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. ^

Alpine permafrost index map

The objective of this study is the production of an Alpine Permafrost Index Map (APIM) covering the entire European Alps. A unified statistical model that is based on Alpine-wide permafrost observations is used for debris and bedrock surfaces across the entire Alps. The explanatory variables of the model are mean annual air temperatures, potential incoming solar radiation and precipitation. Offset terms were applied to make model predictions for topographic and geomorphic conditions that differ from the terrain features used for model fitting. These offsets are based on literature review and involve some degree of subjective choice during model building. The assessment of the APIM is challenging because limited independent test data are available for comparison and these observations represent point information in a spatially highly variable topography. The APIM provides an index that describes the spatial distribution of permafrost and comes together with an interpretation key that helps to assess map uncertainties and to relate map contents to their actual expression in terrain. The map can be used as a first resource to estimate permafrost conditions at any given location in the European Alps in a variety of contexts such as research and spatial planning. Results show that Switzerland likely is the country with the largest permafrost area in the Alps, followed by Italy, Austria, France and Germany. Slovenia and Liechtenstein may have marginal permafrost areas. In all countries the permafrost area is expected to be larger than the glacier-covered area.

Reconstructed glaciation limits in Eurasia (digitized from map Fig.1)

Based on field investigations in northern Russia and interpretation of offshore seismic data, we have made a preliminary reconstruction of the maximum ice-sheet extent in the Barents and Kara Sea region during the Early/Middle Weichselian and the Late Weichselian. Our investigations indicate that the Barents and Kara ice sheets attained their maximum Weichselian positions in northern Russia prior to 50 000 yr BP, whereas the northeastern flank of the Scandinavian Ice Sheet advanced to a maximum position shortly after 17000 calendar years ago. During the Late Weichselian (25 000-10000 yr BP), much of the Russian Arctic remained ice-free. According to our reconstruction, the extent of the ice sheets in the Barents and Kara Sea region during the Late Weichselian glacial maximum was less than half that of the maximum model which, up to now, has been widely used as a boundary condition for testing and refining General Circulation Models (GCMs). Preliminary numerical-modelling experiments predict Late Weichselian ice sheets which are larger than the ice extent implied for the Kara Sea region from dated geological evidence, suggesting very low precipitation.

Geological map of HANSSONHORNA, Heimefrontfjella, Antarctica (Scale 1:25,000)

Topographic data of this geological map were obtained through stereoscopic aerial photo interpretation. The photogrammetric photo flights were undertaken in 1986 by the Institut für Angewandte Geodäsie, Frankfurt. Horizontal ground control points required for aerial photo interpretation were determined by means of Doppler satellite observation during the 2nd German Neuschwabenland Expedition 1985/86. Vertical ground control points were taken from unpublished map drafts at 1:100 000 scale by Norsk Polarinstitutt, Oslo. The elevation above mean sea level was transferred to Heimefrontfjella barometrically. For this reason assertions concerning the absolute elevation (referred to sea level) are uncertain. Contours and spot heights presented on the map were obtained from the photogrammetric evaluation of the photography taken in 1986; relative elevation data (hight differences) are accurate to approximately ±10 m.

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.