7 - Unbalanced Designs and Missing Data

BackgroundMissing data are a common problem in prospective studies with a long follow-up, and the volume, pattern and reasons for missing data may be relevant when estimating the cost of illness. We aimed to evaluate the effects of different methods for dealing with missing longitudinal cost data and for costing caregiver time on total societal costs in Alzheimer’s disease (AD).MethodsGERAS is an 18-month observational study of costs associated with AD. Total societal costs included patient health and social care costs, and caregiver health and informal care costs. Missing data were classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Simulation datasets were generated from baseline data with 10–40 % missing total cost data for each missing data mechanism. Datasets were also simulated to reflect the missing cost data pattern at 18 months using MAR and MNAR assumptions. Naïve and multiple imputation (MI) methods were applied to each dataset and results compared with complete GERAS 18-month cost data. Opportunity and replacement cost approaches were used for caregiver time, which was costed with and without supervision included and with time for working caregivers only being costed.ResultsTotal costs were available for 99.4 % of 1497 patients at baseline. For MCAR datasets, naïve methods performed as well as MI methods. For MAR, MI methods performed better than naïve methods. All imputation approaches were poor for MNAR data. For all approaches, percentage bias increased with missing data volume. For datasets reflecting 18-month patterns, a combination of imputation methods provided more accurate cost estimates (e.g. bias: −1 % vs −6 % for single MI method), although different approaches to costing caregiver time had a greater impact on estimated costs (29–43 % increase over base case estimate).ConclusionsMethods used to impute missing cost data in AD will impact on accuracy of cost estimates although varying approaches to costing informal caregiver time has the greatest impact on total costs. Tailoring imputation methods to the reason for missing data will further our understanding of the best analytical approach for studies involving cost outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0188-1) contains supplementary material, which is available to authorized users.

A common task in the analysis of multi‐environmental trials (MET) by linear mixed models (LMM) is the estimation of variance components (VCs). Most often, MET data are imbalanced (e.g., due to selection). The imbalance mechanism can be missing completely at random (MCAR), missing at random (MAR), or missing not at random. If the missing‐data pattern in MET was caused by selection, it is usually MAR. In this case, likelihood‐based methods are the preferred methods for analysis as they can account for a MAR data pattern. Likelihood‐based methods used to estimate VCs in LMM have the property that all VC estimates are constrained to be non‐negative; thus, the estimators are generally biased. Therefore, there are two potential causes of bias in MET analysis: a data pattern not being MCAR, and the bias of likelihood‐based VC estimators. The current study tries to dissect and quantify both possible sources of bias. A simulation study with MET data typical of cultivar evaluation trials was conducted in which the missing data pattern and the size of VCs were varied. The results showed that for the simulated MET, bias in VC estimates was similar under MCAR and MAR. Thus, the bias is solely due to the likelihood‐based estimation. Bias increases when increasing the ratio of genotype variance to error variance is small. Bias was similar for MAR and MCAR data patterns. Thus, it may be concluded that selection does not increase bias in VC estimation.

Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern-mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome measure at the follow-up time , conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing-data pattern at time with that of the observed subjects at time . The large number of the sensitivity parameters is reduced by treating them as random with a prior distribution having some pre-specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension.

Background: Statistical analysis in palliative and end-of-life care research can be problematic due to high levels of missing data, attrition and response shift as disease progresses. Aim: To develop recommendations about managing missing data, attrition and response shift in palliative and end-of-life care research data. Design: We used the MORECare Transparent Expert Consultation approach to conduct a consultation workshop with experts in statistical methods in palliative and end-of-life care research. Following presentations and discussion, nominal group techniques were used to produce recommendations about attrition, missing data and response shift. These were rated online by experts and analysed using descriptive statistics for consensus and importance. Results: In total, 20 participants attended the workshop and 19 recommendations were subsequently ranked. There was broad agreement across recommendations. The top five recommendations were as follows: A taxonomy should be devised to define types of attrition. Types and amount of missing data should be reported with details of imputation methods. The pattern of missing data should be investigated to inform the imputation approach. A statistical analysis plan should be pre-specified in the protocol. High rates of attrition should be assumed when planning studies and specifying analyses. The leading recommendation for response shift was for more research. Conclusions: When designing studies in palliative and end-of-life care, it is recommended that high rates of attrition should not be seen as indicative of poor design and that a clear statistical analysis plan is in place to account for missing data and attrition.

BackgroundMissing data due to attrition are rampant in substance abuse clinical trials. However, missing data are often ignored in the presentation of substance abuse clinical trials. This paper demonstrates missing data methods which may be used for hypothesis testing.MethodsMethods involving stratifying and weighting individuals based on missing data pattern are shown to produce tests that are robust to missing data mechanisms in terms of Type I error and power. In this article, we describe several methods of combining data that may be used for testing hypotheses of the treatment effect. Furthermore, illustrations of each test's Type I error and power under different missing data percentages and mechanisms are quantified using a Monte-Carlo simulation study.ResultsType I error rates were similar for each method, while powers depended on missing data assumptions. Specifically, power was greatest for the weighted, compared to un-weighted methods, especially for greater missing data percentages.ConclusionResults of this study as well as extant literature demonstrate the need for standards of design and analysis specific to substance abuse clinical trials. Given the known substantial attrition rates and concern for the missing data mechanism in substance abuse clinical trials, investigators need to incorporate missing data methods a priori. That is, missing data methods should be specified at the outset of the study and not after the data have been collected.

