Large Amounts Of Missing Data Research Articles

Efficiency of multiple imputation to test for association in the presence of missing data

The presence of missing data in association studies is an important problem, particularly with high-density single-nucleotide polymorphism (SNP) maps, because the probability that at least one genotype is missing dramatically increases with the number of markers. A possible strategy is to simply ignore the missing data and only use the complete observations, and, consequently, to accept a significant decrease of the sample size. Using Genetic Analysis Workshop 15 simulated data on which we removed some genotypes to generate different levels of missing data, we show that this strategy might lead to an important loss in power to detect association, but may also result in false conclusions regarding the most likely susceptibility site if another marker is in linkage disequilibrium with the disease susceptibility site. We propose a multiple imputation approach to deal with missing data on case-parent trios and evaluated the performance of this approach on the same simulated data. We found that our multiple imputation approach has high power to detect association with the susceptibility site even with a large amount of missing data, and can identify the susceptibility sites among a set of sites in linkage disequilibrium.

Phylogeny of Extant and Fossil Juglandaceae Inferred from the Integration of Molecular and Morphological Data Sets

It is widely acknowledged that integrating fossils into data sets of extant taxa is imperative for proper placement of fossils, resolution of relationships, and a better understanding of character evolution. The importance of this process has been further magnified because of the crucial role of fossils in dating divergence times. Outstanding issues remain, including appropriate methods to place fossils in phylogenetic trees, the importance of molecules versus morphology in these analyses, as well as the impact of potentially large amounts of missing data for fossil taxa. In this study we used the angiosperm clade Juglandaceae as a model for investigating methods of integrating fossils into a phylogenetic framework of extant taxa. The clade has a rich fossil record relative to low extant diversity, as well as a robust molecular phylogeny and morphological database for extant taxa. After combining fossil organ genera into composite and terminal taxa, our objectives were to (1) compare multiple methods for the integration of the fossils and extant taxa (including total evidence, molecular scaffolds, and molecular matrix representation with parsimony [MRP]); (2) explore the impact of missing data (incomplete taxa and characters) and the evidence for placing fossils on the topology; (3) simulate the phylogenetic effect of missing data by creating "artificial fossils"; and (4) place fossils and compare the impact of single and multiple fossil constraints in estimating the age of clades. Despite large and variable amounts of missing data, each of the methods provided reasonable placement of both fossils and simulated "artificial fossils" in the phylogeny previously inferred only from extant taxa. Our results clearly show that the amount of missing data in any given taxon is not by itself an operational guideline for excluding fossils from analysis. Three fossil taxa (Cruciptera simsonii, Paleoplatycarya wingii, and Platycarya americana) were placed within crown clades containing living taxa for which relationships previously had been suggested based on morphology, whereas Polyptera manningii, a mosaic taxon with equivocal affinities, was placed firmly as sister to two modern crown clades. The position of Paleooreomunnea stoneana was ambiguous with total evidence but conclusive with DNA scaffolds and MRP. There was less disturbance of relationships among extant taxa using a total evidence approach, and the DNA scaffold approach did not provide improved resolution or internal support for clades compared to total evidence, whereas weighted MRP retained comparable levels of support but lost crown clade resolution. Multiple internal minimum age constraints generally provided reasonable age estimates, but the use of single constraints provided by extinct genera tended to underestimate clade ages.

REDESCRIPTION AND PHYLOGENETIC POSITION OF CAYPULLISAURUS (ICHTHYOSAURIA: OPHTHALMOSAURIDAE)

Abstract The ophthalmosaurid Caypullisaurus from the Late Jurassic–Early Cretaceous of the Neuquen Basin, Argentina, is redescribed based on new information from recent discoveries. Cladistic analysis of Caypullisaurus, based on previous ichthyopterygian data sets and using NONA, yielded two most parsimonious trees. Two clades are recognized within the Ophthalmosauridae. Caypullisaurus is found to be nested with Brachypterygius and Platypterygius. Simultaneous, unconstrained analysis, using unambiguous character optimization, is suggested as the best way to analyze data sets with large amounts of missing data.

Missing data

Almost all studies have some missing observations. Yet textbooks and software commonly assume that data are complete, and the topic of how to handle missing data is not often discussed...

Video Epitomes

Recently, "epitomes" were introduced as patch-based probability models that are learned by compiling together a large number of examples of patches from input images. In this paper, we describe how epitomes can be used to model video data and we describe significant computational speedups that can be incorporated into the epitome inference and learning algorithm. In the case of videos, epitomes are estimated so as to model most of the small space-time cubes from the input data. Then, the epitome can be used for various modeling and reconstruction tasks, of which we show results for video super-resolution, video interpolation, and object removal. Besides computational efficiency, an interesting advantage of the epitome as a representation is that it can be reliably estimated even from videos with large amounts of missing data. We illustrate this ability on the task of reconstructing the dropped frames in video broadcast using only the degraded video and also in denoising a severely corrupted video.

