Multiple Imputation Techniques Research Articles

Opening the Black Box of Biomarker Measurement Error

Opening the Black Box of Biomarker Measurement Error

Examining the robustness of fully synthetic data techniques for data with binary variables

There is a growing demand for public use data while at the same time there are increasing concerns about the privacy of personal information. One proposed method for accomplishing both goals is to release data sets that do not contain real values but yield the same inferences as the actual data. The idea is to view confidential data as missing and use multiple imputation techniques to create synthetic data sets. In this article, we compare techniques for creating synthetic data sets in simple scenarios with a binary variable.

Techniques for Handling Missing Data in Secondary Analyses of Large Surveys

Using an appropriate method to handle cases with missing data when performing secondary analyses of survey data is important to reduce bias and to reach valid conclusions for the target population. Many published secondary analyses using child health data sets do not discuss the technique employed to treat missing data or simply delete cases with missing data. Missing data may threaten statistical power by reducing sample size or, in more extreme situations, estimates derived by deleting cases with missing values may be biased, particularly if the cases with missing values are systematically different from those with complete data. The aim of this study was to determine which of 4 techniques for handling missing data most closely estimates the true model coefficient when varying proportions of cases are missing data. We performed a simulation study to compare model coefficients when all cases had complete data and when 4 techniques for handling missing data were employed with 10%, 20%, 30%, or 40% of the cases missing data. When >10% of the cases had missing data, the reweight and multiple imputation techniques were superior to dropping cases with missing scores or hot deck imputation. These findings suggest that child health researchers should use caution when analyzing survey data if a large percentage of cases have missing values. In most situations, the technique of dropping cases with missing data should be discouraged. Investigators should consider reweighting or multiple imputation if a large percentage of cases are missing data.

Influences of School Latino Composition and Linguistic Acculturation on a Prevention Program for Youths

This study examined how ethnic composition and linguistic acculturation within schools affected the efficacy of a youth substance use prevention model program. Data come from a randomized trial of the keepin' it REAL program, using a predominantly Mexican American sample of middle school students in Phoenix, Arizona. Schools were randomly assigned to a control group or to one of three culturally tailored intervention versions. We hypothesized that school ethnic and linguistic acculturation composition (percent Latino, percent non-English speaking at home) and individual level of linguistic acculturation jointly would moderate the efficacy of the prevention program, as indicated by students' alcohol, marijuana, and cigarette use. Using multilevel linear modeling and multiple imputation techniques to manage clustered data and attrition, results showed that desired program effects varied by the linguistic acculturation level of the school, the program version, and individual acculturation level. The Latino intervention version was more efficacious in schools with larger percentages of non-English speaking families, but only among less linguistically acculturated Latino students. There were no significant school level program effects connected to the percentage of Latino students at school, the other versions of the program, or among more linguistically acculturated students.

Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study

BackgroundThere is no consensus on the most appropriate approach to handle missing covariate data within prognostic modelling studies. Therefore a simulation study was performed to assess the effects of different missing data techniques on the performance of a prognostic model.MethodsDatasets were generated to resemble the skewed distributions seen in a motivating breast cancer example. Multivariate missing data were imposed on four covariates using four different mechanisms; missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR) and a combination of all three mechanisms. Five amounts of incomplete cases from 5% to 75% were considered. Complete case analysis (CC), single imputation (SI) and five multiple imputation (MI) techniques available within the R statistical software were investigated: a) data augmentation (DA) approach assuming a multivariate normal distribution, b) DA assuming a general location model, c) regression switching imputation, d) regression switching with predictive mean matching (MICE-PMM) and e) flexible additive imputation models. A Cox proportional hazards model was fitted and appropriate estimates for the regression coefficients and model performance measures were obtained.ResultsPerforming a CC analysis produced unbiased regression estimates, but inflated standard errors, which affected the significance of the covariates in the model with 25% or more missingness. Using SI, underestimated the variability; resulting in poor coverage even with 10% missingness. Of the MI approaches, applying MICE-PMM produced, in general, the least biased estimates and better coverage for the incomplete covariates and better model performance for all mechanisms. However, this MI approach still produced biased regression coefficient estimates for the incomplete skewed continuous covariates when 50% or more cases had missing data imposed with a MCAR, MAR or combined mechanism. When the missingness depended on the incomplete covariates, i.e. MNAR, estimates were biased with more than 10% incomplete cases for all MI approaches.ConclusionThe results from this simulation study suggest that performing MICE-PMM may be the preferred MI approach provided that less than 50% of the cases have missing data and the missing data are not MNAR.

