Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Response to chemotherapy, recurrence and survival in advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish BRCA mutations, compared to those without

Objectives. Previous studies have shown a survival advantage in ovarian cancer patients with Ashkenazi-Jewish (AJ) BRCA founder mutations, compared to sporadic ovarian cancer patients. The purpose of this study was to determine if this association exists in ovarian cancer patients with non-Ashkenazi Jewish BRCA mutations. In addition, we sought to account for possible "survival bias" by minimizing any lead time that may exist between diagnosis and genetic testing. ^ Methods. Patients with stage III/IV ovarian, fallopian tube, or primary peritoneal cancer and a non-Ashkenazi Jewish BRCA1 or 2 mutation, seen for genetic testing January 1996-July 2007, were identified from genetics and institutional databases. Medical records were reviewed for clinical factors, including response to initial chemotherapy. Patients with sporadic (non-hereditary) ovarian, fallopian tube, or primary peritoneal cancer, without family history of breast or ovarian cancer, were compared to similar cases, matched by age, stage, year of diagnosis, and vital status at time interval to BRCA testing. When possible, 2 sporadic patients were matched to each BRCA patient. An additional group of unmatched, sporadic ovarian, fallopian tube and primary peritoneal cancer patients was included for a separate analysis. Progression-free (PFS) & overall survival (OS) were calculated by the Kaplan-Meier method. Multivariate Cox proportional hazards models were calculated for variables of interest. Matched pairs were treated as clusters. Stratified log rank test was used to calculate survival data for matched pairs using paired event times. Fisher's exact test, chi-square, and univariate logistic regression were also used for analysis. ^ Results. Forty five advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish (non-AJ) BRCA mutations, 86 sporadic-matched and 414 sporadic-unmatched patients were analyzed. Compared to the sporadic-matched and sporadic-unmatched ovarian cancer patients, non-AJ BRCA mutation carriers had longer PFS (17.9 & 13.8 mos. vs. 32.0 mos., HR 1.76 [95% CI 1.13–2.75] & 2.61 [95% CI 1.70–4.00]). In relation to the sporadic- unmatched patients, non-AJ BRCA patients had greater odds of complete response to initial chemotherapy (OR 2.25 [95% CI 1.17–5.41]) and improved OS (37.6 mos. vs. 101.4 mos., HR 2.64 [95% CI 1.49–4.67]). ^ Conclusions. This study demonstrates a significant survival advantage in advanced-stage ovarian cancer patients with non-AJ BRCA mutations, confirming the previous studies in the Jewish population. Our efforts to account for "survival bias," by matching, will continue with collaborative studies. ^

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

BEST SUBSET SELECTION FOR CATEGORICAL DATA

When choosing among models to describe categorical data, the necessity to consider interactions makes selection more difficult. With just four variables, considering all interactions, there are 166 different hierarchical models and many more non-hierarchical models. Two procedures have been developed for categorical data which will produce the "best" subset or subsets of each model size where size refers to the number of effects in the model. Both procedures are patterned after the Leaps and Bounds approach used by Furnival and Wilson for continuous data and do not generally require fitting all models. For hierarchical models, likelihood ratio statistics (G('2)) are computed using iterative proportional fitting and "best" is determined by comparing, among models with the same number of effects, the Pr((chi)(,k)('2) (GREATERTHEQ) G(,ij)('2)) where k is the degrees of freedom for ith model of size j. To fit non-hierarchical as well as hierarchical models, a weighted least squares procedure has been developed.^ The procedures are applied to published occupational data relating to the occurrence of byssinosis. These results are compared to previously published analyses of the same data. Also, the procedures are applied to published data on symptoms in psychiatric patients and again compared to previously published analyses.^ These procedures will make categorical data analysis more accessible to researchers who are not statisticians. The procedures should also encourage more complex exploratory analyses of epidemiologic data and contribute to the development of new hypotheses for study. ^

Genetic variation in genes for the xenobiotic-metabolizing enzymes CYP1A1, EPHX1, GSTM1, GSTT1, and GSTP1 and susceptibility to colorectal cancer in Lynch syndrome.