Bias arising from missing data in predictive models

Objective The purpose of this study is to determine the effect of three common approaches to handling missing data on the results of a predictive model. Study Design and Setting Monte Carlo simulation study using simulated data was used. A baseline logistic regression using complete data was performed to predict hospital admission, based on the white blood cell count (WBC) (dichotomized as normal or high), presence of fever, or procedures performed (PROC). A series of simulations was then performed in which WBC data were deleted for varying proportions (15–85%) of patients under various patterns of missingness. Three analytic approaches were used: analysis restricted to cases with complete data, missing data assumed to be normal (MAN), and use of imputed values. Results In the baseline analysis, all three predictors were all significantly associated with admission. Using either the MAN approach or imputation, the odds ratio (OR) for WBC was substantially over- or underestimated depending on the missingness pattern, and there was considerable bias toward the null in the OR estimates for fever. In the CC analyses, OR for WBC was consistently biased toward the null, OR for PROC was biased away from the null, and the OR for fever was biased toward or away from the null. Estimates for overall model discrimination were substantially biased using all analytic approaches. Conclusions All three methods of handling large amounts of missing data can lead to biased estimates of the OR and of model performance in predictive models. Predictor variables that are measured inconsistently can affect the validity of such models.

Determining best complete subsets of specimens and characters for multivariate morphometric studies in the presence of large amounts of missing data

Missing data are frequent in morphometric studies of both fossil and recent material. A common method of addressing the problem of missing data is to omit combinations of characters and specimens from subsequent analyses; however, omitting different subsets of characters and specimens can affect both the statistical robustness of the analyses and the resulting biological interpretations. We describe a method of examining all possible subsets of complete data and of scoring each subset by the ‘condition’ (ratio of first eigenvalue to second, or of second to first, depending on context) of the corresponding covariance or correlation matrix, and subsequently choosing the submatrix that either optimizes one of these criteria or matches the estimated condition of the original data matrix. We then describe an extension of this method that can be used to choose the ‘best’ characters and specimens for which some specified proportion of missing data can be estimated using standard imputation techniques such as the expectation-maximization algorithm or multiple imputation. The methods are illustrated with published and unpublished data sets on fossil and extant vertebrates. Although these problems and methods are discussed in the context of conventional morphometric data, they are applicable to many other kinds of data matrices. © 2006 The Linnean Society of London, Biological Journal of the Linnean Society, 2006, 88, 309–328.

Multicomponent fortified human milk for promoting growth in preterm infants.

For term infants, human milk provides adequate nutrition to facilitate growth, as well as potential beneficial effects on immunity and the maternal-infant emotional state. However, the role of human milk in premature infants is less well defined as it contains insufficient quantities of some nutrients to meet the estimated needs of the infant. Observational studies have suggested that infants fed formula have a higher rate of growth than infants who are breast fed. However, there are potential short term and long term benefits from human milk. Commercially-produced multicomponent fortifiers provide additional nutrients to supplement human milk (in the form of protein, calcium, phosphate, and carbohydrate, as well as vitamins and trace minerals). The main objective was to determine if addition of multicomponent nutritional supplements to human milk leads to improved growth, bone metabolism and neurodevelopmental outcomes without significant adverse effects in premature infants. Searches were made of the Cochrane Central Register of Controlled Trials (CENTRAL, The Cochrane Library, Issue 2, 3003), MEDLINE (searched August 29, 2003), previous reviews including cross references, abstracts, conferences and symposia proceedings, expert informants, journal handsearching mainly in the English language. All trials utilising random or quasi-random allocation to supplementation of human milk with multiple nutrients or no supplementation in premature infants within a nursery setting were eligible. Data were extracted using the standard methods of the Cochrane Collaboration and its Neonatal Review Group, with separate evaluation of trial quality and data extraction by each author and synthesis of data using relative risk and weighted mean difference. Supplementation of human milk with multicomponent fortifiers is associated with short term increases in weight gain, linear and head growth. There is no effect on serum alkaline phosphatase levels; it is not clear if there is an effect on bone mineral content. Nitrogen retention and blood urea levels appear to be increased. There are insufficient data to evaluate long term neurodevelopmental and growth outcomes, although there appears to be no effect on growth beyond one year of life. Use of multicomponent fortifiers does not appear to be associated with adverse effects, although the total number of infants studied and the large amount of missing data reduces confidence in this conclusion. Blood urea levels are increased and blood pH levels minimally decreased, but the clinical significance of this is uncertain. Multicomponent fortification of human milk is associated with short-term improvements in weight gain, linear and head growth. Despite the absence of evidence of long-term benefit and insufficient evidence to be reassured that there are no deleterious effects, it is unlikely that further studies evaluating fortification of human milk versus no supplementation will be performed. Further research should be directed toward comparisons between different proprietary preparations and evaluating both short-term and long-term outcomes in search of the "optimal" composition of fortifiers.

