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A functional multiple imputation approach to incomplete longitudinal data.

ABSTRACT: In designed longitudinal studies, information from the same set of subjects are collected repeatedly over time. The longitudinal measurements are often subject to missing data which impose an analytic challenge. We propose a functional multiple imputation approach modeling longitudinal response profiles as smooth curves of time under a functional mixed effects model. We develop a Gibbs sampling algorithm to draw model parameters and imputations for missing values, using a blocking technique for an increased computational efficiency. In an illustrative example, we apply a multiple imputation analysis to data from the Panel Study of Income Dynamics and the Child Development Supplement to investigate the gradient effect of family income on children's health status. Our simulation study demonstrates that this approach performs well under varying modeling assumptions on the time trajectory functions and missingness patterns.

SUBMITTER: He Y

PROVIDER: S-EPMC4453987 | biostudies-literature | 2011 May

REPOSITORIES: biostudies-literature

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A functional multiple imputation approach to incomplete longitudinal data.

He Yulei Y Yucel Recai R Raghunathan Trivellore E TE

Statistics in medicine 20110222 10

In designed longitudinal studies, information from the same set of subjects are collected repeatedly over time. The longitudinal measurements are often subject to missing data which impose an analytic challenge. We propose a functional multiple imputation approach modeling longitudinal response profiles as smooth curves of time under a functional mixed effects model. We develop a Gibbs sampling algorithm to draw model parameters and imputations for missing values, using a blocking technique for ...[more]

PMID: 21341300

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Project description:BackgroundIncomplete categorical variables with more than two categories are common in public health data. However, most of the existing missing-data methods do not use the information from nonresponse (missingness) probabilities.MethodsWe propose a nearest-neighbour multiple imputation approach to impute a missing at random categorical outcome and to estimate the proportion of each category. The donor set for imputation is formed by measuring distances between each missing value with other non-missing values. The distance function is calculated based on a predictive score, which is derived from two working models: one fits a multinomial logistic regression for predicting the missing categorical outcome (the outcome model) and the other fits a logistic regression for predicting missingness probabilities (the missingness model). A weighting scheme is used to accommodate contributions from two working models when generating the predictive score. A missing value is imputed by randomly selecting one of the non-missing values with the smallest distances. We conduct a simulation to evaluate the performance of the proposed method and compare it with several alternative methods. A real-data application is also presented.ResultsThe simulation study suggests that the proposed method performs well when missingness probabilities are not extreme under some misspecifications of the working models. However, the calibration estimator, which is also based on two working models, can be highly unstable when missingness probabilities for some observations are extremely high. In this scenario, the proposed method produces more stable and better estimates. In addition, proper weights need to be chosen to balance the contributions from the two working models and achieve optimal results for the proposed method.ConclusionsWe conclude that the proposed multiple imputation method is a reasonable approach to dealing with missing categorical outcome data with more than two levels for assessing the distribution of the outcome. In terms of the choices for the working models, we suggest a multinomial logistic regression for predicting the missing outcome and a binary logistic regression for predicting the missingness probability.

Project description:BackgroundQuestionnaires used in longitudinal studies may have questions added or removed over time for numerous reasons. Data missing completely at a follow-up survey is a unique issue for longitudinal studies. While such excluded questions lack information at one follow-up survey, they are collected at other follow-up surveys, and covariances observed at other follow-up surveys may allow for the recovery of the missing data. This study utilized data from a large longitudinal cohort study to assess the efficiency and feasibility of using multiple imputation (MI) to recover this type of information.MethodsMillennium Cohort Study participants completed the 9-item Patient Health Questionnaire (PHQ) depression module at 2 time points (2004, 2007). The suicidal ideation item in the module was set to missing for the 2007 assessment. Several single-level MI models using different sets of predictors and forms of suicidal ideation were used to compare self-reported values and imputed values for this item in 2007. Additionally, associations with sleep duration and smoking status, which are related constructs, were compared between self-reported and imputed values of suicidal ideation.ResultsAmong 63,028 participants eligible for imputation analysis, 4.05% reported suicidal ideation on the 2007 survey. The imputation models successfully identified suicidal ideation, with a sensitivity ranging between 34 and 66% and a positive predictive value between 36 and 42%. Specificity remained above 96% and negative predictive value above 97% for all imputed models. Similar associations were found for all imputation models on related constructs, though the dichotomous suicidal ideation imputed from the model using only PHQ depression items yielded estimates that were closest with the self-reported associations for all adjusted analyses.ConclusionsAlthough sensitivity and positive predictive value were relatively low, applying MI techniques allowed for inclusion of an otherwise missing variable. Additionally, correlations with related constructs were estimated near self-reported values. Therefore, the other 8 depression items can be used to estimate suicidal ideation that was completely missing from a survey using MI. However, these imputed values should not be used to estimate population prevalence.

Dataset Information

A functional multiple imputation approach to incomplete longitudinal data.

Publications

A functional multiple imputation approach to incomplete longitudinal data.

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