Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^

Prognosis of amyotrophic lateral sclerosis

Two cohorts of amyotrophic lateral sclerosis (ALS) patients were identified. One incidence-based cohort from Harris County, Texas with 97 cases, and the other a clinic referral series from an ALS clinic in Houston, Texas with 439 cases were followed-up to evaluate the prognosis of ALS. The overall Kaplan-Meier 3-year survival after diagnosis was similar, 0.287 for the incidence cohort and 0.313 for the referral cohort. However, the 5-year survival was much lower for the incidence cohort than the referral cohort (0.037 vs. 0.206). The large difference in 5-year survival was thought to be the results of a stronger unfavorable effect of the prognostic factors in the incidence cohort than in the referral cohort.^ Cohort-specific Weibull regression models were derived to evaluate the cohort-specific prognostic factors and survival probability with adjustment of certain prognostic factors.^ The major prognostic factors were: age at diagnosis, bulbar onset, black ethnicity, and positive family history of ALS in both cohorts. Female gender, simultaneous upper and lower extremities onset were specifically unfavorable factors in the incidence cohort. In the incidence cohort the prognosis was relatively favorable for cases with duration from onset to diagnosis longer than 4 months, however in the referral cohort the relatively favorable prognosis only occurred in cases with duration from onset to diagnosis 1 year or longer and was strongest in cases with duration 5 years and longer. Age at diagnosis modified the effect of bulbar onset in the incidence cohort but not in the referral cohort. The estimated survival with presence of an unfavorable prognostic factor identified in the incidence cohort was higher for the referral cohort than for the incidence cohort. Future studies are indicated to investigate the disease heterogeneity issue of ALS based on survival distribution of ALS. ^

The impact of functional impairment on the survival of patients with Alzheimer's disease

Alzheimer's disease (AD), the most common form of dementia, is the fifth leading cause of death among U.S. adults aged 65 or older. Most AD patients have shorter life expectancy compared with older people without dementia. This disease has become an enormous challenge in the aging society and is also a global problem. Not only do families of patients with Alzheimer's disease need to pay attention to this problem, but also the healthcare system and society as a whole have to confront. In dementia, functional impairment is associated with basic activities of daily living (ADL) and instrumental activities of daily living (IADL). For patients with Alzheimer's disease, problems typically appear in performing IADL and progress to the inability of managing less complex ADL functions of personal care. Thus, assessment of ADLs can be used for early accurate diagnosis of Alzheimer's disease. It should be useful for patients, caregivers, clinicians, and policy planners to estimate the survival of patients with Alzheimer's disease. However, it is unclear that when making predictions of patient outcome according to their histories, time-dependent covariates will provide us with important information on how changes in a patient's status can effect the survival. In this study, we examined the effect of impaired basic ADL as measured by the Physical Self-Maintenance Scale (PSMS) and utilized a multistate survival analysis approach to estimate the probability of death in the first few years of initial visit for AD patients taking into consideration the possibility of impaired basic ADL. The dataset used in this study was obtained from the Baylor Alzheimer's Disease and Memory Disorders Center (ADMDC). No impaired basic ADL and older age at onset of impaired basic ADL were associated with longer survival. These findings suggest that the occurrence of impaired basic ADL and age at impaired basic ADL could be predictors of survival among patients with Alzheimer's disease. ^

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.^

The risk prediction for SPM and its impact on the survival in patients with head and neck squamous cell carcinoma

Head and Neck Squamous Cell Carcinoma (HNSCC) is the sixth common malignancy in the world, with high rates of developing second primary malignancy (SPM) and moderately low survival rates. This disease has become an enormous challenge in the cancer research and treatments. For HNSCC patients, a highly significant cause of post-treatment mortality and morbidity is the development of SPM. Hence, assessment of predicting the risk for the development of SPM would be very helpful for patients, clinicians and policy makers to estimate the survival of patients with HNSCC. In this study, we built a prognostic model to predict the risk of developing SPM in patients with newly diagnosed HNSCC. The dataset used in this research was obtained from The University of Texas MD Anderson Cancer Center. For the first aim, we used stepwise logistic regression to identify the prognostic factors for the development of SPM. Our final model contained cancer site and overall cancer stage as our risk factors for SPM. The Hosmer-Lemeshow test (p-value= 0.15>0.05) showed the final prognostic model fit the data well. The area under the ROC curve was 0.72 that suggested the discrimination ability of our model was acceptable. The internal validation confirmed the prognostic model was a good fit and the final prognostic model would not over optimistically predict the risk of SPM. This model needs external validation by using large data sample size before it can be generalized to predict SPM risk for other HNSCC patients. For the second aim, we utilized a multistate survival analysis approach to estimate the probability of death for HNSCC patients taking into consideration of the possibility of SPM. Patients without SPM were associated with longer survival. These findings suggest that the development of SPM could be a predictor of survival rates among the patients with HNSCC.^