Individuals with Lynch syndrome are predisposed to cancer due to an inherited DNA mismatch repair gene mutation. However, there is significant variability observed in disease expression likely due to the influence of other environmental, lifestyle, or genetic factors. Polymorphisms in genes encoding xenobiotic-metabolizing enzymes may modify cancer risk by influencing the metabolism and clearance of potential carcinogens from the body. In this retrospective analysis, we examined key candidate gene polymorphisms in CYP1A1, EPHX1, GSTT1, GSTM1, and GSTP1 as modifiers of age at onset of colorectal cancer among 257 individuals with Lynch syndrome. We found that subjects heterozygous for CYP1A1 I462V (c.1384A>G) developed colorectal cancer 4 years earlier than those with the homozygous wild-type genotype (median ages, 39 and 43 years, respectively; log-rank test P = 0.018). Furthermore, being heterozygous for the CYP1A1 polymorphisms, I462V and Msp1 (g.6235T>C), was associated with an increased risk for developing colorectal cancer [adjusted hazard ratio for AG relative to AA, 1.78; 95% confidence interval, 1.16-2.74; P = 0.008; hazard ratio for TC relative to TT, 1.53; 95% confidence interval, 1.06-2.22; P = 0.02]. Because homozygous variants for both CYP1A1 polymorphisms were rare, risk estimates were imprecise. None of the other gene polymorphisms examined were associated with an earlier onset age for colorectal cancer. Our results suggest that the I462V and Msp1 polymorphisms in CYP1A1 may be an additional susceptibility factor for disease expression in Lynch syndrome because they modify the age of colorectal cancer onset by up to 4 years.

A loss-of-function variant of PTPN22 is associated with reduced risk of systemic lupus erythematosus.

A gain-of-function R620W polymorphism in the PTPN22 gene, encoding the lymphoid tyrosine phosphatase LYP, has recently emerged as an important risk factor for human autoimmunity. Here we report that another missense substitution (R263Q) within the catalytic domain of LYP leads to reduced phosphatase activity. High-resolution structural analysis revealed the molecular basis for this loss of function. Furthermore, the Q263 variant conferred protection against human systemic lupus erythematosus, reinforcing the proposal that inhibition of LYP activity could be beneficial in human autoimmunity.

Insights into transcription enhancer factor 1 (TEF-1) activity from the solution structure of the TEA domain.

Transcription enhancer factor 1 is essential for cardiac, skeletal, and smooth muscle development and uses its N-terminal TEA domain (TEAD) to bind M-CAT elements. Here, we present the first structure of TEAD and show that it is a three-helix bundle with a homeodomain fold. Structural data reveal how TEAD binds DNA. Using structure-function correlations, we find that the L1 loop is essential for cooperative loading of TEAD molecules on to tandemly duplicated M-CAT sites. Furthermore, using a microarray chip-based assay, we establish that known binding sites of the full-length protein are only a subset of DNA elements recognized by TEAD. Our results provide a model for understanding the regulation of genome-wide gene expression during development by TEA/ATTS family of transcription factors.

Crystal structure of the Anabaena sensory rhodopsin transducer.

We present crystal structures of the Anabaena sensory rhodopsin transducer (ASRT), a soluble cytoplasmic protein that interacts with the first structurally characterized eubacterial retinylidene photoreceptor Anabaena sensory rhodopsin (ASR). Four crystal structures of ASRT from three different spacegroups were obtained, in all of which ASRT is present as a planar (C4) tetramer, consistent with our characterization of ASRT as a tetramer in solution. The ASRT tetramer is tightly packed, with large interfaces where the well-structured beta-sandwich portion of the monomers provides the bulk of the tetramer-forming interactions, and forms a flat, stable surface on one side of the tetramer (the beta-face). Only one of our four different ASRT crystals reveals a C-terminal alpha-helix in the otherwise all-beta protein, together with a large loop from each monomer on the opposite face of the tetramer (the alpha-face), which is flexible and largely disordered in the other three crystal forms. Gel-filtration chromatography demonstrated that ASRT forms stable tetramers in solution and isothermal microcalorimetry showed that the ASRT tetramer binds to ASR with a stoichiometry of one ASRT tetramer per one ASR photoreceptor with a K(d) of 8 microM in the highest affinity measurements. Possible mechanisms for the interaction of this transducer tetramer with the ASR photoreceptor via its flexible alpha-face to mediate transduction of the light signal are discussed.

NMR structure of a complex between the VirB9/VirB7 interaction domains of the pKM101 type IV secretion system.

Type IV secretion (T4S) systems translocate DNA and protein effectors through the double membrane of Gram-negative bacteria. The paradigmatic T4S system in Agrobacterium tumefaciens is assembled from 11 VirB subunits and VirD4. Two subunits, VirB9 and VirB7, form an important stabilizing complex in the outer membrane. We describe here the NMR structure of a complex between the C-terminal domain of the VirB9 homolog TraO (TraO(CT)), bound to VirB7-like TraN from plasmid pKM101. TraO(CT) forms a beta-sandwich around which TraN winds. Structure-based mutations in VirB7 and VirB9 of A. tumefaciens show that the heterodimer interface is conserved. Opposite this interface, the TraO structure shows a protruding three-stranded beta-appendage, and here, we supply evidence that the corresponding region of VirB9 of A. tumefaciens inserts in the membrane and protrudes extracellularly. This complex structure elucidates the molecular basis for the interaction between two essential components of a T4S system.

