Imputation Strategies Research Articles

Alternative imputation techniques for complex metric variables

This paper deals with imputation techniques and strategies. Usually, imputation truly commences after the first data editing, but many preceding operations are needed before that. In this editing step, the missing or deficient items are to be recognized and coded, and then it is decided which of these, if any, should be substituted by imputing. There are a number of imputation methods and their specifications. Consequently, it is not clear what method finally should be chosen, especially when an imputation method may be best in one respect, and another method in the other. In this paper, we consider these questions through the following four imputation methods: (i) random hot decking, (ii) logistic regression imputation, (iii) linear regression imputation, and (iv) regression-based nearest neighbour hot decking. The last two methods are applied with the two different specifications. The two metric variables have been used in empirical tests. The first is very complex, but the second is more ordinary, and thus easier to handle. The empirical examples are based on simulations, which clearly show the biases of the various methods and their specifications. In general, it seems that method (iv) is recommendable although the results from it are not perfect either.

Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation

The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature which can be used. In particular, substitution or imputation strategies are available for rounded zeros. In this paper, existing nonparametric imputation methods—both for the additive and the multiplicative approach—are revised and essential properties of the last method are given. For missing values a generalization of the multiplicative approach is proposed.

Intention-to-treat: methods for dealing with missing values in clinical trials of progressively deteriorating diseases Presented at the International Society for Clinical Biostatistics Twentieth International Meeting, Heidelberg, Germany, September 1999.

Since it came up in the 1960s, the principle of intention-to-treat (ITT) has become widely accepted for the analysis of controlled clinical trials. In this context the question of how to perform such an analysis in the presence of missing information about the main endpoint is of major importance. Uncritical use of several ad hoc strategies for dealing with missing values is common in the practice of clinical trials. On the other hand, little is known about possible dangers and problems of applying these strategies. We therefore performed a detailed investigation of different methods for dealing with missing values in order to develop recommendations for their practical use. A simulation study was performed investigating possible consequences on type I error and power of applying different methods for dealing with missing values. The simulations were based on a clinical trial of osteoporosis, a progressively deteriorating disease. The strategies examined can be roughly classified into numerical imputation strategies (last observation carried forward, mean and regression based methods) and non-parametric strategies (rank and dichotomization based methods). Different drop-out mechanisms and different types of progression of disease are considered. The type I error increases drastically for the different strategies, especially if the courses of disease vary between treatment groups. The loss in power can be substantial. There is no strategy which is adequate for all different combinations of drop-out mechanisms, drop-out rates and courses of disease over time. For drop-out rates less than 20 per cent and similar courses of disease in the treatment groups, missing values might be replaced by the mean of the other group, or counted as treatment failures after dichotomization of the endpoint. For larger drop-out rates or less similar courses of disease, no adequate recommendations can be given. Because of the drastic consequences of increasing drop-out rates, it has to be a primary goal in clinical trials to keep missing values to a minimum. Unobserved information cannot be reliably regained by any methodological resources. As there are no strategies for universal use, reasons for the choice of a certain method have to be provided when designing and analysing clinical trials. Copyright © 2001 John Wiley & Sons, Ltd.

Intention-to-treat: methods for dealing with missing values in clinical trials of progressively deteriorating diseases.

Since it came up in the 1960s, the principle of intention-to-treat (ITT) has become widely accepted for the analysis of controlled clinical trials. In this context the question of how to perform such an analysis in the presence of missing information about the main endpoint is of major importance. Uncritical use of several ad hoc strategies for dealing with missing values is common in the practice of clinical trials. On the other hand, little is known about possible dangers and problems of applying these strategies. We therefore performed a detailed investigation of different methods for dealing with missing values in order to develop recommendations for their practical use. A simulation study was performed investigating possible consequences on type I error and power of applying different methods for dealing with missing values. The simulations were based on a clinical trial of osteoporosis, a progressively deteriorating disease. The strategies examined can be roughly classified into numerical imputation strategies (last observation carried forward, mean and regression based methods) and non-parametric strategies (rank and dichotomization based methods). Different drop-out mechanisms and different types of progression of disease are considered. The type I error increases drastically for the different strategies, especially if the courses of disease vary between treatment groups. The loss in power can be substantial. There is no strategy which is adequate for all different combinations of drop-out mechanisms, drop-out rates and courses of disease over time. For drop-out rates less than 20 per cent and similar courses of disease in the treatment groups, missing values might be replaced by the mean of the other group, or counted as treatment failures after dichotomization of the endpoint. For larger drop-out rates or less similar courses of disease, no adequate recommendations can be given. Because of the drastic consequences of increasing drop-out rates, it has to be a primary goal in clinical trials to keep missing values to a minimum. Unobserved information cannot be reliably regained by any methodological resources. As there are no strategies for universal use, reasons for the choice of a certain method have to be provided when designing and analysing clinical trials.

