Imputation Procedure Research Articles

Non-parametric seismic hazard analysis in the presence of incomplete data

The distribution of earthquake magnitudes plays a crucial role in the estimation of seismic hazard parameters. Due to the complexity of earthquake magnitude distribution, non-parametric approaches are recommended over classical parametric methods. The main deficiency of the non-parametric approach is the lack of complete magnitude data in almost all cases. This study aims to introduce an imputation procedure for completing earthquake catalog data that will allow the catalog to be used for non-parametric density estimation. Using a Monte Carlo simulation, the efficiency of introduced approach is investigated. This study indicates that when a magnitude catalog is incomplete, the imputation procedure can provide an appropriate tool for seismic hazard assessment. As an illustration, the imputation procedure was applied to estimate earthquake magnitude distribution in Tehran, the capital city of Iran.

Early-childhood housing mobility and subsequent PTSD in adolescence: a Moving to Opportunity reanalysis

In a 2014 report on adolescent mental health outcomes in the Moving to Opportunity for Fair Housing Demonstration (MTO), Kessler et al. reported that, at 10- to 15-year follow-up, boys from households randomized to an experimental housing voucher intervention experienced 12-month prevalence of post-traumatic stress disorder (PTSD) at several times the rate of boys from control households. We reanalyze this finding here, bringing to light a PTSD outcome imputation procedure used in the original analysis, but not described in the study report. By bootstrapping with repeated draws from the frequentist sampling distribution of the imputation model used by Kessler et al., and by varying two pseudorandom number generator seeds that fed their analysis, we account for several purely statistical components of the uncertainty inherent in their imputation procedure. We also discuss other sources of uncertainty in this procedure that were not accessible to a formal reanalysis.

Women's adjustment trajectories during IVF and impact on mental health 11-17 years later.

Do patients present different adjustment trajectories during and after IVF treatment? Most women show resilient trajectories during and after IVF treatment but 37% show temporary or chronic maladjustment during IVF and 10% are maladjusted 11-17 years after treatment. Research on patient psychosocial adjustment during treatment has contributed to identifying the most distressful stages of IVF treatment and profiling patients at risk for emotional maladjustment at these specific stages. This knowledge is currently driving the deliverance of psychosocial care at fertility clinics by tailoring it to patients' risk profiles and specific treatment stages. However, current care does not take into consideration how individuals adjust across the entire treatment pathway. This can be assessed by profiling individual adjustment trajectories. A longitudinal cohort study with five assessment moments that combines data from two different studies, the STRESSIVF and OMEGA projects. Participants enrolled in the STRESSIVF study (started IVF in 1998-2000) were assessed before and after the first IVF treatment cycle and 6 months and 2.5 years after the last IVF cycle. A subset participated in the OMEGA project (started IVF in 1995-2000) and reported on their mental health 11-17 years after treatment. Three hundred and forty-eight women participated in the STRESSIVF project and 108 of these in the OMEGA. Anxiety was measured with the State and Trait Anxiety Inventory, depression with the Beck Depression Inventory and mental health with the Mental Health Inventory. Latent class growth mixed modelling was carried out to identify distinct anxiety and depression trajectories over the four STRESSIVF study assessment moments. Multinominal logistic regressions were conducted to investigate predictors of trajectory membership, and stepwise linear regressions were performed to investigate if adjustment trajectories predicted mental health 11-17 years after IVF treatment. A total of 67 and 86% of women showed normal levels of anxiety and depression, respectively, throughout treatment (resilient trajectories), 24 and 33% experienced anxiety and depression only during treatment (recovery trajectories), 4.6 and 4.9% experienced anxiety and depression only after treatment (delayed trajectories), and 4.3% showed chronic anxiety (chronic trajectory, not identified for depression). Non-resilient trajectories were associated with unsuccessful treatment, marital dissatisfaction, lack of social support and negative infertility cognitions. One in 10 women had a delayed or chronic trajectory and these trajectories predicted serious mental health impairment 11-17 years after treatment. The study only focuses on women. In the OMEGA project adjustment was assessed using a mental health measure. Although we could investigate how trajectories predicted mental health, it would have been preferable to map anxiety and depression trajectories up to 11-17 years after treatment. Missing analysis showed selective dropout from the study but this was accounted for by using mixed models and imputation procedures. Finally, data on other life stressors were not collected; therefore any contribution from these events cannot be assessed. Fertility health-care providers have been called upon considering their responsibility in supporting patients in the aftermath of treatment. Results show it is possible to profile different groups of at-risk women at the start of the treatment and tailor psychosocial support to risk profile to promote health adjustment during treatment and thereafter. This study was supported by a grant from the Dutch Cancer Society (2006-3631) and the Praeventiefonds (28-3012). No competing interests exist.

