to provide information on soft tissue composition and bone mineral content. However, in 1999-2004, DXA data were missing in whole or in part for about 21 per cent of the NHANES participants eligible for the DXA examination; and the missingness is associated with important characteristics such as body mass index and age. To handle this missing-data problem, multiple imputation of the missing DXA data was performed. Several features made the project interesting and challenging statistically, including the relationship between missingness on the DXA measures and the values of other variables; the highly multivariate nature of the variables being imputed; the need to transform the DXA variables during the imputation process; the desire to use a large number of non-DXA predictors, many of which had small amounts of missing data themselves, in the imputation models; the use of lower bounds in the imputation procedure; and relationships between the DXA variables and other variables, which helped both in creating and evaluating the imputations. This paper describes the imputation models, methods, and evaluations for this publicly available data resource and demonstrates properties of the imputations via examples of analyses of the data. The analyses suggest that imputation helps to correct biases that occur in estimates based on the data without imputation, and that it helps to increase the precision of estimates as well. Moreover, multiple imputation usually yields larger estimated standard errors than those obtained with single imputation.

Sustainability ranking and improvement of countries

Human society is on a collision course with nature, thus its sustainability is seriously questioned nowadays. To understand this problem better it is essential to define and measure sustainability. In this paper a model that uses fuzzy logic, called SAFE, is used to measure sustainability. The sustainability of a country is based on a multitude of basic indicators. In all 75 indicators for 128 countries are used. This work extends SAFE as follows: (a) The model is amended by an imputation procedure to fill in missing data, (b) the rule bases of SAFE are compiled algebraically, and (c) sustainability thresholds are defined so as to reflect expert opinion and international agreements and norms. Countries are ranked according to their sustainability index. Switzerland and Sweden take the first two places and Mauritania and Sudan the two last ones. A sensitivity analysis pinpoints those basic indicators that affect sustainability the most. Decision makers may focus on these indicators to improve sustainability.

A generic coalescent-based framework for the selection of a reference panel for imputation

An important component in the analysis of genome-wide association studies involves the imputation of genotypes that have not been measured directly in the studied samples. The imputation procedure uses the linkage disequilibrium (LD) structure in the population to infer the genotype of an unobserved single nucleotide polymorphism. The LD structure is normally learned from a dense genotype map of a reference population that matches the studied population. In many instances there is no reference population that exactly matches the studied population, and a natural question arises as to how to choose the reference population for the imputation. Here we present a Coalescent-based method that addresses this issue. In contrast to the current paradigm of imputation methods, our method assigns a different reference dataset for each sample in the studied population, and for each region in the genome. This allows the flexibility to account for the diversity within populations, as well as across populations. Furthermore, because our approach treats each region in the genome separately, our method is suitable for the imputation of recently admixed populations. We evaluated our method across a large set of populations and found that our choice of reference data set considerably improves the accuracy of imputation, especially for regions with low LD and for populations without a reference population available as well as for admixed populations such as the Hispanic population. Our method is generic and can potentially be incorporated in any of the available imputation methods as an add-on.

The Impact of Screening, Brief Intervention and Referral for Treatment in Emergency Department Patients' Alcohol Use: A 3-, 6- and 12-month Follow-up

Aims: This study aims to determine the impact of Screening, Brief Intervention and Referral for Treatment (SBIRT) in reducing alcohol consumption in emergency department (ED) patients at 3, 6, and 12 months following exposure to the intervention. Methods: Patients drinking above the low-risk limits (at-risk to dependence), as defined by National Institute of Alcohol Abuse and Alcoholism (NIAAA), were recruited from 14 sites nationwide from April to August 2004. A quasi-experimental comparison group design included sequential recruitment of intervention and control patients at each site. Control patients received a written handout. The Intervention group received the handout and participated in a brief negotiated interview with direct referral for treatment if indi- cated. Follow-up surveys were conducted at 3, 6, and 12 months by telephone using an Interactive Voice Response (IVR) system. Results: Of the 1132 eligible patients consented and enrolled (581 control, 551 intervention), 699 (63%), 575 (52%) and 433 (38%) completed follow-up surveys via IVR at 3, 6, and 12 months, respectively. Regression analysis adjusting for the clustered sampling design and using multiple imputation procedures to account for subject attrition revealed that those receiving SBIRT reported roughly three drinks less per week than controls (B=�3.00, SE = 1.06, P< 0.05) and the level of maximum drinks per occasion was approximately three-fourths of a drink less than controls (B= -0.76, SE = 0.29, P< 0.05) at 3 months. At 6 and 12 months post-inter- vention, these effects had weakened considerably and were no longer statistically or substantively significant. Conclusion: SBIRT delivered by ED providers appears to have short-term effectiveness in reducing at-risk drinking, but multi-contact interventions or booster programs may be necessary to maintain long-term reductions in risky drinking.