The Level of Democracy during Interregnum Periods: Recoding the polity2 Score

The polity2 variable from the Polity IV project is the most popular measure of a country's political regime. This article contends that the coding rules employed to create a polity2 score during years of so-called interregnum and affected transitions produce a measure of democracy that lacks face validity. Using both single and multiple imputation methods, we construct and evaluate several variables that offer alternative measures to polity2 during such periods. We recommend that scholars using polity2 test whether their results are robust to using our alternatives and using multiple imputation techniques instead. Where robustness cannot be established, scholars need to theoretically justify the choice of either polity2 or one of the alternatives.

Sources of sporadic Yersinia enterocolitica infection in children in Sweden, 2004: a case-control study

Young children account for a large proportion of reported Yersinia enterocolitica infections in Sweden with a high incidence compared with other gastrointestinal infections, such as salmonellosis and campylobacteriosis. A case-control study was conducted to investigate selected risk factors for domestic sporadic yersiniosis in children aged 0-6 years in Sweden. In total, 117 cases and 339 controls were included in the study. To minimize exclusion of observations due to missing data a multiple non-parametric imputation technique was used. The following risk factors were identified in the multivariate analysis: eating food prepared from raw pork products (OR 3.0, 95% CI 1.8-5.1) or treated sausage (OR 1.9, 95% CI 1.1-3.3), use of a baby's dummy (OR 1.9, 95% CI 1.1-3.2) and contact with domestic animals (OR 2.0, 95% CI 1.2-3.4). We believe that the importance of Y. enterocolitica infection in children has been neglected and that results from this study can be used to develop preventive recommendations.

Modeling major lung resection outcomes using classification trees and multiple imputation techniques

Modeling of operative risks associated with major lung resection is potentially inaccurate and inefficient because of incomplete observations for predictor variables (covariates). Missing values do not usually occur randomly, potentially introducing an important source of bias in modeling. Deletion of cases with missing data also results in loss of precision. The current study analyzes incomplete variables as potential predictors of outcomes after major lung resection using imputation techniques. We analyzed major lung resection patients treated from 1980 to 2006 for predictors of pulmonary, cardiovascular, and overall complications, as well as mortality. Predictive variables were initially determined using classification and regression tree (CART) methods. Imputation models were developed and variables with missing values were multiply imputed. We fit a logistic regression model for each outcome using CART variables and any covariates that were of interest clinically. Of 1046 resected patients, serum albumin and diffusing capacity (DLCO%) had a large number of missing values (32% and 13% missing, respectively). Models included 10 covariates for pulmonary complications (p<0.05 for DLCO% and forced expiratory volume in the first second [FEV1%]), 12 covariates for cardiovascular complications (p<0.05 for FEV1%, extent of resection, year of operation, and age), 15 covariates for overall complications (p<0.05 for DLCO%, performance status, serum albumin, and FEV1/FVC ratio), and 12 covariates for death (p<0.05 for DLCO%, extent of resection, and operation year). We identified serum albumin as a previously under-reported and strong predictor of overall complications. Serum albumin was marginally significantly related to pulmonary and cardiovascular outcomes after major lung surgery. Use of imputation techniques for modeling surgical risks has potential value in identifying important predictive variables that may ordinarily be eliminated from analysis or not identified as predictors because of incomplete observations in clinical databases.