Foreign human capital and the earnings gap between immigrants and Canadian-born workers

We use new information on the location of study of immigrants available in the 2006 Canadian Census to estimate returns to Canadian and foreign human capital. We find that controlling for the source of human capital (Canadian versus foreign) helps account for a large share of the immigrant/native-born wage gap. We show that commonly-used imputation procedures (e.g. Friedberg, 2000) that assign domestic and foreign education based on age at arrival tend to overestimate the returns to foreign education and underestimate the returns to foreign work experience. We also find that the immigrant/native-born wage gap is highly heterogeneous across places of birth even after including location of study fixed effects, although this inclusion markedly reduces the negative country of origin effects for countries like China, Pakistan, and India. Finally, we note substantial heterogeneity in the portability of human capital across fields of study.

Early-childhood housing mobility and subsequent PTSD in adolescence: a Moving to Opportunity reanalysis.

In a 2014 report on adolescent mental health outcomes in the Moving to Opportunityfor Fair Housing Demonstration (MTO), Kessler et al. reported that, at 10-to 15-year follow-up, boys from households randomized to an experimental housingvoucher intervention experienced 12-month prevalence of post-traumatic stressdisorder (PTSD) at several times the rate of boys from control households. We reanalyzethis finding here, bringing to light a PTSD outcome imputation procedure usedin the original analysis, but not described in the study report. By bootstrapping withrepeated draws from the frequentist sampling distribution of the imputation modelused by Kessler et al., and by varying two pseudorandom number generator seedsthat fed their analysis, we account for several purely statistical components of theuncertainty inherent in their imputation procedure. We also discuss other sourcesof uncertainty in this procedure that were not accessible to a formal reanalysis.

MULTIPLE IMPUTATION FOR MISSINGNESS DUE TO NONLINKAGE AND PROGRAM CHARACTERISTICS: A CASE STUDY OF THE NATIONAL HEALTH INTERVIEW SURVEY LINKED TO MEDICARE CLAIMS.

Record linkage is a valuable and efficient tool for connecting information from different data sources. The National Center for Health Statistics (NCHS) has linked its population-based health surveys with administrative data, including Medicare enrollment and claims records. However, the linked NCHS-Medicare files are subject to missing data; first, not all survey participants agree to record linkage, and second, Medicare claims data are only consistently available for beneficiaries enrolled in the Fee-for-Service (FFS) program, not in Medicare Advantage (MA) plans. In this research, we examine the usefulness of multiple imputation for handling missing data in linked National Health Interview Survey (NHIS)-Medicare files. The motivating example is a study of mammography status from 1999 to 2004 among women aged 65 years and older enrolled in the FFS program. In our example, mammography screening status and FFS/MA plan type are missing for NHIS survey participants who were not linkage eligible. Mammography status is also missing for linked participants in an MA plan. We explore three imputation approaches: (i) imputing screening status first, (ii) imputing FFS/MA plan type first, (iii) and imputing the two longitudinal processes simultaneously. We conduct simulation studies to evaluate these methods and compare them using the linked NHIS-Medicare files. The imputation procedures described in our paper would also be applicable to other public health-related research using linked data files with missing data issues arising from program characteristics (e.g., intermittent enrollment or data collection) reflected in administrative data and linkage eligibility by survey participants.