Missing value imputation on missing completely at random data using multilayer perceptrons

Data mining is based on data files which usually contain errors in the form of missing values. This paper focuses on a methodological framework for the development of an automated data imputation model based on artificial neural networks. Fifteen real and simulated data sets are exposed to a perturbation experiment, based on the random generation of missing values. These data set sizes range from 47 to 1389 records. A perturbation experiment was performed for each data set where the probability of missing value was set to 0.05. Several architectures and learning algorithms for the multilayer perceptron are tested and compared with three classic imputation procedures: mean/mode imputation, regression and hot-deck. The obtained results, considering different performance measures, not only suggest this approach improves the quality of a database with missing values, but also the best results are clearly obtained using the Multilayer Perceptron model in data sets with categorical variables. Three learning rules (Levenberg-Marquardt, BFGS Quasi-Newton and Conjugate Gradient Fletcher-Reeves Update) and a small number of hidden nodes are recommended.

Influence of depressive and eating disorders on short- and long-term course of weight after surgical and nonsurgical weight loss treatment

Objective To investigate the influence of depressive and eating disorders on short- and long-term weight loss after surgical and non-surgical weight-reduction treatment. Covariations between the disorders were considered. Method In a longitudinal naturalistic study, current diagnoses at baseline and lifetime diagnoses of depressive and eating disorders were assessed in participants who were undertaking a very-low-calorie diet (n = 250) and in bariatric surgery patients (n = 153). Lifetime diagnosis of a mental disorder was defined as presence of a mental disorder only in the past. Body weight was measured at baseline, 1 year after baseline, and 4 years after baseline. Mental comorbidity was assessed through use of standardized interviews at baseline. A structural equation modeling procedure was applied to test the associations between course of weight and mental disorders. Analyses were based on the intention to treat samples. Missing values were replaced by use of multiple imputation procedures. Results Neither depression nor eating disorders were associated with weight changes at the 1-year follow-up, but a specific effect emerged for bariatric surgery patients after 4 years: depression (current and lifetime) predicted smaller body mass index loss, whereas lifetime diagnosis of eating disorder was associated with greater weight loss. Conclusions Individuals who report depressive disorders prior to bariatric surgery should be monitored more closely in order to identify patients who would benefit from additional therapy with the goal of improving weight-loss outcome.

MEASURING INEQUALITIES: DO HOUSEHOLD SURVEYS PAINT A REALISTIC PICTURE?

The paper addresses the issue of the accuracy of standard‐of‐living measurements using household survey data. First, it highlights the fact that lighter data collection processes in some developing countries have added to measurement errors in consumption and income aggregates measurement errors. The paper reasserts the need to apply reference guidelines to the measurement of household consumption in order to compute comparable distribution indicators across countries and over time. Second, it contends that it is hard to analyze inequality solely from consumption patterns without taking income and savings into account. Two solutions are proposed for the correction of income measurement errors: by using savings declarations and by implementing a multiple imputation procedure. The results are based on a careful analysis of the EPM93 survey of Madagascar whose design is quite close to the LSMS household surveys, and the ENV98 survey of Côte d'Ivoire representative of surveys conducted nowadays in most Sub‐Saharan African countries.

