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. ^

Molecular evolution of primate immunodeficiency viruses and hepatitis delta virus

Primate immunodeficiency viruses, or lentiviruses (HIV-1, HIV-2, and SIV), and hepatitis delta virus (HDV) are RNA viruses characterized by rapid evolution. Infection by primate immunodeficiency viruses usually results in the development of acquired immunodeficiency syndrome (AIDS) in humans and AIDS-like illnesses in Asian macaques. Similarly, hepatitis delta virus infection causes hepatitis and liver cancer in humans. These viruses are heterogeneous within an infected patient and among individuals. Substitution rates in the virus genomes are high and vary in different lineages and among sites. Methods of phylogenetic analysis were applied to study the evolution of primate lentiviruses and the hepatitis delta virus. The following results have been obtained: (1) The substitution rate varies among sites of primate lentivirus genes according to the two parameter gamma distribution, with the shape parameter $\alpha$ being close to 1. (2) Primate immunodeficiency viruses fall into species-specific lineages. Therefore, viral transmissions across primate species are not as frequent as suggested by previous authors. (3) Primate lentiviruses have acquired or lost their pathogenicity several times in the course of evolution. (4) Evidence was provided for multiple infections of a North American patient by distinct HIV-1 strains of the B subtype. (5) Computer simulations indicate that the probability of committing an error in testing HIV transmission depends on the number of virus sequences and their length, the divergence times among sequences, and the model of nucleotide substitution. (6) For future investigations of HIV-1 transmissions, using longer virus sequences and avoiding the use of distant outgroups is recommended. (7) Hepatitis delta virus strains are usually related according to the geographic region of isolation. (8) Evolution of HDV is characterized by the rate of synonymous substitution being lower than the nonsynonymous substitution rate and the rate of evolution of the noncoding region. (9) There is a strong preference for G and C nucleotides at the third codon positions of the HDV coding region. ^

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. ^

Clinical and economic outcomes of serious postoperative infections following resection of common respiratory and gastrointestinal solid tumors

Unlike infections occurring during periods of chemotherapy-induced neutropenia, postoperative infections in patients with solid malignancy remain largely understudied. The purpose of this population-based study was to evaluate the clinical and economic burden, as well as the relationship of hospital surgical volume and outcomes associated with serious postoperative infection (SPI) – i.e., bacteremia/sepsis, pneumonia, and wound infection – following resection of common solid tumors.^ From the Texas Discharge Data Research File, we identified all Texas residents who underwent resection of cancer of the lung, esophagus, stomach, pancreas, colon, or rectum between 2002 and 2006. From their billing records, we identified ICD-9 codes indicating SPI and also subsequent SPI-related readmissions occurring within 30 days of surgery. Random-effects logistic regression was used to calculate the impact of SPI on mortality, as well as the association between surgical volume and SPI, adjusting for case-mix, hospital characteristics, and clustering of multiple surgical admissions within the same patient and patients within the same hospital. Excess bed days and costs were calculated by subtracting values for patients without infections from those with infections computed using multilevel mixed-effects generalized linear model by fitting a gamma distribution to the data using log link.^ Serious postoperative infection occurred following 9.4% of the 37,582 eligible tumor resections and was independently associated with an 11-fold increase in the odds of in-hospital mortality (95% Confidence Interval [95% CI], 6.7-18.5, P < 0.001). Patients with SPI required 6.3 additional hospital days (95% CI, 6.1 - 6.5) at an incremental cost of $16,396 (95% CI, $15,927–$16,875). There was a significant trend toward lower overall rates of SPI with higher surgical volume (P=0.037). ^ Due to the substantial morbidity, mortality, and excess costs associated with SPI following solid tumor resections and given that, under current reimbursement practices, most of this heavy burden is borne by acute care providers, it is imperative for hospitals to identify more effective prophylactic measures, so that these potentially preventable infections and their associated expenditures can be averted. Additional volume-outcomes research is also needed to identify infection prevention processes that can be transferred from higher- to lower-volume providers.^