SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^

Health-related quality of life and survival in liver transplant candidates.

Health-related quality of life (HRQOL) is an important measure of the effects of chronic liver disease in affected patients that helps guide interventions to improve well-being. However, the relationship between HRQOL and survival in liver transplant candidates remains unclear. We examined whether the Physical Component Summary (PCS) and Mental Component Summary (MCS) scores from the Short Form 36 (SF-36) Health Survey were associated with survival in liver transplant candidates. We administered the SF-36 questionnaire (version 2.0) to patients in the Pulmonary Vascular Complications of Liver Disease study, a multicenter prospective cohort of patients evaluated for liver transplantation in 7 academic centers in the United States between 2003 and 2006. Cox proportional hazards models were used with death as the primary outcome and adjustment for liver transplantation as a time-varying covariate. The mean age of the 252 participants was 54 +/- 10 years, 64% were male, and 94% were white. During the 422 person years of follow-up, 147 patients (58%) were listed, 75 patients (30%) underwent transplantation, 49 patients (19%) died, and 3 patients were lost to follow-up. Lower baseline PCS scores were associated with an increased mortality rate despite adjustments for age, gender, Model for End-Stage Liver Disease score, and liver transplantation (P for the trend = 0.0001). The MCS score was not associated with mortality (P for the trend = 0.53). In conclusion, PCS significantly predicts survival in liver transplant candidates, and interventions directed toward improving the physical status may be helpful in improving outcomes in liver transplant candidates.

Improving the accuracy of radiation pneumonitis dose response models

The prognosis for lung cancer patients remains poor. Five year survival rates have been reported to be 15%. Studies have shown that dose escalation to the tumor can lead to better local control and subsequently better overall survival. However, dose to lung tumor is limited by normal tissue toxicity. The most prevalent thoracic toxicity is radiation pneumonitis. In order to determine a safe dose that can be delivered to the healthy lung, researchers have turned to mathematical models predicting the rate of radiation pneumonitis. However, these models rely on simple metrics based on the dose-volume histogram and are not yet accurate enough to be used for dose escalation trials. The purpose of this work was to improve the fit of predictive risk models for radiation pneumonitis and to show the dosimetric benefit of using the models to guide patient treatment planning. The study was divided into 3 specific aims. The first two specifics aims were focused on improving the fit of the predictive model. In Specific Aim 1 we incorporated information about the spatial location of the lung dose distribution into a predictive model. In Specific Aim 2 we incorporated ventilation-based functional information into a predictive pneumonitis model. In the third specific aim a proof of principle virtual simulation was performed where a model-determined limit was used to scale the prescription dose. The data showed that for our patient cohort, the fit of the model to the data was not improved by incorporating spatial information. Although we were not able to achieve a significant improvement in model fit using pre-treatment ventilation, we show some promising results indicating that ventilation imaging can provide useful information about lung function in lung cancer patients. The virtual simulation trial demonstrated that using a personalized lung dose limit derived from a predictive model will result in a different prescription than what was achieved with the clinically used plan; thus demonstrating the utility of a normal tissue toxicity model in personalizing the prescription dose.

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. ^

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. ^

A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Impact of hormonal therapy on survival and racial disparities in a large community-based cohort of older men with local/regional prostate cancer

Prostate cancer (CaP) is the most diagnosed non-cutaneous malignancy and the second leading cause of cancer mortality among United States males. Major racial disparities in incidence, survival, as well as treatment persist. The mortality is three times higher among African Americans (AAs) compared with Caucasians. Androgen carcinogenesis has been persistently implicated but results are inconsistent; and hormone manipulation has been the main stay of treatment for metastatic disease, supportive of the androgen carcinogenesis. The survival disadvantage of AAs has been attributed to the differences in socioeconomic factors (SES), tumor stage, and treatment. We hypostasized that HT prolongs survival in CaP and that the racial disparities in survival is influenced by variation in HT and primary therapies as well as SES. To address these overall hypothesis, we first utilized a random-effect meta-analytic design to examine evidence from randomized trials on the efficacy of androgen deprivation therapy in localized and metastatic disease, and assessed, using Cox proportional hazards models, the effectiveness of HT in prolonging survival in a large community-based cohort of older males diagnosed with local/regional CaP. Further we examined the role of HT and primary therapies on the racial disparities in CaP survival. The results indicated that adjuvant HT compared with standard care alone is efficacious in improving overall survival, whereas HT has no significant benefit in the real world experience in increasing the overall survival of older males in the community treated for local/regional disease. Further, racial differences in survival persist and were explained to some extent by the differences in the primary therapies (radical prostatectomy, radiation and watchful waiting) and largely by SES. Therefore, given the increased used of hormonal therapy and the cost-effectiveness today, more RCTs are needed to assess whether or not survival prolongation translates to improved quality of life, and to answer the research question on whether or not the decreased use of radical prostatectomy by AAs is driven by the Clinicians bias or AAs's preference of conservative therapy and to encourage AAs to seek curative therapies, thus narrowing to some degree the persistent mortality disparities between AAs and Caucasians. ^

