MATHEMATICAL STUDIES ON THE EVOLUTIONARY CHANGE OF DNA SEQUENCES

With the aim of understanding the mechanism of molecular evolution, mathematical problems on the evolutionary change of DNA sequences are studied. The problems studied and the results obtained are as follows: (1) Estimation of evolutionary distance between nucleotide sequences. Studying the pattern of nucleotide substitution for the case of unequal substitution rates, a new mathematical formula for estimating the average number of nucleotide substitutions per site between two homologous DNA sequences is developed. It is shown that this formula has a wider applicability than currently available formulae. A statistical method for estimating the number of nucleotide changes due to deletion and insertion is also developed. (2) Biases of the estimates of nucleotide substitutions obtained by the restriction enzyme method. The deviation of the estimate of nucleotide substitutions obtained by the restriction enzyme method from the true value is investigated theoretically. It is shown that the amount of the deviation depends on the nucleotides in the recognition sequence of the restriction enzyme used, unequal rates of substitution among different nucleotides, and nucleotide frequences, but the primary factor is the unequal rates of nucleotide substitution. When many different kinds of enzymes are used, however, the amount of average deviation is generally small. (3) Distribution of restriction fragment lengths. To see the effect of undetectable restriction fragments and fragment differences on the estimate of nucleotide differences, the theoretical distribution of fragment lengths is studied. This distribution depends on the type of restriction enzymes used as well as on the relative frequencies of four nucleotides. It is shown that undetectability of small fragments or fragment differences gives a serious underestimate of nucleotide substitutions when the length-difference method of estimation is used, but the extent of underestimation is small when the site-difference method is used. (4) Evolutionary relationships of DNA sequences in finite populations. A mathematical theory on the expected evolutionary relationships among DNA sequences (nucleons) randomly chosen from the same or different populations is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author). UMI ^

Mathematical and empirical examinations of some epidemiological procedures

In epidemiology literature, it is often required to investigate the relationships between means where the levels of experiment are actually monotone sets forming a partition on the range of sampling values. With this need, the analysis of these group means is generally performed using classical analysis of variance (ANOVA). However, this method has never been challenged. In this dissertation, we will formulate and present our examination of its validity. First, the classical assumptions of normality and constant variance are not always true. Second, under the null hypothesis of equal means, the test statistic for the classical ANOVA technique is still valid. Third, when the hypothesis of equal means is rejected, the classical analysis techniques for hypotheses of contrasts are not valid. Fourth, under the alternative hypothesis, we can show that the monotone property of levels leads to the conclusion that the means are monotone. Fifth, we propose an appropriate method for handing the data in this situation. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Data Accuracy in Medical Record Abstraction

Clinical Research Data Quality Literature Review and Pooled Analysis We present a literature review and secondary analysis of data accuracy in clinical research and related secondary data uses. A total of 93 papers meeting our inclusion criteria were categorized according to the data processing methods. Quantitative data accuracy information was abstracted from the articles and pooled. Our analysis demonstrates that the accuracy associated with data processing methods varies widely, with error rates ranging from 2 errors per 10,000 files to 5019 errors per 10,000 fields. Medical record abstraction was associated with the highest error rates (70–5019 errors per 10,000 fields). Data entered and processed at healthcare facilities had comparable error rates to data processed at central data processing centers. Error rates for data processed with single entry in the presence of on-screen checks were comparable to double entered data. While data processing and cleaning methods may explain a significant amount of the variability in data accuracy, additional factors not resolvable here likely exist. Defining Data Quality for Clinical Research: A Concept Analysis Despite notable previous attempts by experts to define data quality, the concept remains ambiguous and subject to the vagaries of natural language. This current lack of clarity continues to hamper research related to data quality issues. We present a formal concept analysis of data quality, which builds on and synthesizes previously published work. We further posit that discipline-level specificity may be required to achieve the desired definitional clarity. To this end, we combine work from the clinical research domain with findings from the general data quality literature to produce a discipline-specific definition and operationalization for data quality in clinical research. While the results are helpful to clinical research, the methodology of concept analysis may be useful in other fields to clarify data quality attributes and to achieve operational definitions. Medical Record Abstractor’s Perceptions of Factors Impacting the Accuracy of Abstracted Data Medical record abstraction (MRA) is known to be a significant source of data errors in secondary data uses. Factors impacting the accuracy of abstracted data are not reported consistently in the literature. Two Delphi processes were conducted with experienced medical record abstractors to assess abstractor’s perceptions about the factors. The Delphi process identified 9 factors that were not found in the literature, and differed with the literature by 5 factors in the top 25%. The Delphi results refuted seven factors reported in the literature as impacting the quality of abstracted data. The results provide insight into and indicate content validity of a significant number of the factors reported in the literature. Further, the results indicate general consistency between the perceptions of clinical research medical record abstractors and registry and quality improvement abstractors. Distributed Cognition Artifacts on Clinical Research Data Collection Forms Medical record abstraction, a primary mode of data collection in secondary data use, is associated with high error rates. Distributed cognition in medical record abstraction has not been studied as a possible explanation for abstraction errors. We employed the theory of distributed representation and representational analysis to systematically evaluate cognitive demands in medical record abstraction and the extent of external cognitive support employed in a sample of clinical research data collection forms. We show that the cognitive load required for abstraction in 61% of the sampled data elements was high, exceedingly so in 9%. Further, the data collection forms did not support external cognition for the most complex data elements. High working memory demands are a possible explanation for the association of data errors with data elements requiring abstractor interpretation, comparison, mapping or calculation. The representational analysis used here can be used to identify data elements with high cognitive demands.