Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

Outcomes associated with chemotherapy in elderly patients with early stage operable breast cancer

Background. Various clinical trials have proved the efficacy of adjuvant chemotherapy in women with breast cancer. Chemotherapy efficacy and guidelines for its use differ by stage of tumor and age of the patient with no clear recommendations for patients aged 70 and above. Objective. To examine the clinical and economic outcomes associated with chemotherapy use in and to examine the disparities in treatment and survival in elderly patients with early stage operable breast cancer by age and axillary node status. Methods. We studied a cohort of 23,110 node positive and 31,572 node negative women aged 65 and over diagnosed with incident American Joint Committee on Cancer (AJCC) stage I, II or IIIa breast cancer between January 1, 1991 and December 31, 2002 using SEER-Medicare data. Total patient costs were estimated using the phase of care approach and adjusted cost estimates were obtained from regression analysis using a 3% discount rate. Cox proportional hazard ratio of mortality was used to determine the effectiveness of chemotherapy. Propensity score approach was also used to minimize the bias associated with receipt of chemotherapy. To assess disparity in treatment, multivariate logistic regression analyses were performed to assess the relative odds of receiving surgery, chemotherapy and radiation after BCS for African Americans compared to Whites. Results. Regression adjusted cost estimates for all node positive patients receiving chemotherapy was approximately $2,300 and was significantly higher (p<0.05) than for patients not receiving chemotherapy. Mortality was significantly lower in node positive and node negative women aged 65-74 years receiving chemotherapy. There was a significant difference between African American and White women in receiving BCS and radiation after BCS; however this difference was explained by patient demographics, tumor characteristics and socioeconomic status (SES). African American node positive women were 21% less likely to receive chemotherapy than White women (OR, 0.79; CI, 0.68-0.92) in multivariate analysis. Conclusion. Chemotherapy is associated with increased survival in patients aged 65-74 and total costs attributable to chemotherapy differ by phase and age of the patient. Underutilization of systemic adjuvant chemotherapy in African American women requires attention and may serve as potential areas for appropriate intervention.^