During the acquisition of electroencephalographic (EEG) signals, data may be missing or corrupted by noise and artifacts. To reconstruct the incomplete data, EEG signals are firstly converted into a three-order tensor (multi-dimensional data) of shape time × channel × trial. Then, the missing data can be efficiently recovered by applying a tensor completion method (TCM). However, there is not a unique way to organize channels and trials in a tensor, and different numbers of channels are available depending on the EEG setting used, which may affect the quality of the tensor completion results. The main goal of this paper is to evaluate the robustness of EEG completion methods with several designed parameters such as the ordering of channels and trials, the number of channels, and the amount of missing data. In this work, the results of completing missing data by several TCMs were compared. To emulate different scenarios of missing data, three different patterns of missing data were designed. Firstly, the amount of missing data on completion effects was analyzed, including the time lengths of missing data and the number of channels or trials affected by missing data. Secondly, the numerical stability of the completion methods was analyzed by shuffling the indices along channels or trials in the EEG data tensor. Finally, the way that the number of electrodes of EEG tensors influences completion effects was assessed by changing the number of channels. Among all the applied TCMs, the simultaneous tensor decomposition and completion (STDC) method achieves the best performance in providing stable results when the amount of missing data or the electrode number of EEG tensors is changed. In other words, STDC proves to be an excellent choice of TCM, since permutations of trials or channels have almost no influence on the complete results. The STDC method can efficiently complete the missing EEG signals. The designed simulations can be regarded as a procedure to validate whether or not a completion method is useful enough to complete EEG signals.

Approximation of Reliability for Multiple-Trait Animal Models with Missing Data by Canonical Transformation

Missing data in longitudinal studies , Missing data in longitudinal studies , کتابخانه دیجیتال جندی شاپور اهواز

Missing data is a common phenomenon with survey-based research; patterns of missing data may elucidate why participants decline to answer certain questions. To describe patterns of missing data in the Pediatric Quality of Life and Evaluation of Symptoms Technology (PediQUEST) study, and highlight challenges in asking sensitive research questions. Cross-sectional, survey-based study embedded within a randomized controlled trial. Three large children's hospitals: Dana-Farber/Boston Children's Cancer and Blood Disorders Center (DF/BCCDC); Children's Hospital of Philadelphia (CHOP); and Seattle Children's Hospital (SCH). At the time of their child's enrollment, parents completed the Survey about Caring for Children with Cancer (SCCC), including demographics, perceptions of prognosis, treatment goals, quality of life, and psychological distress. Eighty-six of 104 parents completed surveys (83% response). The proportion of missing data varied by question type. While 14 parents (16%) left demographic fields blank, over half (n=48; 56%) declined to answer at least one question about their child's prognosis, especially life expectancy. The presence of missing data was unrelated to the child's diagnosis, time from progression, time to death, or parent distress (p>0.3 for each). Written explanations in survey margins suggested that addressing a child's life expectancy is particularly challenging for parents. Parents of children with cancer commonly refrain from answering questions about their child's prognosis, however, they may be more likely to address general cure likelihood than explicit life expectancy. Understanding acceptability of sensitive questions in survey-based research will foster higher quality palliative care research.

Some transportation planning and traffic operations–intelligent transportation system (ITS) groups are cooperating on data-sharing initiatives, including the use of archived ITS data for planning statistics. However, conventional procedures for the calculation of annual average traffic statistics need to be updated to accommodate the incomplete nature of archived ITS data. The effects of various missing data patterns on several existing and modified annual average statistic calculation procedures were tested. Five locations were chosen for the study: two urban Interstate highways with significant commuter traffic, one urban parkway with commuter traffic and recreational trips, and two rural roads with pronounced seasonal patterns. A complete year of data was obtained for each study location; then missing data patterns (as identified from an empirical study) were simulated by randomly or systematically removing data. At urban locations in which commuter traffic dampens seasonality patterns, a significant amount of missing data (up to 8 months of consecutive missing data) can be tolerated with little to no effect on annual average traffic statistics. All calculation procedures provided similar results at the urban locations. For the two rural locations, 1 month of missing data still resulted in tolerable error for most procedures, whereas 2 months of missing data were close to or exceeded tolerable error levels for most procedures. Modifications of conventional calculation procedures (that account for small gaps in data on a daily basis) are better suited to archived ITS data.

We review the class of inverse probability weighting (IPW) approaches for the analysis of missing data under various missing data patterns and mechanisms. The IPW methods rely on the intuitive idea of creating a pseudo-population of weighted copies of the complete cases to remove selection bias introduced by the missing data. However, different weighting approaches are required depending on the missing data pattern and mechanism. We begin with a uniform missing data pattern (i.e. a scalar missing indicator indicating whether or not the full data is observed) to motivate the approach. We then generalise to more complex settings. Our goal is to provide a conceptual overview of existing IPW approaches and illustrate the connections and differences among these approaches.

Chapter 11 - Treatment of Missing Values

Bayesian inference for Common cause failure rate based on causal inference with missing data

Statistical Data, Missing

Asthma is an important chronic disease of childhood. An intervention programme for managing asthma was designed on principles of self-regulation and was evaluated by a randomized longitudinal study.The study focused on several outcomes, and, typically, missing data remained a pervasive problem. We develop a pattern-mixture model to evaluate the outcome of intervention on the number of hospitalizations with non-ignorable dropouts. Pattern-mixture models are not generally identifiable as no data may be available to estimate a number of model parameters. Sensitivity analyses are performed by imposing structures on the unidentified parameters.We propose a parameterization which permits sensitivity analyses on clustered longitudinal count data that have missing values due to non-ignorable missing data mechanisms. This parameterization is expressed as ratios between event rates across missing data patterns and the observed data pattern and thus measures departures from an ignorable missing data mechanism. Sensitivity analyses are performed within a Bayesian framework by averaging over different prior distributions on the event ratios. This model has the advantage of providing an intuitive and flexible framework for incorporating the uncertainty of the missing data mechanism in the final analysis.