Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

TYPE I INSULIN-LIKE GROWTH FACTOR RECEPTOR TYROSINE KINASE AS A MOLECULAR TARGET IN MANTLE CELL LYMPHOMA

Mantle cell lymphoma (MCL) is an aggressive B-cell lymphoid malignancy representing 5-10% of all non-Hodgkin’s lymphomas. It is distinguished by the t(11;14)(q13;q32) chromosomal translocation that juxtaposes the proto-oncogene CCND1, which encodes cyclin D1 at 11q13 to the IgH gene at 14q32. MCL patients represent about 6% of all new cases of Non-Hodgkin’s lymphomas per year or about 3,500 new cases per year. MCL occurs more frequently in older adults – the average age at diagnosis is the mid-60s with a male-to-female ratio of 2-3:1. It is typically characterized by the proliferation of neoplastic B-lymphocytes in the mantle zone of the lymph node follicle that have a prominent inclination to disseminate to other lymphoid tissues, bone marrow, peripheral blood and other organs. MCL patients have a poor prognosis because they develop resistance/relapse to current non-specific therapeutic regimens. It is of note that the exact molecular mechanisms underlying the pathogenesis of MCL are not completely known. It is reasonable to anticipate that better characterization of these mechanisms could lead to the development of specific and likely more effective therapeutics to treat this aggressive disease. The type I insulin-like growth factor receptor (IGF-IR) is thought to be a key player in several different solid malignancies such as those of the prostate, breast, lung, ovary, skin and soft tissue. In addition, recent studies in our lab showed evidence to support a pathogenic role of IGF-IR in some types of T-cell lymphomas and chronic myeloid leukemia. Constitutively active IGF-IR induces its oncogenic effects through the inhibition of apoptosis and induction of transformation, metastasis, and angiogenesis. Previous studies have shown that signaling through IGF-IR leads to the vi activation of multiple signaling transduction pathways mediated by the receptor-associated tyrosine kinase domain. These pathways include PI3K/Akt, MAP kinase, and Jak/Stat. In the present study, we tested the possible role of IGF-IR in MCL. Our results demonstrate that IGF-IR is over-expressed in mantle cell lymphoma cell lines compared with normal peripheral blood B- lymphocytes. Furthermore, inhibition of IGF-IR by the cyclolignan picropodophyllin (PPP) decreased cell viability and cell proliferation in addition to induction of apoptosis and G2/M cell cycle arrest. Screening of downstream oncogenes and apoptotic proteins that are involved in both IGF-IR and MCL signaling after treatment with PPP or IGF-IR siRNA showed significant alterations that are consistent with the cellular changes observed after PPP treatment. Therefore, our findings suggest that IGF-IR signaling contributes to the survival of MCL and thus may prove to be a legitimate therapeutic target in the future.

PLASMACYTOID DENDRITIC CELLS SENSE SKIN INJURY AND PROMOTE WOUND HEALING THROUGH TYPE I INTERFERONS

Plasmacytoid dendritic cells (pDCs) are a rare population of circulating cells, which selectively express intracellular Toll-like receptors (TLR)-7 and TLR-9 and have the capacity to produce large amounts of type I IFNs (IFN-a/b) in response to viruses or host derived nucleic acid containing complexes. pDCs are normally absent in skin but accumulate in the skin of psoriasis patients where their chronic activation to produce IFN-a/b drives the disease formation. Whether pDCs and their activation to produce IFN-a/b play a functional role in healthy skin is unknown. Here we show that pDCs are rapidly and transiently recruited into healthy human and mouse skin upon epidermal injury. Infiltrating pDCs were found to sense nucleic acids in wounded skin via TLRs, leading to the production of IFN-a/b. The production of IFN-a/b was paralleled by a short lived expression of cathelicidins, which form complexes with extracellular nucleic acids and activated pDCs to produce IFN-a/b in vitro. In vivo, cathelicidins were sufficient but not necessary for the induction of IFN-a/b in wounded skin, suggesting redundancy of this pathway. Depletion of pDCs or inhibition of IFN-a/bR signaling significantly impaired the inflammatory response and delayed re-epithelialization of skin wounds. Thus we uncover a novel role of pDCs in sensing skin injury via TLR mediated recognition of nucleic acids and demonstrate their involvement in the early inflammatory process and wound healing response through the production of IFN-a/b.