Multiple Imputation Technique Applied to Appropriateness Ratings in Cataract Surgery

Missing data such as appropriateness ratings in clinical research are a common problem and this often yields a biased result. This paper aims to introduce the multiple imputation method to handle missing data in clinical research and to suggest that the multiple imputation technique can give more accurate estimates than those of a complete-case analysis. The idea of multiple imputation is that each missing value is replaced with more than one plausible value. The appropriateness method was developed as a pragmatic solution to problem of trying to assess "appropriate" surgical and medical procedures for patients. Cataract surgery was selected as one of four procedures that were evaluated as a part of the Clinical Appropriateness Initiative. We created mild to high missing rates of 10%, 30% and 50% and compared the performance of logistic regression in cataract surgery. We treated the coefficients in the original data as true parameters and compared them with the other results. In the mild missing rate (10%), the deviation from the true coefficients was quite small and ignorable. After removing the missing data, the complete-case analysis did not reveal any serious bias. However, as the missing rate increased, the bias was not ignorable and it distorted the result. This simulation study suggests that a multiple imputation technique can give more accurate estimates than those of a complete-case analysis, especially for moderate to high missing rates (30 - 50%). In addition, the multiple imputation technique yields better accuracy than a single imputation technique. Therefore, multiple imputation is useful and efficient for a situation in clinical research where there is large amounts of missing data.

Hypothesis testing of a change point during cognitive decline among Alzheimer's disease patients.

In this paper, we present a statistical hypothesis test for detecting a change point over the course of cognitive decline among Alzheimer's disease patients. The model under the null hypothesis assumes a constant rate of cognitive decline over time and the model under the alternative hypothesis is a general bilinear model with an unknown change point. When the change point is unknown, however, the null distribution of the test statistics is not analytically tractable and has to be simulated by parametric bootstrap. When the alternative hypothesis that a change point exists is accepted, we propose an estimate of its location based on the Akaike's Information Criterion. We applied our method to a data set from the Neuropsychological Database Initiative by implementing our hypothesis testing method to analyze Mini Mental Status Exam scores based on a random-slope and random-intercept model with a bilinear fixed effect. Our result shows that despite large amount of missing data, accelerated decline did occur for MMSE among AD patients. Our finding supports the clinical belief of the existence of a change point during cognitive decline among AD patients and suggests the use of change point models for the longitudinal modeling of cognitive decline in AD research.

Incomplete taxa, incomplete characters, and phylogenetic accuracy: is there a missing data problem?

ABSTRACT The problem of missing data is often considered to be the most significant obstacle in reconstructing the phylogeny of fossil taxa and their relationships to extant taxa. In this paper, I review the results of recent simulation studies and present new results that explore how missing data affect phylogenetic accuracy, which is defined here as the success of a method at reconstructing the true phylogeny. Missing data cells are typically added to a phylogenetic analysis in the form of incomplete taxa (e.g., highly fragmentary fossil taxa) or incomplete characters (e.g., a set of DNA sequence or soft anatomical characters in an analysis including living and fossil taxa). These two types of incomplete data affect phylogenetic analyses in two very different ways, suggesting that there is not a single “missing data problem.” Recent simulation results show that including incomplete taxa is a problem of including too few characters rather than too many missing data cells—if enough characters are scored in these taxa, even the relationships of highly incomplete taxa (e.g., 95% missing data) can be accurately reconstructed. Including incomplete characters is largely a problem of taxon sampling. Adding incomplete characters can improve accuracy under many conditions, but inadequate taxon sampling in these characters can lead to problems of long branch attraction (which causes methods to reconstruct an incorrect tree). New simulation results show that highly incomplete taxa may have little impact on the relationships estimated for the complete taxa. Thus, adding highly incomplete taxa may not adversely affect relationships among the complete taxa. However, these added taxa may be unable to improve accuracy for the complete taxa if they are too incomplete. These results suggest that analyses which combine data from fossils and molecular data sets can be successful, despite large amounts of missing data. The accuracy of these analyses will depend on adequate sampling of characters for fossil taxa and adequate sampling of taxa for molecular data sets.