The role of cardiovascular comorbidities in ovarian cancer survival

Objective. One facet of cancer care that often goes ignored is comorbidities, or diseases that exist in concert with cancer. Comorbid conditions may affect survival by influencing treatment decisions and prognosis. The purpose of this secondary data analysis was to identify whether a history of cardiovascular comorbidities among ovarian cancer patients influenced survival time at the University of Texas M. D. Anderson Cancer Center. The parent study, Project Peace, has a longitudinal design with an embedded randomized efficacy study which seeks to improve detection of depressive disorders in ovarian, peritoneal, and fallopian tube cancers. ^ Methods. Survival time was calculated for the 249 ovarian cancer patients abstracted by Project Peace staff. Cardiovascular comorbidities were documented as present, based upon information from medical records in addition to self reported comorbidities in a baseline study questionnaire. Kaplan-Meier survival curves were used to compare survival time among patients with a presence or absence of particular cardiovascular comorbidities. Cox Regression proportional models accounted for multivariable factors such as age, staging, family history of cardiovascular comorbidities, and treatment. ^ Results. Among our patient population, there was a statistically significant relationship between shorter survival time and a history of thrombosis, pericardial disease/tamponade, or COPD/pulmonary hypertension. Ovarian cancer patients with a history of thrombosis lived approximately half as long as patients without thrombosis (58.06 months vs. 121.55 months; p=.001). In addition, patients who suffered from pericardial disease/tamponade had poorer survival than those without a history of pericardial disease/tamponade (48 months vs. 80.07 months; p=.002). Ovarian cancer patients with a history of COPD or pulmonary hypertension had a median survival of 60.2 months, while the median survival for patients without these comorbidities was 80.2 months (p=.014). ^ Conclusion. Especially because of its relatively lower survival rate, greater emphasis needs to be placed on the potential influence of cardiovascular comorbid conditions in ovarian cancer.^

Assessing the improved discriminatory power of a new biomarker in prognostic models

Although the area under the receiver operating characteristic (AUC) is the most popular measure of the performance of prediction models, it has limitations, especially when it is used to evaluate the added discrimination of a new biomarker in the model. Pencina et al. (2008) proposed two indices, the net reclassification improvement (NRI) and integrated discrimination improvement (IDI), to supplement the improvement in the AUC (IAUC). Their NRI and IDI are based on binary outcomes in case-control settings, which do not involve time-to-event outcome. However, many disease outcomes are time-dependent and the onset time can be censored. Measuring discrimination potential of a prognostic marker without considering time to event can lead to biased estimates. In this dissertation, we have extended the NRI and IDI to survival analysis settings and derived the corresponding sample estimators and asymptotic tests. Simulation studies were conducted to compare the performance of the time-dependent NRI and IDI with Pencina’s NRI and IDI. For illustration, we have applied the proposed method to a breast cancer study.^ Key words: Prognostic model, Discrimination, Time-dependent NRI and IDI ^

Estrogen-induced gene expression and patient survival in high-grade serous carcinoma of the ovary