LY2109761, a novel transforming growth factor beta receptor type I and type II dual inhibitor, as a therapeutic approach to suppressing pancreatic cancer metastasis.

Most pancreatic cancer patients present with inoperable disease or develop metastases after surgery. Conventional therapies are usually ineffective in treating metastatic disease. It is evident that novel therapies remain to be developed. Transforming growth factor beta (TGF-beta) plays a key role in cancer metastasis, signaling through the TGF-beta type I/II receptors (TbetaRI/II). We hypothesized that targeting TbetaRI/II kinase activity with the novel inhibitor LY2109761 would suppress pancreatic cancer metastatic processes. The effect of LY2109761 has been evaluated on soft agar growth, migration, invasion using a fibroblast coculture model, and detachment-induced apoptosis (anoikis) by Annexin V flow cytometric analysis. The efficacy of LY2109761 on tumor growth, survival, and reduction of spontaneous metastasis have been evaluated in an orthotopic murine model of metastatic pancreatic cancer expressing both luciferase and green fluorescence proteins (L3.6pl/GLT). To determine whether pancreatic cancer cells or the cells in the liver microenvironment were involved in LY2109761-mediated reduction of liver metastasis, we used a model of experimental liver metastasis. LY2109761 significantly inhibited the L3.6pl/GLT soft agar growth, suppressed both basal and TGF-beta1-induced cell migration and invasion, and induced anoikis. In vivo, LY2109761, in combination with gemcitabine, significantly reduced the tumor burden, prolonged survival, and reduced spontaneous abdominal metastases. Results from the experimental liver metastasis models indicate an important role for targeting TbetaRI/II kinase activity on tumor and liver microenvironment cells in suppressing liver metastasis. Targeting TbetaRI/II kinase activity on pancreatic cancer cells or the cells of the liver microenvironment represents a novel therapeutic approach to prevent pancreatic cancer metastasis.

5-HT and GABA modulate intrinsic excitability of type I interneurons in Hermissenda.

The sensory neurons (photoreceptors) in the visual system of Hermissenda are one site of plasticity produced by Pavlovian conditioning. A second site of plasticity produced by conditioning is the type I interneurons in the cerebropleural ganglia. Both photoreceptors and statocyst hair cells of the graviceptive system form monosynaptic connections with identified type I interneurons. Two proposed neurotransmitters in the graviceptive system, serotonin (5-HT) and gamma-aminobutyric acid (GABA), have been shown to modify synaptic strength and intrinsic neuronal excitability in identified photoreceptors. However, the potential role of 5-HT and GABA in plasticity of type I interneurons has not been investigated. Here we show that 5-HT increased the peak amplitude of light-evoked complex excitatory postsynaptic potentials (EPSPs), enhanced intrinsic excitability, and increased spike activity of identified type I(e(A)) interneurons. In contrast, 5-HT decreased spike activity and intrinsic excitability of type I(e(B)) interneurons. The classification of two categories of type I(e) interneurons was also supported by the observation that 5-HT produced opposite effects on whole cell steady-state outward currents in type I(e) interneurons. Serotonin produced a reduction in the amplitude of light-evoked complex inhibitory PSPs (IPSPs), increased spontaneous spike activity, decreased intrinsic excitability, and depolarized the resting membrane potential of identified type I(i) interneurons. In contrast to the effects of 5-HT, GABA produced inhibition in both types of I(e) interneurons and type I(i) interneurons. These results show that 5-HT and GABA can modulate the intrinsic excitability of type I interneurons independent of the presynaptic effects of the same transmitters on excitability and synaptic efficacy of photoreceptors.

Type I hypersensitivity and its pharmacological modulation in {\it Trichinella\/}-induced intestinal fluid secretion and rapid rejection of the parasite in immunized rats

