A Bayesian approach for joint modeling of cluster size and subunit-specific outcomes

In applications that involve clustered data, such as longitudinal studies and developmental toxicity experiments, the number of subunits within a cluster is often correlated with outcomes measured on the individual subunits. Analyses that ignore this dependency can produce biased inferences. This article proposes a Bayesian framework for jointly modeling cluster size and multiple categorical and continuous outcomes measured on each subunit. We use a continuation ratio probit model for the cluster size and underlying normal regression models for each of the subunit-specific outcomes. Dependency between cluster size and the different outcomes is accommodated through a latent variable structure. The form of the model facilitates posterior computation via a simple and computationally efficient Gibbs sampler. The approach is illustrated with an application to developmental toxicity data, and other applications, to joint modeling of longitudinal and event time data, are discussed.     

Multiple censored data in dentistry: A new statistical model for analyzing lesion size in randomized controlled trials

Caries infiltration is a novel treatment option for proximal caries lesions. The idea is to build a diffusion barrier inside the lesion to slow down or stop the caries progression. If a lesion still reaches a critical size, restorative treatment is required. Clinical trials investigating caries infiltration thus produce multiple censored ordinal data. Standard statistical models do not take into account this censoring, and we therefore propose the Multiple Ordered Tobit (MOT) model. The model is implemented in R and compared with standard approaches. Simulation studies demonstrate that for all sample sizes and scenarios the MOT model has the largest statistical power among all methods compared, and it is robust against heteroscedasticity to some extent. Finally, a comparison with dichotomous and ordinal scaled models shows that the use of metric data for the lesion size reduces the required sample size considerably.     

A stochastic model for the sizes of detectable metastases

A stochastic entirely mechanistic model of metastatic progression of cancer is developed. Based on this model the joint conditional distribution of the ordered sizes of detectable metastases given their number, n, is computed. It is shown that this distribution coincides with the joint distribution of order statistics for a random sample of size n derived from some probability distribution, and a formula for the latter is obtained. This formula is specialized for the case of exponentially growing primary and secondary tumors and exponentially distributed metastasis promotion times, and identifiability of model parameters is ascertained. These results allow for estimation of the natural history of cancer. As an example, it is estimated for a breast cancer patient with 31 bone metastases of known sizes. The proposed model for the sizes of detectable metastases provided an excellent fit to these data.     

A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study

Summary .  In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.     

A Markov model for a clinical episode of recurrent genital herpes

A time-homogeneous Markov process is proposed for modeling the clinical course of recurrent genital herpes and is used to obtain estimators for various characteristics of the disease episode. The model has a finite, discrete time parameter and discrete state space, with six transient states corresponding to the six stages a herpes lesion may enter. The healed condition is represented as an absorbing state. The number of lesions present at the onset of the clinical episode and the number of lesions appearing during the course of the episode are assumed to have negative binomial distributions. Clinical trial data are used to examine the assumptions of the model and to estimate its parameters. Estimates of clinical variables based on the model are computed and are compared with those calculated directly to assess how well the model represents the biological process of the disease.     

Vascular endothelial growth factor expression and regulation of murine collagen-induced arthritis

We have examined the expression and function of the angiogenic factor, vascular endothelial growth factor (VEGF) during the evolution of type II collagen-induced arthritis (CIA). Biologically active VEGF was expressed along a time course that paralleled the expression of two specific VEGF receptors, Flk-1 and Flt-1, and the progression of joint disease. Moreover, levels of VEGF expression correlated with the degree of neovascularization, as defined by vWF levels, and arthritis severity. Macrophage- and fibroblast-like cells, which infiltrated inflamed sites and were then activated by other inflammatory mediators, are probably important sources of VEGF and may thus regulate angiogenesis during the development of CIA. Administration of anti-VEGF antiserum to CIA mice before the onset of arthritis delayed the onset, reduced the severity, and diminished the vWF content of arthritic joints. By contrast, administration of anti-VEGF antiserum after the onset of the disease had no effect on the progression or ultimate severity of the arthritis. These data suggest that VEGF plays a crucial role during an early stage of arthritis development, affecting both neovascularization and the progression of experimentally induced synovitis.     