Strategies for Multiple Imputation in Longitudinal Studies

Multiple imputation is increasingly recommended in epidemiology to adjust for the bias and loss of information that may occur in analyses restricted to study participants with complete data ("complete-case analyses"). However, little guidance is available on applying the method, including which variables to include in the imputation model and the number of imputations needed. Here, the authors used multiple imputation to analyze the prevalence of wheeze among 81-month-old children in the Avon Longitudinal Study of Parents and Children (Avon, United Kingdom; 1991-1999) and the association of wheeze with gender, maternal asthma, and maternal smoking. The authors examined how inclusion of different types of variables in the imputation model affected point estimates and precision, and assessed the impact of number of imputations on Monte Carlo variability. Inclusion of variables associated with the outcome in the imputation model increased odds ratios and reduced standard errors. When only 5 or 10 imputations were used, variability due to the imputation procedure was substantial enough to affect conclusions. Careful preliminary analysis identified the scope for multiple imputation to reduce bias and improve efficiency and provided guidance for building the imputation model. When data are missing, such preliminary analyses should be routinely undertaken and reported, regardless of whether multiple imputation is used in the final analysis.

Predicting missing quality of life data that were later recovered: an empirical comparison of approaches

The aim was to compare simple imputation, multiple imputation, and modeling approaches to deal with 'missing' quality of life data. Data were obtained from five clinical trials, which employed a reminder system for follow-up questionnaires. Previous studies have compared imputation strategies by artificially removing data according to prespecified mechanisms. Our approach differs from previous study as actual collected data are utilized. Data obtained by reminder were initially treated as missing. These missing values were imputed using a variety of simple and multiple imputation strategies. The trials were analyzed using the imputed datasets, and the resulting treatment effects compared to analyses using the full dataset including responses following reminders. A repeated measures model was also carried out on the available data and the pattern mixture models were employed. The accuracy of the different strategies was assessed by calculating the bias seen in the calculated treatment difference compared to the actual observed treatment difference. Baseline carried forward or last value carried forward were shown to be the best simple imputation methods in this setting. Multiple imputation using a regression model or predictive mean match model tended to provide treatment difference estimates with the least bias when compared to the actual observed data. Pattern mixture models did not perform well. Overall, the multiple imputation procedures were generally the least biased approaches. A number of imputation and modeling procedures have been investigated but this list is not exhaustive. All the example datasets come from the same data source and perhaps studies from additional disease areas would have been useful. However, we feel the results are generalizable to other quality of life outcomes and clinical areas. Multiple imputation is recommended for missing quality of life data as it makes the assumption of missing at random which in the quality of life setting is more plausible than the assumption of missing completely at random for which most simple imputation methods are based. Pattern mixture models can be complex and did not perform well in this setting.

Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables

Multiple imputation is a popular way to handle missing data. Automated procedures are widely available in standard software. However, such automated procedures may hide many assumptions and possible difficulties from the view of the data analyst. Imputation procedures such as monotone imputation and imputation by chained equations often involve the fitting of a regression model for a categorical outcome. If perfect prediction occurs in such a model, then automated procedures may give severely biased results. This is a problem in some standard software, but it may be avoided by bootstrap methods, penalised regression methods, or a new augmentation procedure.

Software for fitting nonstandard proportional subdistribution hazards models

Fine and Gray (1999) suggested a Cox model for the subdistribution hazard, which is the hazard attached to the cumulative incidence function of interest in a competing risks setting. They also noted that standard Cox software may be used to fit the model provided that the potential censoring times are known for individuals observed to experience a competing event (‘censoring complete data’) and that otherwise an inverse probability of censoring weighting method can be used. Beyersmann and Schumacher (2008) extended the methods of Fine and Gray (1999) to allow for random time-dependent covariates. Shortly after the paper by Beyersmann and Schumacher, Ruan and Gray (2008) suggested a multiple imputation approach for fitting a subdistribution hazards model. The aim of the imputation is to recover the potential censoring times for individuals with an observed competing event. Then standard Cox software may again be used for the analysis, which allows for including time-dependent covariates. We note that the MI approach also allows the fitting of stratified models and frailty models using standard software. We have written an R-package kmi that both implements the multiple imputation procedure and contains a random sample of the censoring complete data used by Beyersmann and Schumacher. The package can be downloaded from the Comprehensive R Archive Network at http://cran.r-project.org. Table 1 reports the analyses either using multiple imputation, with 10 multiple imputations, or using the original censoring complete information for both the random subsample and the whole data set.