Studies were performed to test the hypothesis that type I hypersensitivity underlies worm induced intestinal fluid secretion and the rapid rejection of Trichinella spiralis from immunized rats, and the two events may be related in a cause-effect manner.^ Two approaches were taken. One was to determine whether inhibition of anaphylaxis-mediated Cl$\sp{-}$ and fluid secretion accompanying a secondary infection impedes worm rejection from immune hosts. The other was to determine whether induction of intestinal fluid secretion in nonimmune hosts interfered with worm establishment. In both studies, fluid secretion was measured volumetrically 30 min after a challenge infection and worms were counted.^ In immunized rats indomethacin did not affect the worm-induced fluid secretion when used alone, despite inhibiting mucosal prostaglandin synthesis. Fluid secretion was reduced by treatment with diphenhydramine and further reduced by the combination of diphenhydramine and indomethacin. The paradoxical effects of indomethacin when used alone compared with its coadministration with diphenhydramine is explained by the enhancing effect of indomethacin on histamine release. Abolishing net fluid secretion in these studies had no effect on rapid worm rejection in immune hosts.^ Worm establishment was reduced in recipients of immune serum containing IgE antibodies. Net intestinal fluid secretion induced in normal rats by PGE$\sb2$, cholera toxin, or hypertonic mannitol solution had no effect on worm establishment compared with untreated controls.^ In a related experiment, worm-induced intestinal fluid secretion and worm rejection in immune rats were partially blocked by concurrent injection with 5-HT$\sb2$ and 5-HT$\sb3$ blockers (Ketanserin and MDL-72222), suggesting that 5-HT is involved. This possible involvement was supported in that treatment of nonimmune rats with 5-HT significantly inhibited worm establishment in the intestine.^ Results indicate that anaphylaxis is the basis for both worm-induced intestinal fluid secretion and rapid rejection of T. spiralis in immune rats, but these events are independent of one another. 5-HT is a possible mediator of worm rejection, however, its mechanism of action is related to something other than fluid secretion. ^

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^

The Role of Type I Insulin-Like Growth Factor Receptor Signaling in Breast Cancer Brain Metastasis

Brain metastasis is a common cause of mortality in cancer patients. Approximately 20-30% of breast cancer patients acquire brain metastasis, yet potential therapeutic targets remain largely unknown. The type I insulin-like growth factor receptor (IGF- IR) is known to play a role in the progression of breast cancer and is currently being investigated in the clinical setting for various types of cancer. The present study demonstrates that the IGF-IR signaling axis is constitutively active in brain-seeking sublines of breast cancer cells, driving an increase in in vitro metastatic properties. We demonstrate that IGF-IR signaling is activated in an autocrine manner as a result of IGFBP3 overexpression in brain-seeking cells. Transient and stable knockdown of IGF-IR results in a downregulation of IGF-IR downstream signaling through phospho-AKT, as well as decreased in vitro migration and invasion of MDA- MB-231Br brain-seeking cells. Using an in vivo experimental brain metastasis model, we show that IGF-IR ablation attenuates the establishment of brain metastases and prolongs survival. Finally, we demonstrate that the malignancy of brain-seeking cells is attenuated by pharmacological inhibition with picropodophyllin, an IGF-IR-specific tyrosine kinase inhibitor. Together, our data suggest that the IGF-IR is an important mediator of brain metastasis and its ablation delays the onset of brain metastases in our model system.

Optimal, minimax, and Bayesian two-stage designs in two-dose phase II clinical trials

Background: For most cytotoxic and biologic anti-cancer agents, the response rate of the drug is commonly assumed to be non-decreasing with an increasing dose. However, an increasing dose does not always result in an appreciable increase in the response rate. This may especially be true at high doses for a biologic agent. Therefore, in a phase II trial the investigators may be interested in testing the anti-tumor activity of a drug at more than one (often two) doses, instead of only at the maximum tolerated dose (MTD). This way, when the lower dose appears equally effective, this dose can be recommended for further confirmatory testing in a phase III trial under potential long-term toxicity and cost considerations. A common approach to designing such a phase II trial has been to use an independent (e.g., Simon's two-stage) design at each dose ignoring the prior knowledge about the ordering of the response probabilities at the different doses. However, failure to account for this ordering constraint in estimating the response probabilities may result in an inefficient design. In this dissertation, we developed extensions of Simon's optimal and minimax two-stage designs, including both frequentist and Bayesian methods, for two doses that assume ordered response rates between doses. ^ Methods: Optimal and minimax two-stage designs are proposed for phase II clinical trials in settings where the true response rates at two dose levels are ordered. We borrow strength between doses using isotonic regression and control the joint and/or marginal error probabilities. Bayesian two-stage designs are also proposed under a stochastic ordering constraint. ^ Results: Compared to Simon's designs, when controlling the power and type I error at the same levels, the proposed frequentist and Bayesian designs reduce the maximum and expected sample sizes. Most of the proposed designs also increase the probability of early termination when the true response rates are poor. ^ Conclusion: Proposed frequentist and Bayesian designs are superior to Simon's designs in terms of operating characteristics (expected sample size and probability of early termination, when the response rates are poor) Thus, the proposed designs lead to more cost-efficient and ethical trials, and may consequently improve and expedite the drug discovery process. The proposed designs may be extended to designs of multiple group trials and drug combination trials.^