Background. Assessment of estrogen receptor (ER) expression has inconsistent utility as a prognostic marker in epithelial ovarian carcinoma. In breast and endometrial cancers, the use of estrogen-induced gene panels, rather than ER expression alone, has shown improved prognostic capability. Specifically, over-expression of estrogen-induced genes in these tumors is associated with a better prognosis and signifies estrogen sensitivity that can be exploited with hormone antagonizing agents. It was therefore hypothesized that estrogen-induced gene expression in ovarian carcinoma would successfully predict outcomes and differentiate between tumors of varying estrogen sensitivities. Methods. Two hundred nineteen (219) patients with ovarian cancer who underwent surgery at M. D. Anderson between 2004 and 2007 were identified. Of these, eighty-three (83) patients were selected for inclusion because they had advanced stage, high-grade serous carcinoma of the ovary or peritoneum, had not received neoadjuvant chemotherapy, and had readily available frozen tissue for study. All patients had also received adjuvant treatment with platinum and taxane agents. The expression of seven genes known to be induced by estrogen in the female reproductive tract (EIG121, sFRP1, sFRP4, RALDH2, PR, IGF-1, and ER) was measured using qRT-PCR. Unsupervised cluster analyses of multiple gene permutations were used to categorize patients as high or low estrogen-induced gene expressors. QPCR gene expression results were then compared to ER and PR immunohistochemical (IHC) expression. Cox proportional hazards models were used to evaluate the effects of both individual genes and selected gene clusters on patient survival. Results. Median follow-up time was 38.7 months (range 1-68 months). In a multivariate model, overall survival was predicted by sFRP1 expression (HR 1.10 [1.02-1.19], p=0.01) and EIG121 expression (HR 1.28 [1.10-1.49], p<0.01). A cluster defined by EIG121 and ER was further examined because that combination appeared to reasonably segregate tumors into distinct groups of high and low estrogen-induced gene expressors. Shorter overall survival was associated with high estrogen-induced gene expressors (HR 2.84 [1.11-7.30], p=0.03), even after adjustment for race, age, body mass index, and residual disease at debulking. No difference in IHC ER or PR expression was noted between gene clusters. Conclusion. In sharp contrast to breast and endometrial cancers, high estrogen-induced gene expression predicts shorter overall survival in patients with high-grade serous ovarian carcinoma. An estrogen-induced gene biomarker panel may have utility as prognostic indicator and may be useful to guide management with estrogen antagonists in this population.^

BIOLOGICAL MECHANISMS AND CLINICAL IMPLICATIONS OF BCR-ABL-INDUCED MITOCHONDRIAL OXIDATIVE STRESS AND CELL SURVIVAL IN CHRONIC MYELOID LEUKEMIA

Chronic myeloid leukemia (CML), a myeloproliferative disorder, represents approximately 15-20% of all adult leukemia. The development of CML is clearly linked to the constitutively active protein-tyrosine kinase BCR-ABL, which is encoded by BCR-ABL fusion gene as the result of chromosome 9/22 translocation (Philadelphia chromosome). Previous studies have demonstrated that oxidative stress-associated genetic, metabolic and biological alterations contribute to CML cell survival and drug refractory. Mitochondria and NAD(P)H oxidase (NOX) are the major sources of BCR-ABL-induced cellular reactive oxygen species (ROS) production. However, it is still unknown how CML cells maintain the altered redox status, while escaping from the persistent oxidative stress-induced cell death. Therefore, elucidation of the mechanisms by which CML cells cope with oxidative stress will provide new insights into CML leukemogenesis. The major goal of this study is to identify the survival factors protecting CML cells against oxidative stress and develop novel therapeutic strategies to overcome drug resistance. Several experimental models were used to test CML cell redox status and cellular sensitivity to oxidative stress, including BCR-ABL inducible cell lines, BCR-ABL stably transformed cell lines and BCR-ABL-expressing CML blast crisis cells with differential BCL-XL/BCL-2 expressions. Additionally, an artificial CML cell model with heterogenic BCL-XL/BCL-2 expression was established to assess the correlation between differential survival factor expression patterns and cell sensitivity to Imatinib and oxidative stress. In this study, BCL-XL and GSH have been identified as the major survival factors responsive to BCR-ABL-promoted cellular oxidative stress and play a dominant role in regulating the threshold of oxidative stress-induced apoptosis. Cell survival factors BCL-XL and BCL-2 differentially protect mitochondria under oxidative stress. BCL-XL is an essential survival factor in preventing excessive ROS-induced cell death while BCL-2 seems to play a relatively minor role. Furthermore, the redox modulating reagent β-phenethyl isothiocyanate (PEITC) has been found to efficiently deplete GSH and induce potent cell killing effects in drug-resistant CML cells. Combination of PEITC with BCL-XL/BCL2 inhibitor ABT737 or suppression of BCL-XL by BCR-ABL inhibitor Gleevec dramatically sensitizes CML cells to apoptosis. These results have suggested that elevation of BCL-XL and cellular GSH are important for the development of CML, and that redox-directed therapy is worthy of further clinical investigations in CML.

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. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^