On the emergence of multifocal cancers

Several tumors can exist as multiple lesions within a tissue. The lesions may either arise independently, or they may be monoclonal. The importance of multiple lesions for tumor staging, progression, and treatment is subject to debate. Here we use mathematical models to analyze the emergence of multiple, clonally related lesions within a single tissue. We refer to them as multi-focal cancers. We find that multifocal cancers can arise through a dynamical interplay between tumor promoting and inhibiting factors. This requires that tumor promoters act locally, while tumor inhibitors act over a longer range. An example of such factors may be angiogenesis promoters and inhibitors. The model further suggests that multifocal cancers represent an intermediate stage in cancer progression as the tumor evolves away from inhibition and towards promotion. Different patterns of progression can be distinguished: (i) If tumor inhibition is strong, the initial growth occurs as a unifocal and self contained lesion; progression occurs through bifurcation of the lesion and this gives rise to multiple lesions. As the tumor continues to evolve and pushes the balance between inhibition and promotion further towards promotion, the multiple lesions eventually give rise to a single large mass which can invade the entire tissue. (ii) If tumor inhibition is weaker upon initiation, growth can occur as a single lesion without the occurrence of multiple lesions, until the entire tissue is invaded. The model suggests that the sum of the tumor sizes across all lesions is the best characteristic which correlates with the stage and metastatic potential of the tumor.     

Leishmania braziliensis: effects of bacteria (Staphylococcus aureus and Pasteurella multocida) on the developing cutaneous leishmaniasis lesion in the golden hamster

Experimentally induced lesions of cutaneous leishmaniasis and the effect of concurrent bacterial infection on the development of these lesions were studied in the golden hamster. Male outbred golden hamsters received intradermal injections at the base of the tail with approximately 10(7) promastigotes of Leishmania braziliensis panamensis, or promastigotes combined with Staphylococcus aureus or Pasteurella multocida or both, bacteria only, or sterile Eagle's minimal essential medium (MEME). The size of the resulting lesions was measured at least twice each week. Hamsters were killed at postinoculation Days 6, 13, 20, 27, 41, or 48, and each lesion was measured, aseptically excised, and bisected; half was used for bacteriologic culture and the other half was prepared for light microscopic examination. Lesions resulting from L. b. panamensis alone progressed from initial erythema to a granulomatous nodule and finally to a necrotic granuloma, often capped by a crateriform ulcer. Lesions resulting from a suspension of L. b. panamensis with added S. aureus or S. aureus and P. multocida, were initially larger, more erythemic and contained a greater proportion of neutrophils up to postinoculation Days 14-21 than did lesions resulting from L. b. panamensis alone. Concurrent infections with bacteria such as S. aureus and P. multocida had little effect on the development of ulcerating characteristics of lesions, but when S. aureus was present it appeared to enhance the severity of the early lesions. Between postinoculation Days 14-28, lesions produced by L. b. panamensis, with or without added bacteria had similar developmental progression of sufficient size for optimal testing of antileishmanial compounds.     

An empirical Bayes' approach to joint analysis of multiple microarray gene expression studies

With the prevalence of gene expression studies and the relatively low reproducibility caused by insufficient sample sizes, it is natural to consider joint analysis that could combine data from different experiments effectively to achieve improved accuracy. We present in this article a model-based approach for better identification of differentially expressed genes by incorporating data from different studies. The model can accommodate in a seamless fashion a wide range of studies including those performed at different platforms by fitting each data with different set of parameters, and/or under different but overlapping biological conditions. Model-based inferences can be done in an empirical Bayes' fashion. Because of the information sharing among studies, the joint analysis dramatically improves inferences based on individual analysis. Simulation studies and real data examples are presented to demonstrate the effectiveness of the proposed approach under a variety of complications that often arise in practice.     

Imputation strategies for missing continuous outcomes in cluster randomized trials

In cluster randomized trials, intact social units such as schools, worksites or medical practices - rather than individuals themselves - are randomly allocated to intervention and control conditions, while the outcomes of interest are then observed on individuals within each cluster. Such trials are becoming increasingly common in the fields of health promotion and health services research. Attrition is a common occurrence in randomized trials, and a standard approach for dealing with the resulting missing values is imputation. We consider imputation strategies for missing continuous outcomes, focusing on trials with a completely randomized design in which fixed cohorts from each cluster are enrolled prior to random assignment. We compare five different imputation strategies with respect to Type I and Type II error rates of the adjusted two-sample t -test for the intervention effect. Cluster mean imputation is compared with multiple imputation, using either within-cluster data or data pooled across clusters in each intervention group. In the case of pooling across clusters, we distinguish between standard multiple imputation procedures which do not account for intracluster correlation and a specialized procedure which does account for intracluster correlation but is not yet available in standard statistical software packages. A simulation study is used to evaluate the influence of cluster size, number of clusters, degree of intracluster correlation, and variability among cluster follow-up rates. We show that cluster mean imputation yields valid inferences and given its simplicity, may be an attractive option in some large community intervention trials which are subject to individual-level attrition only; however, it may yield less powerful inferences than alternative procedures which pool across clusters especially when the cluster sizes are small and cluster follow-up rates are highly variable. When pooling across clusters, the imputation procedure should generally take intracluster correlation into account to obtain valid inferences; however, as long as the intracluster correlation coefficient is small, we show that standard multiple imputation procedures may yield acceptable type I error rates; moreover, these procedures may yield more powerful inferences than a specialized procedure, especially when the number of available clusters is small. Within-cluster multiple imputation is shown to be the least powerful among the procedures considered.     