Group comparisons involving missing data in clinical trials: a comparison of estimates and power (size) for some simple approaches

When using ‘intent-to-treat’ approaches to compare outcomes between groups in clinical trials, analysts face a decision regarding how to account for missing observations. Most model-based approaches can be summarized as a process whereby the analyst makes assumptions about the distribution of the missing data in an attempt to obtain unbiased estimates that are based on functions of the observed data. Although pointed out by Rubin as often leading to biased estimates of variances, an alternative approach that continues to appear in the applied literature is to use fixed-value imputation of means for missing observations. The purpose of this paper is to provide illustrations of how several fixed-value mean imputation schemes can be formulated in terms of general linear models that characterize the means of distributions of missing observations in terms of the means of the distributions of observed data. We show that several fixed-value imputation strategies will result in estimated intervention effects that correspond to maximum likelihood estimates obtained under analogous assumptions. If the missing data process has been correctly characterized, hypothesis tests based on variances estimated using maximum likelihood techniques asymptotically have the correct size. In contrast, hypothesis tests performed using the uncorrected variance, obtained by applying standard complete data formula to singly imputed data, can provide either conservative or anticonservative results. Surprisingly, under several non-ignorable non-response scenarios, maximum likelihood based analyses can yield equivalent hypothesis tests to those obtained when analysing only the observed data. Copyright © 2001 John Wiley & Sons, Ltd.

Group comparisons involving missing data in clinical trials: a comparison of estimates and power (size) for some simple approaches

When using 'intent-to-treat' approaches to compare outcomes between groups in clinical trials, analysts face a decision regarding how to account for missing observations. Most model-based approaches can be summarized as a process whereby the analyst makes assumptions about the distribution of the missing data in an attempt to obtain unbiased estimates that are based on functions of the observed data. Although pointed out by Rubin as often leading to biased estimates of variances, an alternative approach that continues to appear in the applied literature is to use fixed-value imputation of means for missing observations. The purpose of this paper is to provide illustrations of how several fixed-value mean imputation schemes can be formulated in terms of general linear models that characterize the means of distributions of missing observations in terms of the means of the distributions of observed data. We show that several fixed-value imputation strategies will result in estimated intervention effects that correspond to maximum likelihood estimates obtained under analogous assumptions. If the missing data process has been correctly characterized, hypothesis tests based on variances estimated using maximum likelihood techniques asymptotically have the correct size. In contrast, hypothesis tests performed using the uncorrected variance, obtained by applying standard complete data formula to singly imputed data, can provide either conservative or anticonservative results. Surprisingly, under several non-ignorable non-response scenarios, maximum likelihood based analyses can yield equivalent hypothesis tests to those obtained when analysing only the observed data.

Imputation strategies for missing data in a school-based multi-centre study: the Pathways study.

Pathways is a multi-centre school-based trial sponsored by the National Heart, Lung, and Blood Institute testing the efficacy of an obesity prevention intervention in American Indian children. During the study's protocol development, we prepared an analysis plan that accounted for missing data. In this paper, we present a case study of the process we used to decide upon the final analysis plan. The primary endpoint of the Pathways study is a comparison of per cent body fat between treatment and usual care groups at the end of a three-year intervention. Other studies on children and Native Americans have had moderate to large amounts of missing data. As a result we were concerned that missing data in Pathways would affect the type I error rate and power of the test of our primary endpoint. We present results from our evaluation of three alternative procedures in this paper. The first is a multiple imputation procedure in which we replace missing values with resampled values from the observed data. The second is based on the Wilcoxon rank sum test; missing data in the intervention group receive the worst ranks. In the third, we use a multiple imputation procedure and replace missing values with predicted values from a regression equation with the coefficients estimated from observed follow-up data and baseline values. We found that the multiple imputation procedure that replaces missing values with predicted values had the best properties of the procedures we considered. The results from our simulation study showed that, for missing data patterns that are relevant to the Pathways study, this procedure has high power and maintains the type I error rate. Published in 2001 by John Wiley & Sons, Ltd.

