Cell Cycle Regulatory Roles of Estrogen Receptor alpha (ERα) in Breast Cancer Cells

Previous studies have shown that Estrogen Receptor alpha (ERα) is an important indicator for diagnosis, prognosis and treatment of breast cancers. However, the question remains as to the role of ERα in the cell in the presence versus absence of 17-β estradiol In this dissertation the role of ERα in both its unliganded and liganded state, with respect to the cell cycle will be explored. The cell line models used in this project are ER-positive MCF-7 cells with and without siRNA to ERα and ER-positive MDA-MB-231 cells that have been engineered to express ERα. Cells were synchronized and the cell cycle progression was monitored by flow cytometric analysis. Using these methods, two specific questions were addressed: Does ERα modulate the cell cycle differently under liganded versus unliganded conditions? And, does the presence of ERα regulate cell cycle phase transitions? The results show for the first time that ERα is cell cycle regulated and modulates the progression of cells through S and G2/M phases of the cell cycle. Ligand bound ERα increases progression through S and G2/M phases, whereas unliganded ERα acts as an inhibitor of cell cycle progression. To further investigate the cell cycle regulated effects of liganded ERα, a luciferase assay was performed and showed that the transcription of target genes such as Progestrone Receptor (PgR) and Trefoil protein (pS2) increased duing S and G2/M phases when ERα is bound to ligand. Additionally, complex formation between cyclin B and ER α was shown by immunoprecipitation and led to the discovery that anaphase promoting complex (APC) is the E3 ligase for both cyclin B and ERα at the termination of M phase. Our findings suggest that unliganded ERα has an inhibitory effect on the progression of the cell cycle. Therefore, it is reasonable to speculate that the combination of drugs that lower estrogen level (such as aromatase inhibitors) and preserves ERα from degradation would provide better outcome for breast cancer treatment. We have shown that APC functions as the E3 ligase for ERα and thus might provide a target to design a specific inhibitor of ERα degradation.

The Role Of IL-8-Mediated Src Family Kinase Activation In Tumor-Tumor And Tumor-Stromal Interactions In Metastasis Of Prostate Cancer

Men with localized prostate cancer (PCa) have a 100% five-year survival rate, but this rate drops to 33% for men with metastatic disease. A better understanding of the metastatic process is needed to develop better therapies for PCa. Aberrant activation of protein tyrosine kinases, including Src Family Kinases (SFKs) contribute to metastasis through numerous functions, one of which leads to increased expression of cytokines, such as IL-8. However, the relationship between Src activity and IL-8 regulation is not completely understood. In cell line models, I determined that IL-8 activates Src and in turn Src activates IL-8 demonstrating a feed forward loop contributing to the migration and invasion of PCa cells. However, IL-8 is also produced by tumor-associated stromal cells. In bone marrow derived stromal cells (HS5), I demonstrated a feed forward loop occurs as was observed in tumor cells. HS5 conditioned media increased Src activity in PCa cells. By silencing IL-8 in HS5 cells, Src activity was decreased to control levels in PCa cells as was migration and invasion. Thus, stromal cells producing IL-8 contribute to metastatic properties of PCa by a paracrine mechanism. To examine the effect of stromal cells on tumor growth and metastatic potential of PCa in vivo, I mixed HS5 and PCa cells and co-injected them intraprostatically. I determined that tumor growth and metastases were increased. By silencing IL-8 in HS5 cells and co-injecting them with PCa cells intraprostatically, tumor growth and metastases were still increased relative to injection of PCa cells alone, but decreased relative to co-injections with PCa cells and HS5 cells. These studies demonstrated: (1) a feed forward loop in both tumor and stromal cells, whereby IL-8 activates Src, derepressing IL-8 expression in PCa cells in vitro; (2) stromal produced IL-8 activates Src and contributes to the migration and invasion of PCa cells in vitro; and (3) stromal produced IL-8 is responsible, in part, for increases in PCa tumor growth and metastatic potential. Together, these studies demonstrated that IL-8-mediated Src activity increases the metastatic potential of PCa and therapeutic agents interfering with the IL-8/SFK signaling axis may be useful for prevention and treatment of metastases.