Bayesian modeling of incidence and progression of disease from cross-sectional data

In the absence of longitudinal data, the current presence and severity of disease can be measured for a sample of individuals to investigate factors related to disease incidence and progression. In this article, Bayesian discrete-time stochastic models are developed for inference from cross-sectional data consisting of the age at first diagnosis, the current presence of disease, and one or more surrogates of disease severity. Semiparametric models are used for the age-specific hazards of onset and diagnosis, and a normal underlying variable approach is proposed for modeling of changes with latency time in disease severity. The model accommodates multiple surrogates of disease severity having different measurement scales and heterogeneity among individuals in disease progression. A Markov chain Monte Carlo algorithm is described for posterior computation, and the methods are applied to data from a study of uterine leiomyoma.     

Progression curves for endometrial lesions

OBJECTIVE: To derive a numeric measure for the progression of endometrial lesions as a baseline study for an eventual assessment of chemopreventive intervention efficacy. STUDY DESIGN: Tissue sections from normal endometrium at the proliferative and secretory phase, simple hyperplasia, atypical hyperplasia from cases free of concomitant adenocarcinoma and adenocarcinoma of the endometrium were recorded at high spatial resolution. Six cases from each diagnostic category were chosen as "typical," and 60 epithelial nuclei were randomly selected for measurement for each case. Discriminant analyses were carried out to derive a direction of progressive change in feature space and to correct the progression curve for the presence of cells not expressing progressive change among the random sample of nuclei. RESULTS: A well-conditioned progression curve was derived based on the mean discriminant function scores for each diagnostic category and the mean nuclear abnormality of the nuclei in each category, as expressed by their deviation in feature values from normal reference nuclei. The lesion signatures showed a clear trend toward extension into the range of higher nuclear abnormalities with increasing progression. There was an indication that abnormal endometrial lesions may comprise cases with distinctly different degrees of nuclear abnormality. CONCLUSION: A numeric assessment of lesion progression for endometrial lesions, based on karyometric measurements, is possible. The data suggest that additional analysis may provide further characterizing information for individual lesions.     

Preneoplastic lesions in rodent kidney induced spontaneously or by non-genotoxic agents: predictive nature and comparison to lesions induced by genotoxic carcinogens

The current literature on non-genotoxic renal carcinogens and the associated neoplastic and preneoplastic lesions has been reviewed in order to determine their occurrence and predictive nature with regard to tumor formation. In addition the mechanisms involved in the genesis of renal tumors are discussed. A more generalized classification of preneoplastic and neoplastic renal lesions was introduced, based on studies conducted with genotoxic and non-genotoxic renal carcinogens. Reports on preneoplastic lesions were found in the literature for control animals as well as animals treated with non-genotoxic carcinogens. Due to the paucity of data regarding preneoplastic lesions in control animals and animals treated with non-genotoxic carcinogens, new data were also generated by rereading kidney slides of control animals of a randomly selected NTP study and kidney slides of male rats treated with the highest dose of ochratoxin A, one of the most potent non-genotoxic renal carcinogens known. The control slides and the slides from the ochratoxin A study indicated that the cytologic and morphologic types of preneoplastic lesions characteristically observed in bioassays using genotoxic carcinogens are also present in control animals and animals treated with non-genotoxic carcinogens. The incidence of preneoplastic lesions was low in control animals and higher in animals treated with non-genotoxic carcinogens. The diverse classifications used in the literature did not allow a direct comparison of lesions and corresponding incidences with those of the newly generated data. However, three major tendencies were observed: (a) whenever a high incidence of preneoplastic lesions was reported, renal neoplasms were also found, (b) the larger the size and the further a lesion had progressed, the higher was the probability of tumor formation, and (c) not all preneoplastic lesions are irreversible, but reversibility seemed to decrease with increasing lesion size and progression. It must be emphasized that the data available for these conclusions are limited. This is not due to the lack of adequate numbers of bioassays with non-genotoxic carcinogens, but rather to the lack of consistent reporting of data. A generalized and more widely used classification which incorporates early lesions would certainly improve the current data base on renal lesions and provide future improvements in the predictive nature of these lesions.     