Handling Baseline Differences and Missing Items in a Longitudinal Study of HIV Risk Among Runaway Youths

Many longitudinal studies in field settings present challenges due to selection bias and incomplete data. A motivating example is provided by an intervention study aimed at preventing HIV transmission among runaway youths housed at shelters in New York City. Two shelters with 167 youths received the intervention, and two shelters with 144 youths received the control treatment. The number of unprotected sexual acts in the prior three months for each youth was assessed at a baseline interview and (to the extent possible) at five follow-up time points. Among observed items, there is strong evidence of a lack of balance on baseline characteristics between the intervention and control groups; meanwhile, beyond occasional missing items among participants interviewed at baseline, there were three items about baseline characteristics added after the study began, resulting in a few items being missing on a large percentage of the study sample. Here, we outline two strategies for handling the complexities of this data set, both of which make use of propensity scores to address the imbalances across treatment groups. One approach relies on available cases and ad hoc choices to simplify the steps leading up to a linear mixed model analysis in SAS PROC MIXED; the other approach uses multiple imputation strategies to reflect uncertainty due to missing values in an analogous linear mixed model analysis. Ultimately we did not find substantial qualitative differences in this setting between the available-case and imputed-data approaches. But in both cases, we find that the considerable imbalance on covariates between treatment arms constrains the ability to draw inferences about the intervention effect, suggesting the importance of evaluating propensity-score distributions in quasi-experimental intervention research.

Imputation: Methods, Simulation Experiments and Practical Examples

SummaryWhen conducting surveys, two kinds of nonresponse may cause incomplete data files: unit nonresponse (complete nonresponse) and item nonresponse (partial nonresponse). The selectivity of the unit nonresponse is often corrected for. Various imputation techniques can be used for the missing values because of item nonresponse. Several of these imputation techniques are discussed in this report. One is the hot deck imputation. This paper describes two simulation experiments of the hot deck method. In the first study, data are randomly generated, and various percentages of missing values are then non‐randomly‘added’to the data. The hot deck method is used to reconstruct the data in this Monte Carlo experiment. The performance of the method is evaluated for the means, standard deviations, and correlation coefficients and compared with the available case method. In the second study, the quality of an imputation method is studied by running a simulation experiment. A selection of the data of the Dutch Housing Demand Survey is perturbed by leaving out specific values on a variable. Again hot deck imputations are used to reconstruct the data. The imputations are then compared with the true values. In both experiments the conclusion is that the hot deck method generally performs better than the available case method. This paper also deals with the questions which variables should be imputed and what the duration of the imputation process is. Finally the theory is illustrated by the imputation approaches of the Dutch Housing Demand Survey, the European Community Household Panel Survey (ECHP) and the new Dutch Structure of Earnings Survey (SES). These examples illustrate the levels of missing data that can be experienced in such surveys and the practical problems associated with choosing an appropriate imputation strategy for key items from each survey.

The relation of psychosocial dimensions of work with coronary heart disease risk factors: a meta-analysis of five United States data bases.

The relation of job psychologic demands and decision latitude to four coronary heart disease risk factors (cholesterol, smoking, and systolic and diastolic blood pressures) was tested among 12,555 men in five investigations conducted in the United States during the period 1959-1980 (National Health and Nutrition Examination Surveys I and II, National Health Examination Survey, Western Collaborative Group Study, and Exercise Heart Survey). Using an imputation strategy, the authors attached measures of the two job characteristics above to persons in each data base by occupation. In 19 possible tests, decision latitude was related (p less than 0.05) to cholesterol and smoking in two instances in the predicted direction in the Exercise Heart Survey, when controlling for Type I error rate. Psychologic demands were not related to any of the risk factors. When a meta-analysis was performed across data bases, all relations were in the predicted direction except for the relation of psychologic demands to systolic pressure, and two of these were statistically significant (p less than 0.05): the relation of job decision latitude to smoking and to systolic pressure. The interaction of psychologic demands and decision latitude was not related to any of the risk factors when two common forms of an interaction were tested. These results indicate that psychosocial aspects of work, in particular the decision latitude of the job, may be related to some cardiovascular risk factors.

Nonresponse in a Periodic Sample Survey

A parametric model is developed for analyzing the updated historical (ratio of identicals) imputation strategy in a periodic survey. A test is then developed for comparing alternative formulations of the historical values. The benefits of exponentially smoothing in this context are demonstrated using monthly gasoline sales data.

Crohn's disease in Nottingham: a search for time-space clustering.

All cases of Crohn's disease in the Nottingham area were ascertained and the date and place of domicile and work at the time of onset of symptoms noted. Applying the Knox and Pike and Smith tests for clustering of patients in time and space, no significant results were observed. Further analysis of differences in time-space clustering between a group of patients and matched controls is in hand.