A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Role of the cyclin dependent kinase-4 in normal and neoplastic proliferation

In the last few years, our laboratory has studied the regulatory mechanisms of proliferation and differentiation in epidermal tissues. Our results showed differences in the roles of cyclin dependent-kinases 4 and 6, and the three D-type cyclins, during normal epidermal proliferation and neoplastic development. Thus, to elucidate the role of the different cell cycle regulators, we developed transgenic mice that overexpress CDK4 (K5-CDK4), or their cognate D-type cyclins, in epithelial tissues. The most severe phenotype was observed in K5-CDK4 animals that developed dermal fibrosis, epidermal hyperplasia and hypertrophy. Forced expression of CDK4 in the epidermal basal cell layer increased the malignant conversion of skin papillomas to squamous cell carcinomas (SCC). Contrastingly, lack of CDK4 completely inhibited tumor development, suggesting that CDK4 is required in this process. Biochemical studies demonstrated that p21 Cip1 and p27Kip1 inhibitors are sequestered by CDK4 resulting in indirect activation of Cyclin E/CDK2, implicating the non-catalytic activity of CDK4 in deregulation of the cell cycle progression. ^ It has been proposed that the proliferative and oncogenic role of Myc is linked to its ability to induce the transcription of CDK4, cyclin D1, and cyclin D2 in vitro. Deregulation of Myc oncogene has been found in several human cancers. Also it has been demonstrated that CDK4 has the ability to functionally inactivate the product of the tumor suppressor gene Rb, providing a link between Myc and the CDK4/cyclin D1/pRb/p16 pathway in some malignant tumors. Here, we sought to determine the role of CDK4 as a mediator of Myc activities by developing a Myc overexpressing mouse nullizygous for CDK4. We demonstrated that lack of CDK4 results in reduced keratinocyte proliferation and epidermal thickness in K5-Myc/CDK4-null mice. In addition, complete reversion of tumor development was observed. All together, this work demonstrates that CDK4 acts as an oncogene independent of the D-type cyclin levels and it is an important mediator of the tumorigenesis induced by Myc. In addition, we showed that the sequestering activity of CDK4 is critical for the development of epidermal hyperplasia during normal proliferation, malignant progression from papillomas to squamous cell carcinomas, and tumorigenesis induced by Myc. ^

DEVELOPMENT OF A BEAM-SPECIFIC PLANNING TARGET VOLUME AND A ROBUST PLAN ANALYSIS TOOL FOR PROTON THERAPY

Proton therapy is growing increasingly popular due to its superior dose characteristics compared to conventional photon therapy. Protons travel a finite range in the patient body and stop, thereby delivering no dose beyond their range. However, because the range of a proton beam is heavily dependent on the tissue density along its beam path, uncertainties in patient setup position and inherent range calculation can degrade thedose distribution significantly. Despite these challenges that are unique to proton therapy, current management of the uncertainties during treatment planning of proton therapy has been similar to that of conventional photon therapy. The goal of this dissertation research was to develop a treatment planning method and a planevaluation method that address proton-specific issues regarding setup and range uncertainties. Treatment plan designing method adapted to proton therapy: Currently, for proton therapy using a scanning beam delivery system, setup uncertainties are largely accounted for by geometrically expanding a clinical target volume (CTV) to a planning target volume (PTV). However, a PTV alone cannot adequately account for range uncertainties coupled to misaligned patient anatomy in the beam path since it does not account for the change in tissue density. In order to remedy this problem, we proposed a beam-specific PTV (bsPTV) that accounts for the change in tissue density along the beam path due to the uncertainties. Our proposed method was successfully implemented, and its superiority over the conventional PTV was shown through a controlled experiment.. Furthermore, we have shown that the bsPTV concept can be incorporated into beam angle optimization for better target coverage and normal tissue sparing for a selected lung cancer patient. Treatment plan evaluation method adapted to proton therapy: The dose-volume histogram of the clinical target volume (CTV) or any other volumes of interest at the time of planning does not represent the most probable dosimetric outcome of a given plan as it does not include the uncertainties mentioned earlier. Currently, the PTV is used as a surrogate of the CTV’s worst case scenario for target dose estimation. However, because proton dose distributions are subject to change under these uncertainties, the validity of the PTV analysis method is questionable. In order to remedy this problem, we proposed the use of statistical parameters to quantify uncertainties on both the dose-volume histogram and dose distribution directly. The robust plan analysis tool was successfully implemented to compute both the expectation value and its standard deviation of dosimetric parameters of a treatment plan under the uncertainties. For 15 lung cancer patients, the proposed method was used to quantify the dosimetric difference between the nominal situation and its expected value under the uncertainties.