English

The issue of handling sensor measurements data over single and multiple lag delays also known as outof-sequence measurement (OOSM) has been considered. It is argued that this problem can also be addressed using model-based imputation strategies and their application in comparison to Kalman filter (KF)-based approaches for a multi-sensor tracking prediction problem has also been demonstrated. The effectiveness of two model-based imputation procedures against five OOSM methods was investigated in Monte Carlo simulation experiments. The delayed measurements were either incorporated (or fused) at the time these were finally available (using OOSM methods) or imputed in a random way with higher probability of delays for multiple lags and lower probability of delays for a single lag (using single or multiple imputation). For single lag, estimates of target tracking computed from the observed data and those based on a data set in which the delayed measurements were imputed were equally unbiased; however, the KF estimates obtained using the Bayesian framework (BF-KF) were more precise. When the measurements were delayed in a multiple lag fashion, there were significant differences in bias or precision between multiple imputation (MI) and OOSM methods, with the former exhibiting a superior performance at nearly all levels of probability of measurement delay and range of manoeuvring indices. Researchers working on sensor data are encouraged to take advantage of software to implement delayed measurements using MI, as estimates of tracking are more precise and less biased in the presence of delayed multi-sensor data than those derived from an observed data analysis approach. Defence Science Journal, 2010, 60(1), pp.87-99 , DOI:http://dx.doi.org/10.14429/dsj.60.115

Improving Data Quality, Accuracy, and Response in On-Board Surveys

Transit agencies conduct origin–destination on-board surveys periodically to gather information regarding travel patterns and demographic data of their users and to collect customer satisfaction information. These surveys constitute a highly valuable means of obtaining important information on an agency's customers to provide a basis for effective transit planning and for regional travel demand modeling efforts. This paper describes the application of innovative technologies in the data collection process to improve data quality, data completeness, and data collection management. This includes the simultaneous collection of boarding and alighting count data at the stop level using Global Positioning System–enabled personal digital assistants, association of distributed surveys to boarding locations, and a web-based sample and productivity management system. These technologies allow for automatic collection of boarding location, arrival and departure times, and transit trip times. An imputation procedure was developed to derive the most likely alighting location of each collected sample. Joint application of these technologies reduces survey length and thereby minimizes respondent burden.

A comparison of imputation procedures and statistical tests for the analysis of two-dimensional electrophoresis data

BackgroundNumerous gel-based softwares exist to detect protein changes potentially associated with disease. The data, however, are abundant with technical and structural complexities, making statistical analysis a difficult task. A particularly important topic is how the various softwares handle missing data. To date, no one has extensively studied the impact that interpolating missing data has on subsequent analysis of protein spots.ResultsThis work highlights the existing algorithms for handling missing data in two-dimensional gel analysis and performs a thorough comparison of the various algorithms and statistical tests on simulated and real datasets. For imputation methods, the best results in terms of root mean squared error are obtained using the least squares method of imputation along with the expectation maximization (EM) algorithm approach to estimate missing values with an array covariance structure. The bootstrapped versions of the statistical tests offer the most liberal option for determining protein spot significance while the generalized family wise error rate (gFWER) should be considered for controlling the multiple testing error.ConclusionsIn summary, we advocate for a three-step statistical analysis of two-dimensional gel electrophoresis (2-DE) data with a data imputation step, choice of statistical test, and lastly an error control method in light of multiple testing. When determining the choice of statistical test, it is worth considering whether the protein spots will be subjected to mass spectrometry. If this is the case a more liberal test such as the percentile-based bootstrap t can be employed. For error control in electrophoresis experiments, we advocate that gFWER be controlled for multiple testing rather than the false discovery rate.

Handling out-of-sequence data using model-based statistical imputation

The issue of handling sensor measurement data over single and multiple lag delays is considered using model-based imputation strategies for a multi-sensor tracking prediction problem. The effectiveness of two model-based imputation procedures against five out-of-sequence measurement (OOSM) methods is investigated using Monte Carlo simulation experiments. For single lag, estimates of target tracking computed from the observed data and those based on imputed data were equally unbiased; however, the Kalman filter (KF) estimates obtained using the Bayesian framework (BF-KF) were more precise. For multi-lag delayed measurements, there were significant differences in precision between multiple imputation and OOSM methods, with the former exhibiting a superior performance at nearly all levels of probability of measurement delay and range of manoeuvring indices.

