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A number of methods have been developed to analyze longitudinal data with dropout. However, there is no uniformly accepted approach. Model performance, in terms of the bias and accuracy of the estimator, depends on the underlying missing data mechanism and it is unclear how existing methods will perform when little is known about the missing data mechanism. Here we evaluate methods for estimating change over time in longitudinal studies with informative dropout in three settings: using a linear mixed effect (LME) estimator in the presence of multiple types of dropout; proposing an update to the pattern mixture modeling (PMM) approach in the presence of imprecision in identifying informative dropouts; and utilizing this new approach in the presence of prognostic factor by dropout interaction. We demonstrate that amount of dropout, the proportion of dropout that is informative, and the variability in outcome all affect the performance of an LME estimator in data with a mixture of informative and non-informative dropout. When the amount of dropout is moderate to large (>20% overall) the potential for relative bias greater than 10% increases, especially with large variability in outcome measure, even under scenarios where only a portion of the dropouts are informative. Under conditions where LME models do not perform well, it is necessary to take the missing data mechanism into account. We develop a method that extends the PMM approach to account for uncertainty in identifying informative dropouts. In scenarios with this uncertainty, the proposed method outperformed the traditional method in terms of bias and coverage. In the presence of interaction between dropout and a prognostic factor, the LME model performed poorly, in terms of bias and coverage, in estimating prognostic factor-specific slopes and the interaction between the prognostic factor and time. The update to the PMM approach, proposed here, outperformed both the LME and traditional PMM. Our work suggests that investigators must be cautious with any analysis of data with informative dropout. We found that particular attention must be paid to the model assumptions when the missing data mechanism is not well understood.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18071号 / 理博第3949号 / 新制||理||1569(附属図書館) / 30929 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 永江 知文, 准教授 成木 恵, 教授 鶴 剛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18673号 / 理博第4022号 / 新制||理||1580(附属図書館) / 31606 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 永江 知文, 教授 谷森 達, 准教授 成木 恵 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Faculty of Engineering and Built Enviroment School of Civil and Enviromental Engineering 0105772w imasengo@yahoo.com / The problem of missing data, insufficient length of hydrological data series and poor quality is common in developing countries. This problem is much more prevalent in developing countries than it is in developed countries. This situation can severely affect the outcome of the water systems managers’ decisions (e.g. reliability of the design, establishment of operating policies for water supply, etc). Thus, numerous data interpolation (infilling) techniques have evolved in hydrology to deal with the missing data. The current study presents merely a methodology by combining different approaches and coping with missing (limited) hydrological data using the theories of entropy, artificial neural networks (ANN) and expectation-maximization (EM) techniques. This methodology is simply formulated into a model named ENANNEX model. This study does not use any physical characteristics of the catchment areas but deals only with the limited information (e.g. streamflow or rainfall) at the target gauge and its similar nearby base gauge(s). The entropy concept was confirmed to be a versatile tool. This concept was firstly used for quantifying information content of hydrological variables (e.g. rainfall or streamflow). The same concept (through directional information transfer index, i.e. DIT) was used in the selection of base/subject gauge. Finally, the DIT notion was also extended to the evaluation of the hydrological data infilling technique performance (i.e. ANN and EM techniques). The methodology was applied to annual total rainfall; annual mean flow series, annual maximum flows and 6-month flow series (means) of selected catchments in the drainage region D “Orange” of South Africa. These data regimes can be regarded as useful for design-oriented studies, flood studies, water balance studies, etc. The results from the case studies showed that DIT is as good index for data infilling technique selection as other criteria, e.g. statistical and graphical. However, the DIT has the feature of being non-dimensionally informational index. The data interpolation iii techniques viz. ANNs and EM (existing methods applied and not yet applied in hydrology) and their new features have been also presented. This study showed that the standard techniques (e.g. Backpropagation-BP and EM) as well as their respective variants could be selected in the missing hydrological data estimation process. However, the capability for the different data interpolation techniques of maintaining the statistical characteristics (e.g. mean, variance) of the target gauge was not neglected. From this study, the relationship between the accuracy of the estimated series (by applying a data infilling technique) and the gap duration was then investigated through the DIT notion. It was shown that a decay (power or exponential) function could better describe that relationship. In other words, the amount of uncertainty removed from the target station in a station-pair, via a given technique, could be known for a given gap duration. It was noticed that the performance of the different techniques depends on the gap duration at the target gauge, the station-pair involved in the missing data estimation and the type of the data regime. This study showed also that it was possible, through entropy approach, to assess (preliminarily) model performance for simulating runoff data at a site where absolutely no record exist: a case study was conducted at Bedford site (in South Africa). Two simulation models, viz. RAFLER and WRSM2000 models, were then assessed in this respect. Both models were found suitable for simulating flows at Bedford.