Correction

Abstract‘Multiple imputation for correcting verification bias’ by Harel O, Zhou XH (Statistics in Medicine 2006; 25:3769–3786) and ‘Rejoinder to Multiple imputation for correcting verification bias’ (Statistics in Medicine 2007; 26:3047–3050). A calculation error in the breast cancer example using diaphanography data presented in our paper was recently brought to our attention. In this example, the code calculating the sensitivity and specificity for the multiple imputation (MI) techniques had a typo resulting in column summation instead of row summation. As a result, the reported sensitivity and specificity were actually positive predictive and negative predictive values. The reported values for the methods not requiring MI (Naive 1 and B&amp;G 2) were correct. The corrected table is reported in Table I.We want to emphasize that the conclusions in Harel and Zhou 1 are still valid. The conclusions were based on a simulation study for which their results are valid.We apologize for any inconvenience caused to Statistics in Medicine readers. Results comparing five MI methods, the B&amp;G as existing method and naive method of sensitivity and specificity—diaphanography data for breast cancer. Sensitivity Specificity Procedure Est SE CI Est SE CI Naive 0.788 0.071 (0.649, 0.927) 0.800 0.054 (0.694, 0.906) B&amp;G 0.292 0.080 (0.134, 0.449) 0.973 0.008 (0.958, 0.988) Logit B&amp;G 0.292 0.388 (0.161, 0.469) 0.973 0.288 (0.954, 0.985) A&amp;C 0.304 0.075 (0.145, 0.462) 0.972 0.007 (0.959, 0.985) Rubin 0.297 0.079 (0.165, 0.475) 0.974 0.007 (0.957, 0.984) Wilson 0.292 0.035 (0.223, 0.361) 0.972 0.006 (0.960, 0.983) Jeffrey 0.299 — (0.222, 0.359) 0.974 — (0.961, 0.984) Z&amp;L 0.301 — (0.235, 0.373) 0.973 — (0.960, 0.983)

Estimating local and global measures of association for bivariate interval censored data with a smooth estimate of the density

Measures of association for bivariate interval censored data have not yet been studied extensively. Betensky and Finkelstein (Statist. Med. 1999; 18:3101-3109) proposed to calculate Kendall's coefficient of concordance using a multiple imputation technique, but their method becomes computer intensive for moderate to large data sets. We suggest a different approach consisting of two steps. Firstly, a bivariate smooth estimate of the density of log-event times is determined. The smoothing technique is based on a mixture of Gaussian densities fixed on a grid with weights determined by a penalized likelihood approach. Secondly, given the smooth approximation several local and global measures of association can be estimated readily. The performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from the Signal-Tandmobiel study.

A generalized log‐rank test for interval‐censored failure time data via multiple imputation

Interval-censored (IC) failure time data often occur in follow-up studies where subjects can only be followed periodically and the failure time can only be known to lie in an interval. In this paper we propose a modified log-rank test for the problem of comparing two or more IC samples. Our log-rank statistic and covariance matrix are calculated by a multiple imputation technique. Through simulation studies, we find that the performance of the proposed test is comparable to that of the test proposed by Finkelstein (Biometrics 1986; 42(4):845-854) and is better than that of the two existing log-rank type tests proposed by Sun (Lifetime Data Anal. 2001; 7:363-375) and Zhao and Sun (Stat. Med. 2004; 23(10):1621-1629) due to the differences in the method of multiple imputation and the covariance matrix estimation. Our covariance matrix estimator is similar to the estimator used by Follmann et al. (Biometrics 2003; 59:420-429) for clustered data. The proposed method is illustrated by means of an example involving patients with breast cancer.

Travel Time Prediction

As reported in the literature for the applications of intelligent transportation systems with traffic detectors, various missing data patterns are frequently observed in such systems and may dramatically degrade their performance. This study presents two imputation approaches for contending with the missing data issues in travel time prediction. The first model is based on the concept of multiple imputation technique to predict directly the travel times under various missing data patterns. The second model that serves as the supplemental component is to estimate the missing detector values using neighboring detector data and historical traffic patterns. Both models have been incorporated with reliability indicators so as to assess the quality of imputed data and its applicability for use in prediction. The numerical example based on 10 roadside detectors on I-70 in Maryland has demonstrated that both developed models outperformed existing methods and offer the potential for field implementation.