Osteopontin (OPN) and neoplastic disease: Circulating levels and tissue distribution

OPN is a secreted phosphate containing protein which is expressed by osteoblasts and a variety of other cells in vivo. Data from in vitro studies has accumulated which relates OPN to cellular transformation. We hypothesize that OPN expression is associated with neoplastic disease in humans as suggested by cell culture models. The overall objective of the current study was to determine the tissue distribution of OPN in human malignancy and to determine whether or not a correlation exists between OPN serum levels and malignancy. At the inception of this project, no study had been made demonstrating the relevance of OPN expression with naturally occurring neoplastic disease in humans. To date, few studies have reported OPN distribution in human neoplasia and are limited by either the number of specimens analyzed or the technique used in analysis. In this dissertation study, OPN was purified from human milk and $\alpha$-OPN antiserum developed and characterized. Following antibody development, the distribution and prevalence of OPN in human oral squamous cell carcinoma and human prostate carcinoma was evaluated using immunohistochemical localization. OPN immunolocalization was found in a high percentage of oral epithelial dysplasia and oral squamous cell carcinoma in humans. One oral squamous cell carcinoma cells line, UMSCC-1, was found to express OPN mRNA using Northern blotting. OPN localized to a high percentage of primary prostate adenocarcinomas. OPN localized to 52% of androgen dependent cases and 100% of androgen independent cases. Androgen dependent cell lines such as LNCap and NbE showed minimal OPN mRNA expression while the androgen independent lines C4-2 and PC3 produced ample OPN mRNA. An OPN sandwich assay was developed and used to determine the serum level of OPN in normal males, patients with BPH (benign prostate hypertrophy), and patients with prostate carcinoma. No statistically significant difference was found in OPN serum levels among the three groups. However, a trend of increasing OPN in the serum was noted in patients with BPH and prostate cancer. ^

Repeat length and RNA expression level are not primary determinants in CUG expansion toxicity in Drosophila models.

Evidence for an RNA gain-of-function toxicity has now been provided for an increasing number of human pathologies. Myotonic dystrophies (DM) belong to a class of RNA-dominant diseases that result from RNA repeat expansion toxicity. Specifically, DM of type 1 (DM1), is caused by an expansion of CUG repeats in the 3'UTR of the DMPK protein kinase mRNA, while DM of type 2 (DM2) is linked to an expansion of CCUG repeats in an intron of the ZNF9 transcript (ZNF9 encodes a zinc finger protein). In both pathologies the mutant RNA forms nuclear foci. The mechanisms that underlie the RNA pathogenicity seem to be rather complex and not yet completely understood. Here, we describe Drosophila models that might help unravelling the molecular mechanisms of DM1-associated CUG expansion toxicity. We generated transgenic flies that express inducible repeats of different type (CUG or CAG) and length (16, 240, 480 repeats) and then analyzed transgene localization, RNA expression and toxicity as assessed by induced lethality and eye neurodegeneration. The only line that expressed a toxic RNA has a (CTG)(240) insertion. Moreover our analysis shows that its level of expression cannot account for its toxicity. In this line, (CTG)(240.4), the expansion inserted in the first intron of CG9650, a zinc finger protein encoding gene. Interestingly, CG9650 and (CUG)(240.4) expansion RNAs were found in the same nuclear foci. In conclusion, we suggest that the insertion context is the primary determinant for expansion toxicity in Drosophila models. This finding should contribute to the still open debate on the role of the expansions per se in Drosophila and in human pathogenesis of RNA-dominant diseases.

Subnanometer-resolution structures of the grass carp reovirus core and virion.

Grass carp reovirus (GCRV) is a member of the Aquareovirus genus of the family Reoviridae, a large family of double-stranded RNA (dsRNA) viruses infecting plants, insects, fishes and mammals. We report the first subnanometer-resolution three-dimensional structures of both GCRV core and virion by cryoelectron microscopy. These structures have allowed the delineation of interactions among the over 1000 molecules in this enormous macromolecular machine and a detailed comparison with other dsRNA viruses at the secondary-structure level. The GCRV core structure shows that the inner proteins have strong structural similarities with those of orthoreoviruses even at the level of secondary-structure elements, indicating that the structures involved in viral dsRNA interaction and transcription are highly conserved. In contrast, the level of similarity in structures decreases in the proteins situated in the outer layers of the virion. The proteins involved in host recognition and attachment exhibit the least similarities to other members of Reoviridae. Furthermore, in GCRV, the RNA-translocating turrets are in an open state and lack a counterpart for the sigma1 protein situated on top of the close turrets observed in mammalian orthoreovirus. Interestingly, the distribution and the organization of GCRV core proteins resemble those of the cytoplasmic polyhedrosis virus, a cypovirus and the structurally simplest member of the Reoviridae family. Our results suggest that GCRV occupies a unique structure niche between the simpler cypoviruses and the considerably more complex mammalian orthoreovirus, thus providing an important model for understanding the structural and functional conservation and diversity of this enormous family of dsRNA viruses.