A simulation study of the effects of small center enrollment in multi -center clinical trials

Multi-center clinical trials are very common in the development of new drugs and devices. One concern in such trials, is the effect of individual investigational sites enrolling small numbers of patients on the overall result. Can the presence of small centers cause an ineffective treatment to appear effective when treatment-by-center interaction is not statistically significant?^ In this research, simulations are used to study the effect that centers enrolling few patients may have on the analysis of clinical trial data. A multi-center clinical trial with 20 sites is simulated to investigate the effect of a new treatment in comparison to a placebo treatment. Twelve of these 20 investigational sites are considered small, each enrolling less than four patients per treatment group. Three clinical trials are simulated with sample sizes of 100, 170 and 300. The simulated data is generated with various characteristics, one in which treatment should be considered effective and another where treatment is not effective. Qualitative interactions are also produced within the small sites to further investigate the effect of small centers under various conditions.^ Standard analysis of variance methods and the "sometimes-pool" testing procedure are applied to the simulated data. One model investigates treatment and center effect and treatment-by-center interaction. Another model investigates treatment effect alone. These analyses are used to determine the power to detect treatment-by-center interactions, and the probability of type I error.^ We find it is difficult to detect treatment-by-center interactions when only a few investigational sites enrolling a limited number of patients participate in the interaction. However, we find no increased risk of type I error in these situations. In a pooled analysis, when the treatment is not effective, the probability of finding a significant treatment effect in the absence of significant treatment-by-center interaction is well within standard limits of type I error. ^

Transcriptional regulation of cell lineage-specific expression of the murine type I collagen genes and of osteoblast differentiation

The aim of my project is to examine the mechanisms of cell lineage-specific transcriptional regulation of the two type I collagen genes by characterizing critical cis-acting elements and trans-acting factors. I hypothesize that the transcription factors that are involved in the cell lineage-specific expression of these genes may have a larger essential role in cell lineage commitment and differentiation. I first examined the proximal promoters of the proα1(I) and the proα2(I) collagen genes for cell type-specific DNA-protein interactions, using in vitro DNaseI and in vivo DMS footprinting. These experiments demonstrated that the cis-acting elements in these promoters are accessible to ubiquitous DNA-binding proteins in fibroblasts that express these genes, but not in other cells that do not express these genes. I speculate that in type I collagen-expressing cells, cell type-specific enhancer elements facilitate binding of ubiquitous proteins to the proximal promoters of these genes. Subsequently, examination of the upstream promoter of the proα(I) collagen gene by transgenic mice experiments delineated a 117 bp sequence (-1656 to -1540 bp) as the minimum element required for osteoblast-specific expression. This 117 bp element contained two segments that appeared to have different functions: (1) the A-segment, which was necessary to obtain osteoblast-specific expression and (2) the C-segment, which was dispensable for osteoblast-specific expression, but was necessary to obtain high-level expression. In experiments to identify trans-acting factors that bind to the 117 bp element, I have demonstrated that the cell lineage-restricted homeodomain proteins, Dlx2, Dlx5 and mHOX, bound to the A-segment and that the ubiquitous transcription factor, Sp1, bound to the C-segment of this element. These results suggested a model where the binding of cell lineage-restricted proteins to the A-segment and of ubiquitous proteins to the C-segment of the 117 bp element of the proα1 (I) collagen gene activated this gene in osteoblasts. These results, combined with additional evidence that Dlx2, Dlx5 and mHOX are probably involved in osteoblast differentiation, support my hypothesis that the transcription factors involved in osteoblast-specific expression of type I collagen genes may have essential role in osteoblast lineage commitment and differentiation. ^