A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening

This paper presents a mathematical algorithm that computes the sizes and growth rates of breast cancer detected in a hypothetical population that is screened for the disease. The algorithm works by simulating the outcomes of the hypothetical population twice, first without screening and then with screening. The simulation without screening relies on an underlying model of the natural history of the disease. The simulation with screening uses this natural history model to track the growth of breast tumors backwards in the time starting from the time they would have been detected without screening. The method of tracking tumor growth backward in time is different from methods that track tumor growth forward in time by starting from an estimated time of tumor onset. The screening algorithm combines the natural history model, the method tracking of tumor growth backward in time, the age group, the interval between screening exams, and the detection threshold of the screening exam to compute the joint distribution of tumor size and growth rate among screen-detected and interval patients. The algorithm also computes the sensitivity and leadtime distribution. It allows for arbitrary age groups, detection thresholds and screening intervals and may contribute to the design of future screening trials.     

Fate of the initial follicle pool: empirical and mathematical evidence supporting its sufficiency for adult fertility

The importance of the initial follicle pool in fertility in female adult mammals has recently been debated. Utilizing a mathematical model of the dynamics of follicle progression (primordial to primary to secondary), we examined whether the initial follicle pool is sufficient for adult fertility through reproductive senescence in CD1 mice. Follicles in each stage were counted from postnatal day 6 through 12 months and data were fit to a series of first-order differential equations representing two mechanisms: an initial pool of primordial follicles as the only follicle source (fixed pool model), or an initial primordial follicle pool supplemented by germline stem cells (stem cell model). The fixed pool model fit the experimental data, accurately representing the maximum observed primary follicle number reached by 4-6 months of age. Although no germline stem cells could be identified by SSEA-1 immunostaining, the stem cell model was tested using a range of de novo primordial follicle production rates. The stem cell model failed to describe the observed decreases in follicles over time and did not parallel the accumulation and subsequent reduction in primary follicles during the early fertile lifespan of the mouse. Our results agree with established dogma that the initial endowment of ovarian follicles is not supplemented by an appreciable number of stem cells; rather, it is sufficient to ensure the fertility needs of the adult mouse.     

Karyometric image analysis for intraepithelial and invasive cervical lesions

OBJECTIVE: To derive an objective, numeric measure for the progression of intraepithelial and invasive squamous cell cervical lesions. STUDY DESIGN: Thin-layer cervical cytology preparations from colposcopically confirmed normal cervix, low grade squamous intraepithelial lesions, high grade squamous intraepithelial lesions and carcinoma were identified from a cross-sectional study. Fifty-nine cases representing 4 diagnostic categories were selected, and 2,375 nuclei from epithelial cells representative of the diagnostic category were randomly selected for imaging and measurement from these cases. Additionally, 1,378 visually normal appearing intermediate cells from low and high grade squamous intraepithelial lesions, as well as from carcinoma cases, were identified for analysis. The nuclei were quantitatively characterized, and discriminant analyses were performed to derive a progression curve from normal cytology to carcinoma. RESULTS: The lesion signatures show a clear increase in nuclear abnormality with increasing progression. A progression curve was derived based on mean discriminant function scores for each diagnostic category and on the mean nuclear abnormality values for the nuclei in each category, as expressed by their deviation in feature values from normal reference nuclei. CONCLUSION: A numeric assessment of lesion progression for cervical precancerous and cancerous lesions based on karyometric measurements is possible and may provide an objective, precise characterization of each lesion as well as a basis for improved performance in automated cytology-based cervical cancer screening.     