ICT and development: A new indicator for international comparisons

The use and diffusion of Information and Communication Technologies (ICT) can be seen as a mechanism for reducing the global divide. Two aspects are crucial: Counting on accurate time-series data and the definition of the components defining ICT indicators. We carry out a multiple imputation technique to estimate missing ICT data using the Expectation Maximisation approach. The resulting dataset (170 countries, from 1991 to 2003) allows us to propose a confident ICT index, based on national capabilities (NaCap Index). It attempts to capture countries' differences in educational and structural elements, determinant factors for positive impacts from the use of ICT.

Diagnostics for Multiple Imputations

Multiple imputation technique is becoming a popular method for analyzing data with missing values. Several methods have been proposed for creating multiple imputations and most of these methods assume that the data are missing at random (MAR). However, limited diagnostic tools are available to check whether the imputations created by these methods are reasonable. This article develops a set of diagnostic tools based on certain conditional distributions of the observed and imputed values. These conditional distributions should be similar if the assumed model for creating multiple imputations is a good fit. The tools are formulated in terms of numerical summaries and graphical displays and could be easily implemented using the standard complete data software packages. For implementing these methods the exact nature of the model used by the imputer is not needed. The method is illustrated using a data set with large number of variables of different types with varying amount of missing values.

Sequential imputation for missing values

As missing values are often encountered in gene expression data, many imputation methods have been developed to substitute these unknown values with estimated values. Despite the presence of many imputation methods, these available techniques have some disadvantages. Some imputation techniques constrain the imputation of missing values to a limited set of genes, whereas other imputation methods optimise a more global criterion whereby the computation time of the method becomes infeasible. Others might be fast but inaccurate. Therefore in this paper a new, fast and accurate estimation procedure, called SEQimpute, is proposed. By introducing the idea of minimisation of a statistical distance rather than a Euclidean distance the method is intrinsically different from the thus far existing imputation methods. Moreover, this newly proposed method can be easily embedded in a multiple imputation technique which is better suited to highlight the uncertainties about the missing value estimates. A comparative study is performed to assess the estimation of the missing values by different imputation approaches. The proposed imputation method is shown to outperform some of the existing imputation methods in terms of accuracy and computation speed.

Baseline patient characteristics and mortality associated with longitudinal intervention compliance

Lin et al. (http://www.biostatsresearch.com/upennbiostat/papers/, 2006) proposed a nested Markov compliance class model in the Imbens and Rubin compliance class model framework to account for time-varying subject noncompliance in longitudinal randomized intervention studies. We use superclasses, or latent compliance class principal strata, to describe longitudinal compliance patterns, and time-varying compliance classes are assumed to depend on the history of compliance. In this paper, we search for good subject-level baseline predictors of these superclasses and also examine the relationship between these superclasses and all-cause mortality. Since the superclasses are completely latent in all subjects, we utilize multiple imputation techniques to draw inferences. We apply this approach to a randomized intervention study for elderly primary care patients with depression.

Neighborhood Effects on the Efficacy of a Program to Prevent Youth Alcohol Use

This study examines how neighborhood characteristics affect program efficacy. Data come from a randomized trial of a substance use prevention program called keepin′ it REAL, which was administered to a predominantly Mexican American sample of 4,622 middle school students in Phoenix, Arizona, beginning in 1998. Multilevel models and multiple imputation techniques address clustered data and attrition. Among less linguistically acculturated Latinos, living in poorer neighborhoods and those with many single-mother families decreased program effectiveness in combating alcohol use. High neighborhood immigrant composition increased program effectiveness. Unexpectedly, the program was also more effective in neighborhoods with higher rates of crime. There were no significant effects on program efficacy for the more linguistically acculturated Latinos and non-Hispanic White students. Findings are discussed in light of theories of neighborhood social disorganization, immigrant adaptation, and social isolation.