Bias Arising from Missing Data in Predictive Models

Abstract Objective The purpose of this study is to determine the effect of three common approaches to handling missing data on the results of a predictive model. Study Design and Setting Monte Carlo simulation study using simulated data was used. A baseline logistic regression using complete data was performed to predict hospital admission, based on the white blood cell count (WBC) (dichotomized as normal or high), presence of fever, or procedures performed (PROC). A series of simulations was then performed in which WBC data were deleted for varying proportions (15–85%) of patients under various patterns of missingness. Three analytic approaches were used: analysis restricted to cases with complete data, missing data assumed to be normal (MAN), and use of imputed values. Results In the baseline analysis, all three predictors were all significantly associated with admission. Using either the MAN approach or imputation, the odds ratio (OR) for WBC was substantially over- or underestimated depending on the missingness pattern, and there was considerable bias toward the null in the OR estimates for fever. In the CC analyses, OR for WBC was consistently biased toward the null, OR for PROC was biased away from the null, and the OR for fever was biased toward or away from the null. Estimates for overall model discrimination were substantially biased using all analytic approaches. Conclusions All three methods of handling large amounts of missing data can lead to biased estimates of the OR and of model performance in predictive models. Predictor variables that are measured inconsistently can affect the validity of such models.

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.

Patient-assessed measures of health outcome in asthma: A comparison of four approaches

The study compares the psychometric properties of four different approaches to patient-assessed health outcomes in asthma, including the Asthma Quality of Life Questionnaire (AQLQ), Newcastle Asthma Symptoms Questionnaire (NASQ), SF-12 and EuroQol. The instruments were administered by means of a self-completed postal questionnaire to 394 patients recruited from general practices in the North East of England. Patients completed a follow-up questionnaire at 6 months. The levels of missing data were assessed and instrument scores compared using correlational analysis. Scores were related to self-reports of smoking behaviour, socioeconomic status and health transition. Responsiveness was assessed using standardized response means. Two hundred and thirty-five patients took part in the study giving a response rate of 59·6%. There was a relatively large amount of missing data for the individualized section of the AQLQ. Correlational analysis provided evidence of convergent validity between the specific instruments; the largest correlation was found between NASQ scores and the asthma symptoms scale of the AQLQ (r=0·84). The NASQ was found to be the most powerful at discriminating between smokers and non-smokers. All four instruments were linearly related to self-reported asthma transition (P<0·05); the specific instruments having the strongest association. The specific instruments showed good levels of responsiveness with the NASQ producing a large SRM of 0·82. SRMs for the AQLQ were of a moderate to large size (0·32–0·77) and the SRMs for the SF-12 and EuroQol were of a small size. The two specific instruments are capable of greater levels of discrimination between groups of patients and are more responsive to changes in health than the generic SF-12 and EuroQol. The greater responsiveness of the NASQ is probably due to its focus being restricted to symptoms of asthma compared to the broader focus of the AQLQ domains. The NASQ has a strong relationship with the AQLQ and is a more practical instrument that is more acceptable to patients. However, the AQLQ does measure broader patient concerns. The SF-12 and EuroQol have greater potential to capture side-effects and have wider scope for application in economic evaluation.

New Species and Notes on the Natural History of Markea (Solanaceae) from Colombia and Ecuador

New Species and Notes on the Natural History of Markea (Solanaceae) from Colombia and Ecuador

Paleobotany in cladistics and cladistics in paleobotany: enlightenment and uncertainty

Data on fossil taxa can, and should, be incorporated into cladistic analyses. Potential problems with such analyses include large amounts of missing data, and uncertainty about homology of parts that are present. Ambiguity of character data may also occur with extant taxa, but rarely to the extent that it occurs in fossil data. Such ambiguity reduces the strength of the test of character congruence among taxa, in effect relaxing the criterion of parsimony. In order to minimize such effects, composite fossil taxa should be avoided when possible, and polymorphisms reduced by breaking terminals into monomorphic subunits. When results including fossils differ radically from those that exclude fossils, such differences should be approached with caution, keeping in mind the reduced strength of the parsimony analysis when large numbers of cells in a matrix are scored as ambiguous. At this point, there is no simple way to compare the “strength” of parsimony between two data sets that have different numbers of characters and/or taxa in relation to missing data. However, methods under development may provide ways to incorporate the effect of missing values into relative measures of group support such as Bremer support, character removal, and the bootstrap.

The Urge to Merge

This paper describes a procedure used to link Medicaid claims data to California vital statistics records for very low birthweight infants. The linkage involved about 53,000 infants born from 1980 to 1987 and 1.46 million claims for delivery/birth-related hospital admissions during the same period. Because the two data files did not share a unique identifier, record linkage required combining evidence across several linking variables: delivery hospital, delivery/birth date or hospitalization period, names, mother's age, and zip code. To combine the various pieces of evidence, we used record linkage theory to compute scores that measure the likelihood of a match, i.e., that two records correspond to the same delivery. These scores appropriately weight the various pieces of evidence for or against a match. Implementation required dealing with large amounts of missing data in one of the files, errors and variations in reported names, and the need to minimize the number of incorrect links. The approach applies to a wide range of linkage problems. The ability to combine existing datasets to form new datasets containing analysis variables from each facilitates analyses that would otherwise be impossible, or prohibitively expensive.