Since the bizarre disappearance of his wife, mountaineer Abbot Boone's life has spiraled into a pit of alcoholism and alienation. But then a wealthy and desperate widow hires Boone for an impossible task: to recover her husband's dead body from the peaks of Mount Everest. With nothing to lose and debts mounting, Boone enlists a team of exiles and misfits to attempt the climb. But if Boone is to conquer the mountain, he will first have to survive the pressure cooker of Everest Base Camp, brutal subzero temperatures, and ultimately confront the mystery of his own grief

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In this thesis, I am interested in estimating the difference between dependent proportions from a 2 × 2 contingency table when there are missing data. The Expectation-Maximization (EM) algorithm is used to obtain an estimate for the difference between correlated proportions. To obtain the standard error of this difference I employ a resampling technique known as bootstrapping. The performance of the bootstrap standard error is evaluated for different sample sizes and different fractions of missing information. Finally, a 100(1-α)% bootstrap confidence interval is proposed and its coverage is evaluated through simulation.

Missing data are ubiquitous in many domains such as healthcare. Depending on how they are missing, the (conditional) independence relations in the observed data may be different from those for the complete data generated by the underlying causal process (which are not fully observable) and, as a consequence, simply applying existing causal discovery methods to the observed data may give wrong conclusions. It is then essential to extend existing causal discovery approaches to find true underlying causal structure from such incomplete data. In this thesis, we aim at solving this problem for data that are missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). With missingness mechanisms represented by the Missingness Graph, we present conditions under which addition corrected to derive conditional independence/dependence relations in the complete data. Combined with the correction method that gives closed-form, consistent tests of conditional independence, the proposed causal discovery method, as an extension of the PC algorithm, is shown to give asymptotically correct results. Experiment results illustrate that with further reasonable assumptions, the proposed algorithm can correct the conditional independence for values MCAR, MAR and rather general cases of values MNAR. / Saknade data är allestädes närvarande på många områden, t.ex. sjukvård. Beroende på hur de saknas kan de (villkorliga) oberoende förhållandena i de observerade uppgifterna skilja sig från de för de fullständiga data som genereras av den underliggande orsaksprocessen (som inte är fullt observerbara) och som en följd av att helt enkelt tillämpa befintlig kausal upptäckt metoder för de observerade data kan ge felaktiga slutsatser. Det är då viktigt att förlänga befintliga metoder för kausala upptäckter för att hitta en sann underliggande kausalstruktur från sådana ofullständiga data. I denna avhandling strävar vi efter att lösa detta problem för data som saknas helt slumpmässigt (MCAR), saknas slumpmässigt (MAR) eller saknas inte slumpmässigt (MNAR). Med missmekanismer representerade av Missfallsgrafen presenterar vi förhållanden under vilka tillägg korrigerade för att härleda villkorliga oberoende/beroendeförhållanden i de fullständiga uppgifterna.Kombinerad med korrigeringsmetoden som ger sluten form, konsekventa test av villkorligt oberoende, visas att den föreslagnaorsaks-sökningsmetoden, som en förlängning av PC-algoritmen, ger asymptotiskt korrekta resultat. Experimentresultat illustrera att med ytterligare rimliga antaganden kan den föreslagna algoritmen korrigera det villkorliga oberoende för värdena MCAR, MAR och ganska generella fall av värden MNAR.

The recent call to reconstruct a detailed picture of the tree of life for all organisms has forever changed the field of molecular phylogenetics. Sequencing technology has improved to the point that scientics can now routinely sequence complete plastid/mitochondrial genomes and thus, vast amounts of data can be used to reconstruct phylogenies. These data are accumulating in DNA sequence repositories, such as GenBank, where everyone can benefit from the vast growth of information. The trend of generating genomic-region rich datasets has far outpaced the expasion of datasets by sampling a broader array of taxa. We show here that expanding a dataset both by increasing genomic regions and species sampled using GenBank data, despite the inherent missing DNA that comes with GenBank data, can provide a robust phylogeny for the plant order Caryophyllales (angiosperms). We also investigate the utility of trnK intron in phylogeny reconstruction at relativley deep evolutionary history (the caryophyllid order) by comparing it with rapidly evolving matK. We show that trnK intron is comparable to matK in terms of the proportion of variable sites, parsimony informative sites, the distribution of those sites among rate classes, and phylogenetic informativness across the history of the order. This is especailly useful since trnK intron is often sequenced concurrently with matK which saves on time and resources by increasing the phylogenetic utility of a single genomic region (rapidly evolving matK/trnK). Finally, we show that the inclusion of RNA edited sites in datasets for phylogeny reconstruction did not appear to impact resolution or support in the Gnetales indicating that edited sites in such low proportions do not need to be a consideration when building datasets. We also propose an alternate start codon for matK in Ephedra based on the presense of a 38 base pair indel in several species that otherwise result in pre-mature stop codons, and present 20 RNA edited sites in two Zamiaceae and three Pinaceae species. / Ph. D.