Risk of Cerebral Venous Thrombosis in Obese Women

Obesity is a risk factor for deep vein thrombosis of the leg and pulmonary embolism. To date, however, whether obesity is associated with adult cerebral venous thrombosis (CVT) has not been assessed. To assess whether obesity is a risk factor for CVT. A case-control study was performed in consecutive adult patients with CVT admitted from July 1, 2006 (Amsterdam), and October 1, 2009 (Berne), through December 31, 2014, to the Academic Medical Center in Amsterdam, the Netherlands, or Inselspital University Hospital in Berne, Switzerland. The control group was composed of individuals from the control population of the Multiple Environmental and Genetic Assessment of Risk Factors for Venous Thrombosis study, which was a large Dutch case-control study performed from March 1, 1999, to September 31, 2004, and in which risk factors for deep vein thrombosis and pulmonary embolism were assessed. Data analysis was performed from January 2 to July 12, 2015. Obesity was determined by body mass index (BMI). A BMI of 30 or greater was considered to indicate obesity, and a BMI of 25 to 29.99 was considered to indicate overweight. A multiple imputation procedure was used for missing data. We adjusted for sex, age, history of cancer, ethnicity, smoking status, and oral contraceptive use. Individuals with normal weight (BMI <25) were the reference category. The study included 186 cases and 6134 controls. Cases were younger (median age, 40 vs 48 years), more often female (133 [71.5%] vs 3220 [52.5%]), more often used oral contraceptives (97 [72.9%] vs 758 [23.5%] of women), and more frequently had a history of cancer (17 [9.1%] vs 235 [3.8%]) compared with controls. Obesity (BMI ≥30) was associated with an increased risk of CVT (adjusted odds ratio [OR], 2.63; 95% CI, 1.53-4.54). Stratification by sex revealed a strong association between CVT and obesity in women (adjusted OR, 3.50; 95% CI, 2.00-6.14) but not in men (adjusted OR, 1.16; 95% CI, 0.25-5.30). Further stratification revealed that, in women who used oral contraceptives, overweight and obesity were associated with an increased risk of CVT in a dose-dependent manner (BMI 25.0-29.9: adjusted OR, 11.87; 95% CI, 5.94-23.74; BMI ≥30: adjusted OR, 29.26; 95% CI, 13.47-63.60). No association was found in women who did not use oral contraceptives. Obesity is a strong risk factor for CVT in women who use oral contraceptives.

Random forest as an imputation method for education and psychology research: its impact on item fit and difficulty of the Rasch model

ABSTRACTThis paper presents a non-parametric imputation technique, named random forest, from the machine learning field. The random forest procedure has two main tuning parameters: the number of trees grown in the prediction and the number of predictors used. Fifty experimental conditions were created in the imputation procedure, with different combinations of predictors (from 1 to 10) and number of trees (10, 50, 100, 500 and 1000). We examined how each experimental condition affected the items fit and the difficulty of an inductive reasoning test to the dichotomous Rasch model. The results point that using random forest to impute missing values is a reliable technique to be used in psychological researches, since it led to statistically significant differences in the infit’s median only in 4% of the experimental conditions investigated, compared to the original data set result. However, researchers should be aware that in 32% of the experimental conditions, the imputation procedure significantly increased the median of the estimated items’ difficulty, compared to the original data set.