A BAYESIAN APPROACH TO DOSE-RESPONSE ASSESSMENT AND DRUG-DRUG INTERACTION ANALYSIS: APPLICATION TO IN VITRO STUDIES

The considerable search for synergistic agents in cancer research is motivated by the therapeutic benefits achieved by combining anti-cancer agents. Synergistic agents make it possible to reduce dosage while maintaining or enhancing a desired effect. Other favorable outcomes of synergistic agents include reduction in toxicity and minimizing or delaying drug resistance. Dose-response assessment and drug-drug interaction analysis play an important part in the drug discovery process, however analysis are often poorly done. This dissertation is an effort to notably improve dose-response assessment and drug-drug interaction analysis. The most commonly used method in published analysis is the Median-Effect Principle/Combination Index method (Chou and Talalay, 1984). The Median-Effect Principle/Combination Index method leads to inefficiency by ignoring important sources of variation inherent in dose-response data and discarding data points that do not fit the Median-Effect Principle. Previous work has shown that the conventional method yields a high rate of false positives (Boik, Boik, Newman, 2008; Hennessey, Rosner, Bast, Chen, 2010) and, in some cases, low power to detect synergy. There is a great need for improving the current methodology. We developed a Bayesian framework for dose-response modeling and drug-drug interaction analysis. First, we developed a hierarchical meta-regression dose-response model that accounts for various sources of variation and uncertainty and allows one to incorporate knowledge from prior studies into the current analysis, thus offering a more efficient and reliable inference. Second, in the case that parametric dose-response models do not fit the data, we developed a practical and flexible nonparametric regression method for meta-analysis of independently repeated dose-response experiments. Third, and lastly, we developed a method, based on Loewe additivity that allows one to quantitatively assess interaction between two agents combined at a fixed dose ratio. The proposed method makes a comprehensive and honest account of uncertainty within drug interaction assessment. Extensive simulation studies show that the novel methodology improves the screening process of effective/synergistic agents and reduces the incidence of type I error. We consider an ovarian cancer cell line study that investigates the combined effect of DNA methylation inhibitors and histone deacetylation inhibitors in human ovarian cancer cell lines. The hypothesis is that the combination of DNA methylation inhibitors and histone deacetylation inhibitors will enhance antiproliferative activity in human ovarian cancer cell lines compared to treatment with each inhibitor alone. By applying the proposed Bayesian methodology, in vitro synergy was declared for DNA methylation inhibitor, 5-AZA-2'-deoxycytidine combined with one histone deacetylation inhibitor, suberoylanilide hydroxamic acid or trichostatin A in the cell lines HEY and SKOV3. This suggests potential new epigenetic therapies in cell growth inhibition of ovarian cancer cells.

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

Single nucleotide polymorphism (SNP) selection for genotype-phenotype association studies

With hundreds of single nucleotide polymorphisms (SNPs) in a candidate gene and millions of SNPs across the genome, selecting an informative subset of SNPs to maximize the ability to detect genotype-phenotype association is of great interest and importance. In addition, with a large number of SNPs, analytic methods are needed that allow investigators to control the false positive rate resulting from large numbers of SNP genotype-phenotype analyses. This dissertation uses simulated data to explore methods for selecting SNPs for genotype-phenotype association studies. I examined the pattern of linkage disequilibrium (LD) across a candidate gene region and used this pattern to aid in localizing a disease-influencing mutation. The results indicate that the r2 measure of linkage disequilibrium is preferred over the common D′ measure for use in genotype-phenotype association studies. Using step-wise linear regression, the best predictor of the quantitative trait was not usually the single functional mutation. Rather it was a SNP that was in high linkage disequilibrium with the functional mutation. Next, I compared three strategies for selecting SNPs for application to phenotype association studies: based on measures of linkage disequilibrium, based on a measure of haplotype diversity, and random selection. The results demonstrate that SNPs selected based on maximum haplotype diversity are more informative and yield higher power than randomly selected SNPs or SNPs selected based on low pair-wise LD. The data also indicate that for genes with small contribution to the phenotype, it is more prudent for investigators to increase their sample size than to continuously increase the number of SNPs in order to improve statistical power. When typing large numbers of SNPs, researchers are faced with the challenge of utilizing an appropriate statistical method that controls the type I error rate while maintaining adequate power. We show that an empirical genotype based multi-locus global test that uses permutation testing to investigate the null distribution of the maximum test statistic maintains a desired overall type I error rate while not overly sacrificing statistical power. The results also show that when the penetrance model is simple the multi-locus global test does as well or better than the haplotype analysis. However, for more complex models, haplotype analyses offer advantages. The results of this dissertation will be of utility to human geneticists designing large-scale multi-locus genotype-phenotype association studies. ^