Master Albert Schirmer, one of the principal Performers on the German Stage, in London

Signatur des Originals: S 36/G02163

View of the Gallery prepared for the reception of their Majesties, the Royal Family, Directors, & principal Personage in the Kingdom, at the Commemoration of Handel in Westminster Abbey

Signatur des Originals: S 36/G02676

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Growth and development of body fat distribution from skinfold measurements: Longitudinal principal components

Longitudinal principal components analyses on a combination of four subcutaneous skinfolds (biceps, triceps, subscapular and suprailiac) were performed using data from the London Longitudinal Growth Study. The main objectives were to discover at what age during growth sex differences in body fat distribution occur and to see if there is continuity in body fatness and body fat distribution from childhood into the adult status (18 years). The analyses were done for four age sectors (3mon-3yrs, 3yrs-8yrs, 8yrs-18yrs and 3yrs-18yrs). Longitudinal principal component one (LPC1) for each age interval in both sexes represents the population mean fat curve. Component two (LPC2) is a velocity of fatness component. Component three (LPC3) in the 3mon-3yrs age sector represents infant fat wave in both sexes. In the next two age sectors component three in males represents peaks and shifts in fat growth (change in velocity), while in females it represents body fat distribution. Component four (LPC4) in the same two age sectors is a reversal in the sexes of the patterns seen for component three, i.e., in males it is body fat distribution and in females velocity shifts. Components five and above represent more complicated patterns of change (multiple increases and decreases across the age interval). In both sexes there is strong tracking in fatness from middle childhood to adolescence. In males only there is also a low to moderate tracking of infant fat with middle to late childhood fat. These data are strongly supported in the literature. Several factors are known to predict adult fatness among the most important being previous levels of fatness (at earlier ages) and the age at rebound. In addition we found that the velocity of fat change in middle childhood was highly predictive of later fatness (r $\approx -$0.7), even more so than age at rebound (r $\approx -$0.5). In contrast to fatness (LPC1), body fat distribution (LPC3-LPC4) did not track well even though significant components of body fat distribution occur at each age. Tracking of body fat distribution was higher in females than males. Sex differences in body fat distribution are non existent. Some sex differences are evident with the peripheral-to-central ratios after age 14 years. ^

The application of principal component analysis on human development indicators: Temporal approach from 1999 to 2010

Background and Objective. Ever since the human development index was published in 1990 by the United Nations Development Programme (UNDP), many researchers started searching and corporative studying for more effective methods to measure the human development. Published in 1999, Lai’s “Temporal analysis of human development indicators: principal component approach” provided a valuable statistical way on human developmental analysis. This study presented in the thesis is the extension of Lai’s 1999 research. ^ Methods. I used the weighted principal component method on the human development indicators to measure and analyze the progress of human development in about 180 countries around the world from the year 1999 to 2010. The association of the main principal component obtained from the study and the human development index reported by the UNDP was estimated by the Spearman’s rank correlation coefficient. The main principal component was then further applied to quantify the temporal changes of the human development of selected countries by the proposed Z-test. ^ Results. The weighted means of all three human development indicators, health, knowledge, and standard of living, were increased from 1999 to 2010. The weighted standard deviation for GDP per capita was also increased across years indicated the rising inequality of standard of living among countries. The ranking of low development countries by the main principal component (MPC) is very similar to that by the human development index (HDI). Considerable discrepancy between MPC and HDI ranking was found among high development countries with high GDP per capita shifted to higher ranks. The Spearman’s rank correlation coefficient between the main principal component and the human development index were all around 0.99. All the above results were very close to outcomes in Lai’s 1999 report. The Z test result on temporal analysis of main principal components from 1999 to 2010 on Qatar was statistically significant, but not on other selected countries, such as Brazil, Russia, India, China, and U.S.A.^ Conclusion. To synthesize the multi-dimensional measurement of human development into a single index, the weighted principal component method provides a good model by using the statistical tool on a comprehensive ranking and measurement. Since the weighted main principle component index is more objective because of using population of nations as weight, more effective when the analysis is across time and space, and more flexible when the countries reported to the system has been changed year after year. Thus, in conclusion, the index generated by using weighted main principle component has some advantage over the human development index created in UNDP reports.^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^