MR Imaging Evaluation of Intracerebral Hemorrhages and T2 Hyperintense White Matter Lesions Appearing after Radiation Therapy in Adult Patients with Primary Brain Tumors

The purpose of our study was to determine the frequency and severity of intracerebral hemorrhages and T2 hyperintense white matter lesions (WMLs) following radiation therapy for brain tumors in adult patients. Of 648 adult brain tumor patients who received radiation therapy at our institute, magnetic resonance (MR) image data consisting of a gradient echo (GRE) and FLAIR T2-weighted image were available three and five years after radiation therapy in 81 patients. Intracerebral hemorrhage was defined as a hypointense dot lesion appearing on GRE images after radiation therapy. The number and size of the lesions were evaluated. The T2 hyperintense WMLs observed on the FLAIR sequences were graded according to the extent of the lesion. Intracerebral hemorrhage was detected in 21 (25.9%) and 35 (43.2) patients in the three- and five-year follow-up images, respectively. The number of intracerebral hemorrhages per patient tended to increase as the follow-up period increased, whereas the size of the intracerebral hemorrhages exhibited little variation over the course of follow-up. T2 hyperintense WMLs were observed in 27 (33.3%) and 32 (39.5) patients in the three and five year follow-up images, respectively. The age at the time of radiation therapy was significantly higher (p < 0.001) in the patients with T2 hyperintense WMLs than in those without lesions. Intracerebral hemorrhages are not uncommon in adult brain tumor patients undergoing radiation therapy. The incidence and number of intracerebral hemorrhages increased over the course of follow-up. T2 hyperintense WMLs were observed in more than one-third of the study population.     

Stress amplifications in dental non-carious cervical lesions

This study aims to investigate the influence of the presence, shape and depth of NCCLs on the mechanical response of a maxillary second premolar subjected to functional and non-functional occlusal loadings using 3-D finite element (FE) analysis. A three-dimensional model of a maxillary second premolar and its supporting bone was constructed based on the contours of their cross-sections. From the sound model, cervical defects having either V- or U-shapes, as found clinically, were subtracted in three different depths. The models were loaded with 105 N to simulate normal chewing forces according to a functional occlusal loading (F1) vertically applied and two non-functional loadings (F2 and F3) obliquely oriented. Two alveolar bone crest heights were tested. Ansys™ FE software was used to compute stress distributions and maximum principal stress for each of the models. The presence of a lesion had no effect on the overall stress distribution of the system, but affected local stress concentrations. Non-functional loadings exhibited tensile stresses concentrating at the cervical areas and root surfaces, while the functional loading resulted in homogeneous stress distributions within the tooth. V-shaped lesions showed higher stress levels concentrated at the zenith of the lesion, whereas in U-shaped defect stresses concentrated over a wider area. As the lesions advanced in depth, the stress was amplified at their deepest part. A trend of stress amplification was observed with decreasing bone height. These results suggest a non-linear lesion progression with time, with the progression rate increasing with patient's age (deeper lesions and lower bone support).     

Atherosclerotic lesion progression is attenuated by reconstitution with bone marrow from macrophage-specific cholesteryl ester hydrolase transgenic mice

Accumulation of cholesteryl ester (CE)-enriched macrophage foam cells is central to the development of atherosclerotic lesions. Intracellular CE hydrolysis is the rate-limiting step in the removal of free cholesterol from macrophage foam cells. Enhancing this process by transgenic overexpression of CE hydrolase (CEH) resulted in a significant decrease in diet-induced atherosclerosis in LDL receptor-deficient (LDLR-/-) mice. However, for development of this step as an antiatherosclerotic target it is imperative to demonstrate that increase in CE hydrolysis after initiation of lesion formation will also attenuate further lesion progression. The objective of the present study was to directly address this issue using an animal model. LDLR-/- mice were fed a high-fat high-cholesterol diet (Western Diet) for 8 wk to initiate lesion formation and were then divided into three groups. Group 1 mice were killed to determine baseline lesion development. Mice in groups 2 and 3 were irradiated and transplanted with either LDLR-/- or LDLR-/-CEH transgenic bone marrow and maintained on Western Diet. Atherosclerotic lesion progression was assessed after 12 wk. While a more than fourfold increase in total lesions (compared to group 1) was seen in group 2 receiving LDLR-/- marrow, a significantly lower increase (<2-fold) was noted in mice reconstituted with CEH transgenic marrow (group 3). Lesions in group 3 mice were also more cellular with smaller necrotic cores. Lesion progression is associated with a switch in macrophage phenotype from anti-inflammatory M2 to proinflammatory M1 phenotype and is consistent with reduced lesion progression. Aortas from group 3 mice contained a significantly higher percentage of macrophages in M2 phenotype (Ly6C(lo)). These data demonstrate for the first time that enhancing macrophage CE hydrolysis even after lesion initiation can still attenuate further lesion progression and also switches the phenotype of lesion-associated macrophages to anti-inflammatory M2 phenotype establishing intracellular CE hydrolysis as an anti-atherosclerotic as well as anti-inflammatory target.