High-resolution microarray analysis of chromosome 20q in human colon cancer metastasis model systems

Amplification of human chromosome 20q DNA is the most frequently occurring chromosomal abnormality detected in sporadic colorectal carcinomas and shows significant correlation with liver metastases. Through comprehensive high-resolution microarray comparative genomic hybridization and microarray gene expression profiling, we have characterized chromosome 20q amplicon genes associated with human colorectal cancer metastasis in two in vitro metastasis model systems. The results revealed increasing complexity of the 20q genomic profile from the primary tumor-derived cell lines to the lymph node and liver metastasis derived cell lines. Expression analysis of chromosome 20q revealed a subset of over expressed genes residing within the regions of genomic copy number gain in all the tumor cell lines, suggesting these are Chromosome 20q copy number responsive genes. Bases on their preferential expression levels in the model system cell lines and known biological function, four of the over expressed genes mapping to the common intervals of genomic copy gain were considered the most promising candidate colorectal metastasis-associated genes. Validation of genomic copy number and expression array data was carried out on these genes, with one gene, DNMT3B, standing out as expressed at a relatively higher levels in the metastasis-derived cell lines compared with their primary-derived counterparts in both the models systems analyzed. The data provide evidence for the role of chromosome 20q genes with low copy gain and elevated expression in the clonal evolution of metastatic cells and suggests that such genes may serve as early biomarkers of metastatic potential. The data also support the utility of the combined microarray comparative genomic hybridization and expression array analysis for identifying copy number responsive genes in areas of low DNA copy gain in cancer cells. ^

Using small area estimation and geographic information systems technology to target health services for the uninsured

The three articles that comprise this dissertation describe how small area estimation and geographic information systems (GIS) technologies can be integrated to provide useful information about the number of uninsured and where they are located. Comprehensive data about the numbers and characteristics of the uninsured are typically only available from surveys. Utilization and administrative data are poor proxies from which to develop this information. Those who cannot access services are unlikely to be fully captured, either by health care provider utilization data or by state and local administrative data. In the absence of direct measures, a well-developed estimation of the local uninsured count or rate can prove valuable when assessing the unmet health service needs of this population. However, the fact that these are “estimates” increases the chances that results will be rejected or, at best, treated with suspicion. The visual impact and spatial analysis capabilities afforded by geographic information systems (GIS) technology can strengthen the likelihood of acceptance of area estimates by those most likely to benefit from the information, including health planners and policy makers. ^ The first article describes how uninsured estimates are currently being performed in the Houston metropolitan region. It details the synthetic model used to calculate numbers and percentages of uninsured, and how the resulting estimates are integrated into a GIS. The second article compares the estimation method of the first article with one currently used by the Texas State Data Center to estimate numbers of uninsured for all Texas counties. Estimates are developed for census tracts in Harris County, using both models with the same data sets. The results are statistically compared. The third article describes a new, revised synthetic method that is being tested to provide uninsured estimates at sub-county levels for eight counties in the Houston metropolitan area. It is being designed to replicate the same categorical results provided by a current U.S. Census Bureau estimation method. The estimates calculated by this revised model are compared to the most recent U.S. Census Bureau estimates, using the same areas and population categories. ^

Distribution of quality adjusted life expectancy: A systems approach

Statistical methods are developed which assess survival data for two attributes; (1) prolongation of life, (2) quality of life. Health state transition probabilities correspond to prolongation of life and are modeled as a discrete-time semi-Markov process. Imbedded within the sojourn time of a particular health state are the quality of life transitions. They reflect events which differentiate perceptions of pain and suffering over a fixed time period. Quality of life transition probabilities are derived from the assumptions of a simple Markov process. These probabilities depend on the health state currently occupied and the next health state to which a transition is made. Utilizing the two forms of attributes the model has the capability to estimate the distribution of expected quality adjusted life years (in addition to the distribution of expected survival times). The expected quality of life can also be estimated within the health state sojourn time making more flexible the assessment of utility preferences. The methods are demonstrated on a subset of follow-up data from the Beta Blocker Heart Attack Trial (BHAT). This model contains the structure necessary to make inferences when assessing a general survival problem with a two dimensional outcome. ^