Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Dynamic contrast agent -enhanced magnetic resonance imaging assessment of tumor microvasculature

Dynamic contrast agent-enhanced magnetic resonance imaging (DCE MRI) data, when analyzed with the appropriate pharmacokinetic models, have been shown to provide quantitative estimates of microvascular parameters important in characterizing the angiogenic activity of malignant tissue. These parameters consist of the whole blood volume per unit volume of tissue, v b, transport constant from the plasma to the extravascular, extracellular space (EES), k1 and the transport constant from the EES to the plasma, k2. Parameters vb and k1 are expected to correlate with microvascular density (MVD) and vascular permeability, respectively, which have been suggested to serve as surrogate markers for angiogenesis. In addition to being a marker for angiogenesis, vascular permeability is also useful in estimating tumor penetration potential of chemotherapeutic agents. ^ Histological measurements of the intratumoral microvascular environment are limited by their invasiveness and susceptibility to sampling errors. Also, MVD and vascular permeability, while useful for characterizing tumors at a single time point, have shown less utility in longitudinal studies, particularly when used to monitor the efficacy of antiangiogenic and traditional chemotherapeutic agents. These limitations led to a search for a non-invasive means of characterizing the microvascular environment of an entire tumor. ^ The overall goal of this project was to determine the utility of DCE MRI for monitoring the effect of antiangiogenic agents. Further applications of a validated DCE MRI technique include in vivo measurements of tumor microvascular characteristics to aid in determining prognosis at presentation and in estimating drug penetration. DCE MRI data were generated using single- and dual-tracer pharmacokinetic models with different molecular-weight contrast agents. The resulting pharmacokinetic parameters were compared to immunohistochemical measurements. The model and contrast agent combination yielding the best correlation between the pharmacokinetic parameters and histological measures was further evaluated in a longitudinal study to evaluate the efficacy of DCE MRI in monitoring the intratumoral microvascular environment following antiangiogenic treatment. ^