Copyright (c) 2009 All rights reserved. http://works.bepress.com/mithat_gonen Recent documents in Mithat Gönen en-us Fri, 11 Sep 2009 20:11:22 PDT 3600 http://works.bepress.com/mithat_gonen/15 http://works.bepress.com/mithat_gonen/15 Mon, 08 Oct 2007 20:06:38 PDT Mithat Gonen ROC Curves http://works.bepress.com/mithat_gonen/14 http://works.bepress.com/mithat_gonen/14 Mon, 08 Oct 2007 13:39:19 PDT Mithat Gonen Clinical Trials Multivariate Analysis Statistical Models http://works.bepress.com/mithat_gonen/13 http://works.bepress.com/mithat_gonen/13 Wed, 23 May 2007 09:13:23 PDT Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after an unspecified monotone transformation, is normally distributed conditional on the outcome. Here we present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve) have simple analytic forms. Closed-form expressions for the functional estimates and their corresponding asymptotic variances are derived. This family accommodates the comparison of multiple markers, covariate adjustments and clustered data through a regression formulation. Evaluation of the underlying assumptions, model fitting and model selection can be performed using any off the shelf proportional hazards statistical software package. Mithat Gonen ROC Curves http://works.bepress.com/mithat_gonen/12 http://works.bepress.com/mithat_gonen/12 Wed, 23 May 2007 09:08:38 PDT Topics covered include non-parametric methods, transformation models for continuous data, the binormal model for ordinal data and validation of multivariate prediction models. Censored data and data mining applications are also covered. SAS code and macros are provided. Mithat Gonen ROC Curves http://works.bepress.com/mithat_gonen/11 http://works.bepress.com/mithat_gonen/11 Wed, 18 Oct 2006 11:22:52 PDT At the end of the dose-escalation stage of Phase I trials investigators occasionally enroll additional patients at the maximum tolerated dose (MTD) to further explore the tolerability of the regimen. There is no statistical justification for doing so; neither are there any guidelines regarding the use of toxicity information from this additional cohort with respect to the modification of MTD if necessary. This article addresses both of these issues using a Bayesian approach to model the probability of dose limiting toxicity (DLT) at the MTD. This approach takes the sequential nature of the Phase I design into account and provides predictive and posterior distributions through which various probabilities of interest can be calculated. The results suggest that MTD is usually not well-defined with a cohort of 3-6 patients in the traditional dose escalation schema. Therefore enrolling additional patients at the MTD is recommended. Also demonstrated are different ways to use the posterior density, after the additional cohort is enrolled, to decide whether the MTD is unacceptably toxic. Mithat Gonen Clinical Trials Bayesian methods http://works.bepress.com/mithat_gonen/10 http://works.bepress.com/mithat_gonen/10 Wed, 18 Oct 2006 11:02:09 PDT Subgroup analysis is a common secondary objective in clinical trials. In oncology where the outcome is often binary (such as tumor response) or time-to-event (such as survival), subgroup analysis can be formulated using an interaction term in using logistic or proportional hazards regression models. We focus on a case study of planning a randomized trial in metastatic colorectal cancer possibly involving a treatment-marker interaction. We present a method that can be used to compute the power of interaction tests for a given sample size or to compute the necessary sample sizes for a desired level of power for the planned subgroup analysis. The principle idea is borrowed from analysis of variance and uses appropriate contrasts after a variance-stabilizing transformation. This method is conceptually and operationally simple. It can be applied to binary- or ordinal-marker measurements and existing sample size tables or software can be used. The accuracy of the approximation is shown to be reasonable by simulation studies. Mithat Gonen Clinical Trials http://works.bepress.com/mithat_gonen/9 http://works.bepress.com/mithat_gonen/9 Wed, 18 Oct 2006 08:58:38 PDT This article is concerned with a dose-response study where the doses are subject-specific. The motivating example is a study on the use of radioiodine in metastatic thyroid cancer where the dose is individualized for each subject based on pharmacokinetic models of clearance of the agent. The goal is to design a study that will estimate the probability of response within a specified precision. This setup does not fit into well-studied dose-response designs primarily because doses are subject-specific. Here the dose-response relationship is modeled using logistic regression and a second-order approximation to the asymptotic variance of the model parameters is developed. The resulting procedure is simple to apply and requires minimal assumptions regarding the distribution of the dose levels. Simulation studies establish that, for a reasonable range of parameter values, the approximation is reasonably accurate. A Monte Carlo procedure is developed as well for cases when the approximation performs poorly. The proposed method is applied to the thyroid cancer study, including elicitation of parameters and a sensitivity analysis. Computer code in SAS and R are provided in the appendix. Mithat Gonen Clinical Trials http://works.bepress.com/mithat_gonen/8 http://works.bepress.com/mithat_gonen/8 Wed, 18 Oct 2006 08:40:53 PDT McNemar's test is used to compare the distribution of two paired binary random variables. When the data are clustered adjustment is needed to ensure that it is still a valid test. This article presents two approximations for calculating the power and sample size for the adjusted McNemar's test for clustered data, working with a particular adjustment. A simulation study is conducted to demonstrate the accuracy of these approximations. The method is also applied to the design of a study involving positron emission tomography in detecting metastatic colorectal cancer and sensitivity of sample size computations to the design parameters are explored in this context. Mithat Gonen Clinical Trials http://works.bepress.com/mithat_gonen/7 http://works.bepress.com/mithat_gonen/7 Tue, 17 Oct 2006 15:51:27 PDT Mithat Gonen Statistical Theory and Methods http://works.bepress.com/mithat_gonen/6 http://works.bepress.com/mithat_gonen/6 Tue, 17 Oct 2006 14:16:00 PDT In clinical studies involving multiple variables, simultaneous tests are often considered where both the outcomes and hypotheses are correlated. This article proposes a multivariate mixture prior on treatment effects that allows positive probability of zero effect for each hypothesis, correlations among effect sizes, correlations among binary outcomes of zero versus nonzero effect, as well as correlations among the observed test statistics (conditional on the effects). We develop Bayesian multiple testing procedure for the multivariate two-sample situation with unknown covariance structure, and obtain the posterior probabilities of no difference between treatment regimens for specific variables. Prior selection methods and robustness issues are discussed in the context of a clinical example. Mithat Gonen Bayesian methods