A Randomized Trial Comparing Human e-Mail Counseling, Computer-Automated Tailored Counseling, and No Counseling in an Internet Weight Loss Program

Several studies have shown that e-mail counseling improves weight loss achieved in self-directed Internet programs. Computer-tailored feedback offers a population-based alternative to human e-mail counseling. One hundred ninety-two adults, aged 49.2 +/- 9.8 years, having a body mass index (calculated as weight in kilograms divided by height in meters squared) of 32.7 +/- 3.5, were randomized to 1 of 3 Internet treatment groups: No counseling, computer-automated feedback, or human e-mail counseling. All participants received 1 weight loss group session, coupons for meal replacements, and access to an interactive Web site. The human e-mail counseling and computer-automated feedback groups also had access to an electronic diary and message board. The human e-mail counseling group received weekly e-mail feedback from a counselor, and the computer-automated feedback group received automated, tailored messages. Retention was 82% at 3 months and 80% at 6 months for all 3 groups. At 3 months, completers in both the computer-automated feedback (-5.3 +/- 4.2 kg) and human e-mail counseling (-6.1 +/- 3.9 kg) groups had significantly greater weight losses compared with the no counseling group (-2.8 +/- 3.5 kg) and these groups did not differ from each other. At 6 months, weight losses were significantly greater in the human e-mail counseling group (-7.3 +/- 6.2 kg) than in the computer-automated feedback (-4.9 +/- 5.9 kg) or no counseling (-2.6 +/- 5.7 kg) groups. Intent-to-treat analyses using single or multiple imputation techniques showed the same pattern of significance. Providing automated computer-tailored feedback in an Internet weight loss program was as effective as human e-mail counseling at 3 months. Further research is needed to improve the efficacy of automated computer-tailored feedback as a population-based weight loss approach.

Taking ‘Don’t Knows’ as Valid Responses: A Multiple Complete Random Imputation of Missing Data

Incomplete data is a common problem of survey research. Recent work on multiple imputation techniques has increased analysts awareness of the biasing effects of missing data and has also provided a convenient solution. Imputation methods replace non-response with estimates of the unobserved scores. In many instances, however, non-response to a stimulus does not result from measurement problems that inhibit accurate surveying of empirical reality, but from the inapplicability of the survey question. In such cases, existing imputation techniques replace valid non-response with counterfactual estimates of a situation in which the stimulus is applicable to all respondents. This paper suggests an alternative imputation procedure for incomplete data for which no true score exists: multiple complete random imputation, which overcomes the biasing effects of missing data and allows analysts to model respondents valid I don't know answers.

Clinical features, complications, and outcome in adults with pneumococcal meningitis: a prospective case series

Bacterial meningitis is a grave disease of high incidence, especially in less developed countries. Here, we describe its clinical presentation, spectrum of complications, prognostic factors, and outcome in adults with pneumococcal meningitis. From October, 1998, to April, 2002, we assessed 352 episodes of community-acquired pneumococcal meningitis, confirmed by culture of cerebrospinal fluid (CSF), which occurred in patients older than 16 years. Predictors for an unfavourable outcome (Glasgow outcome scale score 1-4) were identified by logistic regression with multiple imputation techniques. 245 (70%) episodes of pneumococcal meningitis were associated with an underlying disorder. Cranial CT was done for 85% of episodes and revealed underlying disorders in 17% (50/299) and meningitis-associated intracranial complications in 39% (117/299). Independent predictors for an unfavourable outcome were a low score on the Glasgow coma scale, cranial nerve palsies, a raised erythrocyte sedimentation rate, a CSF leucocyte count less than 1000 cells per mm(3), and a high CSF protein concentration on admission. Overall in-hospital mortality was 30%. Prevalence of neurological and systemic complications did not differ between patients aged younger than 60 years and those aged 60 years and older; however, systemic complications were the cause of death in 59% (32/54) of fatal episodes in patients aged 60 years and older, whereas neurological complications were the cause of death in 65% (20/31) of fatal episodes in younger patients. Pneumococcal meningitis is associated with high mortality and morbidity rates in adults. Whereas neurological complications are the leading cause of death in younger patients, elderly patients die predominantly from systemic complications.