Lowering missing item values in quality-of-life questionnaires: an interventional study

Missing item values (MIV) often occur in quality-of-life (QoL) questionnaires. This study aimed to examine whether the use of introductory exemplary questions reduces the number of MIV and what patient-related factors influence effectiveness of such a QoL form training. In a randomized controlled study in ten primary care practice settings, a total of 215 consecutively recruited patients with at least one chronic disease were requested to complete the Medical Outcomes Study 36 Items Short Form (SF-36) questionnaire, German version 1.0. Prior to filling out the QoL form, a sample of randomly selected patients answered three simple written questions similar in wording and appearance to the original SF-36 questionnaire. In total, 126 (58.6%) patients completed the SF-36 questionnaire without MIV. Despite MIV the forms of 46 (21.4%) patients were still computable, i.e., scoring of scales was possible after use of the standardized SF-36 imputation algorithm. After the imputation procedure, MIV significantly hampered generating computable sum scales in 29 (26.6%) of the control group and 14 (13.2%) of the interventional group (P<0.05). A univariate analysis suggested no evidence that the number of MIV was reduced by the intervention. However, intervention led to a significant decrease of MIV in males but not in females. The education status affected the number of missing data independent of intervention. This cross-sectional study showed that the prior use of three self-created questions similar in wording and appearance to the SF-36 questionnaire significantly reduces MIV in male patients. School qualification of QoL respondents inversely correlated with the number of questionnaire MIV, but independent of education status all subjects did benefit from the QoL form training.

The impact of dichotomization in longitudinal data analysis: a simulation study

In this paper, a simulation study is conducted to systematically investigate the impact of dichotomizing longitudinal continuous outcome variables under various types of missing data mechanisms. Generalized linear models (GLM) with standard generalized estimating equations (GEE) are widely used for longitudinal outcome analysis, but these semi-parametric approaches are only valid under missing data completely at random (MCAR). Alternatively, weighted GEE (WGEE) and multiple imputation GEE (MI-GEE) were developed to ensure validity under missing at random (MAR). Using a simulation study, the performance of standard GEE, WGEE and MI-GEE on incomplete longitudinal dichotomized outcome analysis is evaluated. For comparisons, likelihood-based linear mixed effects models (LMM) are used for incomplete longitudinal original continuous outcome analysis. Focusing on dichotomized outcome analysis, MI-GEE with original continuous missing data imputation procedure provides well controlled test sizes and more stable power estimates compared with any other GEE-based approaches. It is also shown that dichotomizing longitudinal continuous outcome will result in substantial loss of power compared with LMM.

Missing Data Imputation in Time Series of Air Pollution

ISEE-0841 Background and Objective: Missing data is a frequent problem in epidemiological studies on the effects of air pollution on health. Air quality monitoring stations can present failures and stay off-line for several days. These gaps can distort the exposure assessment since the missing data mechanism is often ignored in the analysis. Analyses based only on the available observations can yield biased estimates of the association as well as overestimate the precision. We propose an imputation procedure for multivariate time series data, e.g. daily concentrations of atmospheric contaminants, based on the EM algorithm. The time component of the series can be modelled by using splines, regression models, or ARIMA models with multiple covariance regime. Methods: A simulation study was carried out in order to evaluate the validity of the proposed method and compare it with those available as default in most software packages for statistical analysis. The accuracy and agreement of the methods were also evaluated and a penalty criterion due to the lost information was proposed in order to account for the imputation uncertainty in the analysis. Results: (i) data analysis using only the complete units tended to underestimate the association between the air contaminants and the health events even when only a small amount of data is missing; (ii) mean and median imputation overestimated the association and estimates show high dispersion and low agreement between when compared to the original values; (iii) multivariate procedures presented better performance and accuracy than the univariate ones; (iv) multivariate methods with temporal adjustment presented higher accuracy and precision. This last approach also presented smaller prediction error and higher agreement between the imputed and the original values. Conclusion: The methods proposed in this work are implemented as an open source library called mtsdi for the statistical software R.