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.

THE MECHANISM OF TUMORIGENESIS IN THE IMMORTALIZED HUMAN PANCREATIC CELL LINES: CELL CULTURE MODELS OF HUMAN PANCREATIC CANCER

The mechanism of tumorigenesis in the immortalized human pancreatic cell lines: cell culture models of human pancreatic cancer Pancreatic ductal adenocarcinoma (PDAC) is the most lethal cancer in the world. The most common genetic lesions identified in PDAC include activation of K-ras (90%) and Her2 (70%), loss of p16 (95%) and p14 (40%), inactivation p53 (50-75%) and Smad4 (55%). However, the role of these signature gene alterations in PDAC is still not well understood, especially, how these genetic lesions individually or in combination contribute mechanistically to human pancreatic oncogenesis is still elusive. Moreover, a cell culture transformation model with sequential accumulation of signature genetic alterations in human pancreatic ductal cells that resembles the multiple-step human pancreatic carcinogenesis is still not established. In the present study, through the stepwise introduction of the signature genetic alterations in PDAC into the HPV16-E6E7 immortalized human pancreatic duct epithelial (HPDE) cell line and the hTERT immortalized human pancreatic ductal HPNE cell line, we developed the novel experimental cell culture transformation models with the most frequent gene alterations in PDAC and further dissected the molecular mechanism of transformation. We demonstrated that the combination of activation of K-ras and Her2, inactivation of p16/p14 and Smad4, or K-ras mutation plus p16 inactivation, was sufficient for the tumorigenic transformation of HPDE or HPNE cells respectively. We found that these transformed cells exhibited enhanced cell proliferation, anchorage-independent growth in soft agar, and grew tumors with PDAC histopathological features in orthotopic mouse model. Molecular analysis showed that the activation of K-ras and Her2 downstream effector pathways –MAPK, RalA, FAK, together with upregulation of cyclins and c-myc were involved in the malignant transformation. We discovered that MDM2, BMP7 and Bmi-1 were overexpressed in the tumorigenic HPDE cells, and that Smad4 played important roles in regulation of BMP7 and Bmi-1 gene expression and the tumorigenic transformation of HPDE cells. IPA signaling pathway analysis of microarray data revealed that abnormal signaling pathways are involved in transformation. This study is the first complete transformation model of human pancreatic ductal cells with the most common gene alterations in PDAC. Altogether, these novel transformation models more closely recapitulate the human pancreatic carcinogenesis from the cell origin, gene lesion, and activation of specific signaling pathway and histopathological features.

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. ^

Body fat distribution and serum lipids in children and adolescents

Previous studies of normal children have linked body fat but not body fat distribution (BFD), to higher blood pressures, lipids, and insulin resistance (Berenson et al., 1988) BFD is a well-established risk factor for cardiovascular disease in adults (Björntorp, 1988). This study investigates the relation of BFD and serum lipids at baseline in children from Project HeartBeat!, a study of the growth and development of cardiovascular risk factors in 678 children in three cohorts measured initially at ages 8, 11, and 14 years. Initially, two of four indices of BFD were significantly related to the lipids: ratio of upper to lower body skinfolds (ln US:LS) and conicity (C Index). A factor analysis reduced the information in the serum lipids to two vectors: (1) total cholesterol + LDL-cholesterol and (2) HDL-cholesterol − triglycerides, which together accounted for 85% of the lipid variation. Using each serum lipid and vector as separate dependent variables, linear and quadratic regression models were constructed to examine the predictive ability of the two BFD variables, controlling for total body fat, gender, ethnicity (Black, non-Black) and maturation. Linear models provided an acceptable fit. Percent body fat (%BF) was a significant predictor in each and every lipid model, independent of age, maturation, or ethnicity (p ≤ 0.05). No BFD variable entered the equation for total or LDL-cholesterol, although there was a significant maturity by BFD interaction for LDL (ln US:LS was a significant predictor in more mature individuals). Both %BF and BFD (by way of Conicity) were significant predictors of HDL-cholesterol and triglycerides (p ≤ 0.01). All models were statistically significant at a high level (p ≤ 0.01), but adjusted R 2's for all models were low (0.05–0.15). Body fat distribution is a significant predictor of lipids in normal children, but secondarily to %BF, and for LDL-cholesterol in particular, the relation is dependent on maturity status. ^