Dealing with missing covariates in epidemiologic studies: a comparison between multiple imputation and a full Bayesian approach

Incomplete data are generally a challenge to the analysis of most large studies. The current gold standard to account for missing data is multiple imputation, and more specifically multiple imputation with chained equations (MICE). Numerous studies have been conducted to illustrate the performance of MICE for missing covariate data. The results show that the method works well in various situations. However, less is known about its performance in more complex models, specifically when the outcome is multivariate as in longitudinal studies. In current practice, the multivariate nature of the longitudinal outcome is often neglected in the imputation procedure, or only the baseline outcome is used to impute missing covariates. In this work, we evaluate the performance of MICE using different strategies to include a longitudinal outcome into the imputation models and compare it with a fully Bayesian approach that jointly imputes missing values and estimates the parameters of the longitudinal model. Results from simulation and a real data example show that MICE requires the analyst to correctly specify which components of the longitudinal process need to be included in the imputation models in order to obtain unbiased results. The full Bayesian approach, on the other hand, does not require the analyst to explicitly specify how the longitudinal outcome enters the imputation models. It performed well under different scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

A note on multiple imputation for method of moments estimation

Multiple imputation is a popular imputation method for general purpose estimation. Rubin(1987) provided an easily applicable formula for the variance estimation of multiple imputation. However, the validity of the multiple imputation inference requires the congeniality condition of Meng(1994), which is not necessarily satisfied for method of moments estimation. This paper presents the asymptotic bias of Rubin's variance estimator when the method of moments estimator is used as a complete-sample estimator in the multiple imputation procedure. A new variance estimator based on over-imputation is proposed to provide asymptotically valid inference for method of moments estimation.

Handling attrition and non-response in longitudinal data with an application to a study of Australian youth

A standard concern with long term longitudinal studies is that of attrition over time. Together with initial non-response this typically leads to biased model estimates unless a suitable form of adjustment is carried out. The standard approach to this has been to compute weights based upon the propensity to respond and to drop out and then carry out weighted analyses to compensate for response bias. In the present paper [the authors] argue that this approach is statistically inefficient, because it drops incomplete data records, is inflexible, and in practice gives rise to undue complexity involving a proliferation of weighting systems for different analyses. Instead [the authors] set out an alternative approach that makes use of recently developed imputation procedures for handling missing data and show how this can be used to improve the quality of the statistical analysis. An example analysis is given using the Longitudinal Study of Australian Youth (LSAY).

Stochastic EM algorithm of a finite mixture model from hurdle Poisson distribution with missing responses

ABSTRACTIn this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic EM algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology.

Imputation technique: replacing missing values in longitudinal data

In longitudinal studies, many cases are found missing in the follow-up data. These missing cases may arise due to item non response or unit non response. A data set with missing observations is often completed by using imputed values. The unit non response is usually carried out by some weighting adjustment. The item non response is made by the method called imputation. Imputation is a technique to replace a missing/incomplete or strange value with a more or less artificial value. There are plenty of methods available to impute the missing values in a longitudinal data. Imputation is useful because they make the data set easier to analyze, ensure consistency between the results from different analyses and reduce non response bias from item non response. But it is not necessary that the imputed value reduces the bias of the data, sometimes they may lead more bias also. It depends on the imputation procedure which we choose and also the form of estimate. The aim of this article is to sensitize doctors and post-graduate medical students about this useful analytical technique.

The Negative Relationship between Size and the Probability of Weekly Attendance in Churches in the United States

Are people less likely to attend large churches? Using nationally representative data, I find a negative relationship between size and the probability of attendance for Conservative, Mainline, and black Protestants and for Catholics in parishes larger than 500 attenders. The addition of control variables does not change these patterns. These results support the theory that group cohesion lies at the heart of the size-participation relationship in churches. With the rapid growth of megachurches in the United States, a negative relationship between size and frequency of attendance could serve to accelerate aggregate declines in attendance. Methodologically, this article demonstrates how Bayesian hierarchical models can handle complex data structures and imputation procedures in a unified model.

Using Spatial Factor Analysis to Measure Human Development

In this paper, we propose a Bayesian factor analysis model with the purpose of serving as an alternate approach to calculating the UNDP’s Human Development Index, as well as providing a general methodology which can be used to augment existing indices or build new ones. In addition to addressing several potential issues of the official HDI, we also estimate an alternative “green HDI” index by adding a new environmental variable, and build a novel MDG index as an example of constructing a new index with a more complex variable structure. Under our methodology, we find the “living standard” dimension provides a greater proportional contribution to human development than it is assigned by the official HDI while the “longevity” dimension provides a lower proportional contribution. The results also show considerable levels of general disagreement when compared to the ranks of the official HDI. We show that incorporating an environmental variable increases the amount of disagreement between model based ranks and the official HDI, but decreases the amount of uncertainty associated with model ranks. In addition, we report the sensitivity of our methods to the choice of functional form and data imputation procedures.

