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. ^

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. ^

Minerals, native metals, and intermetallides in bottom sediments of the Markov Deep, Mid-Atlantic Ridge

Bottom sediments of the Markov Deep contain rather large (>0.1 mm) grains of native minerals and intermetallides of noble and nonferrous metals that can be concentrated in placers. Intermetallides of Pt and Fe are likely to be derivates of the gold-hematite-barite assemblage that forms at late (low-depth) stages of hydrothermal massive sulfide formation. Mineral association of native forms of lead, tin, and copper with Zn-bearing copper may be related to hydrothermal transformation of ultrabasic and basic rocks accompanied by massive sulfide copper mineralization. The association of these minerals of native elements in bottom sediments can also serve as a prospecting guide for sulfide mineralization both at the Sierra Leone site, in particular, and on the seafloor, in general.

Composition of minerals and rocks from the Markov Deep, Central Atlantic

The paper presents materials on composition and texture of weakly serpentinized ultrabasic rocks from the western and eastern walls of the Markov Deep (5°30.6'-5°32.4'N) in the rift valley of the Mid-Atlantic Ridge. Predominant harzburgites with protogranular and porphyroclastic textures contain two major generations of minerals: the first generation composes the bulk of rocks and consists of Ol_89.8-90.4 + En_90.2-90.8 + Di_91.8 + Chr (Cr#32.3-36.6, Mg#67.2-70.0), while the second generation composes very thin branching veinlets and consists of PlAn_32-47 + Ol_74.3-77.1 + Opx_55.7-71.9 + Cpx_67.5 + Amph_53.7-74.2 + Ilm. Syndeformational olivine neoblasts in recrystallization zones are highly magnesian. Concentrations and covariations of major elements in harzburgites indicate that these rocks are depleted in mantle residues (high Mg# of minerals and whole-rock samples and low in CaO, Al2O3, and TiO2) that are significantly enriched in trace HFSE and REE (Zr, Hf, Y, LREE, and all REE). Mineralogy and geochemistry of harzburgites were formed by interaction of mantle residues with hydrous, strongly fractionated melts that impregnated them. Mineral composition of veinlets in harzburgites and mineralogical-geochemical characteristics of related plagiogranites and gabbronorites suggest that these plagiogranites were produced by melt residuals after crystallization of gabbronorites. Modern characteristics of harzburgites were shaped by the following processes: (i) partial melting of mantle material simultaneously with its subsolidus deformations, (ii) brittle-plastic deformations associated with cataclastic flow and recrystallization, and (iii) melt percolation along zones of maximal stress relief and interaction of this melt with magnesian mantle residue.

Chemical composition of minerals and rocks from the Sierra Leone segment of the Mid-Atlantic Ridge and from the Markov depression, Central Atlantic

Silicic Fe-Ti-oxide magmatic series was the first recognized in the Sierra Leone axial segment of the Mid-Atlantic Ridge near 6°N. The series consists of intrusive rocks (harzburgites, lherzolites, bronzitites, norites, gabbronorites, hornblende Fe-Ti-oxide gabbronorites and gabbronorite-diorites, quartz diorites, and trondhjemites) and their subvolcanic (ilmenite-hornblende dolerites) and, possibly, volcanic analogues (ilmenite-bearing basalts). Deficit of most incompatible elements in the rocks of the series suggests that parental melts derived from a source that had already been melted. Correspondingly, these melts could not be MORB derivatives. Origin of the series is thought to be related to melting of the hydrated oceanic lithosphere during emplacement of an asthenospheric plume (protuberance on the surface of large asthenospheric lens beneath MAR). Genesis of different melts was supposedly controlled by ascent of a chamber of hot mantle magmas thought this lithosphere in compliance with the zone melting mechanism. Melt acquired fluid components from heated rocks at peripheries of the plume and became enriched in Fe, Ti, Pb, Cu, Zn, and other components mobile in fluids.