Changes in serum lipids with change and fluctuation in body mass index and body fat distribution in Mexican Americans with type 2 diabetes

This dissertation was written in the format of three journal articles. Paper 1 examined the influence of change and fluctuation in body mass index (BMI) over an eleven-year period, on changes in serum lipid levels (total, HDL, and LDL cholesterol, triglyceride) in a population of Mexican Americans with type 2 diabetes. Linear regression models containing initial lipid value, BMI and age, BMI change (slope of BMI), and BMI fluctuation (root mean square error) were used to investigate associations of these variables with change in lipids over time. Increasing BMI over time was associated with gains in total and LDL cholesterol and triglyceride levels in women. Fluctuation of BMI was not associated with detrimental lipid profiles. These effects were independent of age and were not statistically significant in men. In Mexican-American women with type 2 diabetes, weight reduction is likely to result in more favorable levels of total and LDL cholesterol and triglyceride, without concern for possible detrimental effects of weight fluctuation. Weight reduction may not be as effective in men, but does not appear to be harmful either. ^ Paper 2 examined the associations of upper and total body fat with total cholesterol, HDL and LDL cholesterol, and triglyceride levels in the same population. Multilevel analysis was used to predict serum lipid levels from total body fat (BMI and triceps skinfold) and upper body fat (subscapular skinfold), while controlling for the effects of sex, age and self-correlations across time. Body fat was not strikingly associated with trends in serum lipid levels. However, upper body fat was strongly associated with triglyceride levels. This suggests that loss of upper body fat may be more important than weight loss in management of the hypertriglyceridemia commonly seen in type 2 diabetes. ^ Paper 3 was a review of the literature reporting associations between weight fluctuation and lipid levels. Few studies have reported associations between weight fluctuation and total, LDL, and HDL cholesterol and triglyceride levels. The body of evidence to date suggests that weight fluctuation does not strongly influence levels of total, LDL and HDL cholesterol and triglyceride. ^

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Factors that affect non-adherence to first line antiretroviral medications among HIV infected children and adolescents in Botswana

The aims of the study were to determine the prevalence of and factors that affect non-adherence to first line antiretroviral (ARV) medications among HIV infected children and adolescents in Botswana. The study used secondary data from Botswana-Baylor Children's Clinical Center of Excellence for the period of June 2008 to February 10th, 2010. The study design was cross-sectional and case-comparison between non-adherent and adherent participants was used to examine the effects of socio-demographic and medication factors on non-adherence to ARV medications. A case was defined as non-adherent child with adherence level < 95% based on pill count and measurement of liquid formulations. The comparison group consisted of children with adherence levels ≥95%.^ A total of 842 participants met the eligibility criteria for determination of the prevalence of non-adherence and 338 participants (169 cases and 169 individuals) were used in the analysis to estimate the effects of factors on non-adherence. ^ Univariate and multivariable logistic regression were used to estimate the association between non-adherence (outcome) and socio-demographic and medication factors (exposures). The prevalence of non-adherence for participants on first line ARV medications was 20.0% (169/842).^ Increase in age (OR (95% CI): 1.10 (1.04–1.17) p = 0.001) was associated with nonadherence, while increase in number of caregivers (OR (95% CI): 0.72 (0.56–0.93) p = 0.01) and increase in number of monthly visits (OR (95% CI): 0.92 (0.86–0.99) p = 0.02), were associated with good adherence in both the unadjusted and the adjusted models. For the categorical variables, having more than two caregivers (OR (95% CI): 0.66 (0.28–0.84), p = 0.002) was associated with good adherence even in the adjusted model. ^ Conclusion. The prevalence of non-adherence to antiretroviral medicines among the study population was estimated to be 20.0%. In previous studies, adherence levels of ≥ 95% have been associated with better clinical outcomes and suppression of virus to prevent development of resistance. Older age, fewer numbers of caregivers and fewer monthly visits were associated with non-adherence. Strategies to improve and sustain adherence especially among older children are needed. The role of caregivers and social support should be investigated further.^

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. ^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^