The NLstart2run study: Economic burden of running-related injuries in novice runners participating in a novice running program.

To investigate the economic burden of running-related injuries (RRI) occurred during the 6-week 'Start-to-Run' program of the Dutch Athletics Federation in 2013. Prospective cohort study. This was a monetary cost analysis using the data prospectively gathered alongside the RRI registration in the NLstart2run study. RRI data were collected weekly. Cost diaries were applied two and six weeks after the RRI registration to collect data regarding healthcare utilisation (direct costs) and absenteeism from paid and unpaid work (indirect costs). RRI was defined as running-related pain that hampered running ability for three consecutive training sessions. From the 1696 participants included in the analysis, 185 reported a total of 272 RRIs. A total of 26.1% of the cost data (71 RRIs reported by 50 participants) were missing. Therefore, a multiple imputation procedure was performed. The economic burden (direct plus indirect costs) of RRIs was estimated at €83.22 (95% CI €50.42-€116.02) per RRI, and €13.35 (95% CI €7.07-€19.63) per participant. The direct cost per RRI was €56.93 (95% CI €42.05-€71.81) and the indirect cost per RRI was €26.29 (95% CI €0.00-€54.79). The indirect cost was higher for sudden onset RRIs than for gradual onset RRIs, with a mean difference of €33.92 (95% CI €17.96-€49.87). Direct costs of RRIs were 2-fold higher than the indirect costs, and sudden onset RRIs presented higher costs than gradual onset RRIs. The results of this study are important to provide information to public health agencies and policymakers about the economic burden of RRIs in novice runners.

Doubly Robust Inference for the Distribution Function in the Presence of Missing Survey Data

AbstractItem non‐response in surveys occurs when some, but not all, variables are missing. Unadjusted estimators tend to exhibit some bias, called the non‐response bias, if the respondents differ from the non‐respondents with respect to the study variables. In this paper, we focus on item non‐response, which is usually treated by some form of single imputation. We examine the properties of doubly robust imputation procedures, which are those that lead to an estimator that remains consistent if either the outcome variable or the non‐response mechanism is adequately modelled. We establish the double robustness property of the imputed estimator of the finite population distribution function under random hot‐deck imputation within classes. We also discuss the links between our approach and that of Chambers and Dunstan. The results of a simulation study support our findings.

Cost and Utility Analysis of a Store-and-Forward Teledermatology Referral System: A Randomized Clinical Trial.

The costs and utility of teledermatology are important features of implementation. Such an analysis requires a description of the perspective of the entity that will bear the cost. To assess the costs and utility of a store-and-forward teledermatology referral process compared with a conventional referral process from the perspectives of the Department of Veterans Affairs (VA) and society. Three hundred ninety-one randomized participants were referred from remote sites of primary care to the dermatology services of 2 VA medical facilities for ambulatory skin conditions from December 2008 through June 2010, and follow-up was completed in March 2011. The time trade-off utility measures and costs were collected during a 9-month period among participants in a 2-site parallel group randomized clinical trial. The perspectives of the VA and society were evaluated. The multiple imputation procedure or weighted means were used for missing data elements. Data were analyzed from January to July 2014. Referrals were managed using store-and-forward teledermatology or a conventional text-based referral process. Total costs from the perspectives of the VA and society incurred during the 9-month follow-up were used to derive per-participant costs. Utility, using the time trade-off method, was the measure of effectiveness. From the VA perspective, the total cost for conventional referrals was $66 145 (minimum, $58 697; maximum, $71 635), or $338 (SD, $291) per participant (196 participants); the total cost for teledermatology referrals was $59 917 (mimimum, $51 794; maximum, $70 398), or $308 (SD, $298) per participant (195 participants). The $30 difference in per-participant cost was not statistically significant (95% CI, -$79 to $20). From the societal perspective, the total cost for conventional referrals was $106 194 (minimum, $98 746; maximum, $111 684), or $542 (SD, $403) per participant (196 participants); the total cost for teledermatology referrals was $89 523 (minimum, $81 400; maximum, $100 400) or $460 (SD, $428) per participant. This $82 difference in per-participant cost was statistically significant (95% CI, -$12 to -$152). From baseline to the 9-month follow-up, the time trade-off utility value improved by 0.02 in the conventional referral group and 0.03 in the teledermatology group. This difference was not statistically significant (P = .50). Compared with conventional referrals, store-and-forward teledermatology referrals were performed at a comparable cost (VA perspective) or at a lower cost (societal perspective) with no evidence of a difference in utility as measured by the time trade-off method. clinicaltrials.gov Identifier: NCT00488293.

A Bayesian Approach to Parameter Estimation in the Presence of Spatial Missing Data

The missing data problem has been widely addressed in the literature. The traditional methods for handling missing data may be not suited to spatial data, which can exhibit distinctive structures of dependence and/or heterogeneity. As a possible solution to the spatial missing data problem, this paper proposes an approach that combines the Bayesian Interpolation method [Benedetti, R. & Palma, D. (1994) Markov random field-based image subsampling method, Journal of Applied Statistics, 21(5), 495–509] with a multiple imputation procedure. The method is developed in a univariate and a multivariate framework, and its performance is evaluated through an empirical illustration based on data related to labour productivity in European regions.

Multiple imputation for non-response when estimating HIV prevalence using survey data.

BackgroundMissing data are a common feature in many areas of research especially those involving survey data in biological, health and social sciences research. Most of the analyses of the survey data are done taking a complete-case approach, that is taking a list-wise deletion of all cases with missing values assuming that missing values are missing completely at random (MCAR). Methods that are based on substituting the missing values with single values such as the last value carried forward, the mean and regression predictions (single imputations) are also used. These methods often result in potential bias in estimates, in loss of statistical information and in loss of distributional relationships between variables. In addition, the strong MCAR assumption is not tenable in most practical instances.MethodsSince missing data are a major problem in HIV research, the current research seeks to illustrate and highlight the strength of multiple imputation procedure, as a method of handling missing data, which comes from its ability to draw multiple values for the missing observations from plausible predictive distributions for them. This is particularly important in HIV research in sub-Saharan Africa where accurate collection of (complete) data is still a challenge. Furthermore the multiple imputation accounts for the uncertainty introduced by the very process of imputing values for the missing observations. In particular national and subgroup estimates of HIV prevalence in Zimbabwe were computed using multiply imputed data sets from the 2010–11 Zimbabwe Demographic and Health Surveys (2010–11 ZDHS) data. A survey logistic regression model for HIV prevalence and demographic and socio-economic variables was used as the substantive analysis model. The results for both the complete-case analysis and the multiple imputation analysis are presented and discussed.ResultsAcross different subgroups of the population, the crude estimates of HIV prevalence are generally not identical but their variations are consistent between the two approaches (complete-case analysis and multiple imputation analysis). The estimates of standard errors under the multiple imputation are predominantly smaller, hence leading to narrower confidence intervals, than under the complete case analysis. Under the logistic regression adjusted odds ratios vary greatly between the two approaches. The model based confidence intervals for the adjusted odds ratios are wider under the multiple imputation which is indicative of the inclusion of a combined measure of the within and between imputation variability.ConclusionsThere is considerable variation between estimates obtained between the two approaches. The use of multiple imputations allows the uncertainty brought about by the imputation process to be measured. This consequently yields more reliable estimates of the parameters of interest and reduce the chances of declaring significant effects unnecessarily (type I error). In addition, the utilization of the powerful and flexible statistical computing packages in R enhances the computations.