Educational Resources
Computational Biology and Biostatistics Summer Research Program
- Research Projects - Summer 2001-
The following research topics were from the Summer 2001 Research Program in Biostatistics. Next year's program will probably have different topics, but on the same level as the ones listed below. Research project descriptions from previous years are also available.
To take existing results on the triple-screen assay and present them in a manner most useful to physicians and their patients.
Knowledge/Skills needed:
Ability to make very basic probability calculations.
Knowledge/Skills obtained:
The student who takes on this project will learn the fundamentals and terminology of screening assays. These will be applied to an assay for birth defects but are equally applicable to a variety of tests such as for cancer, AIDS, and other diseases. She or he will also gain experience in reading the medical literature. This may be the most challenging and, not coincidentally, rewarding aspect of the project.
Abstract:
The triple screen assay is a blood test given to pregnant women in order to determine their risk for fetal defects, in particular chromosomal abnormalities such as Downs' syndrome. It is midway in complexity between two other types of information. The simplest is the potential mother's age: risk of Downs' syndrome rises dramatically with maternal age, from nearly nonexistent at age 20 to one in fifteen at age 45. In general, however, age is not an accurate predictor. The most precise and simultaneously most invasive way to predict Downs' syndrome is through amniocentesis in which fluid is taken from the amniotic sac via a needle (a related invasive method is also used). The triple screen provides a fairly accurate predictor through a simple blood test. All of these methods are used in order to give parents an advance warning of fetal birth defects and perhaps allow them to terminate the pregnancy.
Use simulations to evaluate the extent to which estimated adjudication rates affect estimates of event-free survival when a subset of reported events remain unadjudicated.
Knowledge/Skills needed:
Basic understanding of Bernoulli/Binomial distribution.
Knowledge/Skills obtained:
Understanding of Kaplan-Meier survival estimates, simple simulation techniques and basic use of SPlus (or R).
Abstract:
In many clinical trials, it is necessary to estimate and compare event-free survival for the treatment groups involved. The events of interest may be, for example, myocardial infarction, stroke, or other cardiovascular events requiring hospitalization. Furthermore, these events may require a classification committee to determine whether or not events reported by the treating physicians meet the criteria established for these events (adjudication). When events have been reported but have yet to be classified, we may use previously adjudicated events to estimate the rates at which reported events meet criteria, and in turn use these estimates to adjust estimates of event-free survival. Since estimated rates are used, error may be introduced into the survival estimates. We will investigate the extent to which these errors affect the estimates of event-free survival.
To classify untreated eyes based on visual acuity patterns over the 1st three years of the Early Treatment Diabetic Retinopathy Study. To determine meaningful attributes describing clusters of eyes. To associate clusters of eyes with morphologic changes in the eye.
Knowledge/Skills needed:
Introductory statistics course. Prior knowledge of clustering techniques or statistical software desirable (not necessary).
Knowledge/Skills obtained:
Knowledge of available clustering algorithms; advantages and disadvantages of various clustering algorithms; use of computer software (SAS or S-Plus) implementing clustering algorithms; interpretation of clusters.
Abstract:
The Early Treatment Diabetic Retinopathy Study (ETDRS) was a clinical trial of early photocoagulation v. deferral of photocoagulation for the treatment of diabetic retinopathy and diabetic macular edema. Data from this study has been used to develop scales for the severity of diabetic retinopathy and diabetic macular edema. During the trial, visual acuity measurements were recorded at baseline and subsequently every 4 months. The goal of this project is to find meaningful clusters of visual acuity scores in eyes assigned to deferral of photocoagulation over the 1st three years of the ETDRS. A secondary goal is to determine if particular visual acuity patterns are associated with specific morphologic (severity of diabetic retinopathy or severity of diabetic macular edema) changes.
To become familiar with basic mathematical models of population dynamics and their applications.
Knowledge/Skills needed:
A knowledge of differential equations would be useful.
Computational skills required.
Knowledge/Skills obtained:
The student will become familiar with:
Basic models of population dynamics
Analytical methods to solve simple systems of differential equations
Numerical methods to solve DEs using MAPLE
Abstract:
Basic mathematical models of population dynamics have proven useful in areas such as tumor cell modeling. Such models can be used to determine optimal treatment protocols, estimate tumor growth rates, and identify factors affecting changes in tumor cell population number. The simplest models are well understood and characterized. However, conceptually straightforward extensions can result in complexities that make closed form solutions difficult or impossible to obtain. In this project, we will review basic differential equation models of population dynamics along with both analytical and numerical methods of solving DEs. Time permitting, we will extend standard models to address questions in a study of rat mammary tumor cell populations.
Determine whether Markov Chain Monte Carlo (MCMC) analysis gives an advantage over inducing the maximum likelihood Bayes Net when modeling gene expression data.
Knowledge/Skills needed:
Computer programming, knowledge of data structures and algorithms.
Knowledge/Skills obtained:
Knowledge of Bayes Nets, MCMC by Metropolis-Hastings, familiarity with gene expression data.
Abstract:
Bayesian networks have been used to model gene expression data, to determine which genes influence the expression of other genes. A Bayesian network is a directed graph without cycles that represents a probability distribution. Recent approaches have used greedy search algorithms to identify Bayesian network structures that fit the data well. Some extensions can handle hidden variables. These approaches all produce a most plausible structure, from which gene expression patterns can be queried. The purpose of this project is to test whether the Metropolis- Hastings algorithm can be used to obtain more accurate answers.
To summarize the one or more of the various approaches to analyzing functional data.
Knowledge/Skills needed:
Familiarity with one or more of the following:
Linear regression
Principal components analysis
Analysis of variance
Knowledge/Skills obtained:
Familiarity with functional data and how standard statistical techniques can be expanded to handle this more complex type of data.
Abstract:
``Functional data'' is a relatively new statistical term for a broad class of data. Data are functional when each of the main sampling units (humans, rats, machines, slabs of metal) produces a data curve. A common example is data gathered over time. Each subject receives a pre-assigned treatment and then a response (say blood level of a particular compound) is recorded at a series of time points. The data from each subject is then a set of (time, response) points that can be plotted as a curve. Typical goals in analyzing functional data include estimating the ``typical curve'' for the population from which the sample of individuals was drawn, estimating individual curves, and testing for differences between treatment groups.
In this project we will summarize the one or more methods currently used to analyze functional data and describe their strengths and weaknesses.
Title of Project:
An Introduction to Parametric Distributions Used in Survival Analysis and Loss Modeling
To summarize various parametric distributions. Estimation and inference of quantities of interest for various data sets. Creation of Excel worksheet for hands-on demonstration of distribution and impact of changes of parameter values.
Knowledge/Skills needed:
Basic probability distribution function terminology.
Knowledge/Skills obtained:
Knowledge of many distributions, and advantages and disadvantages of each. Understanding of the cumulative distribution, survival function, probability density function, and hazard function for each distribution. Diagnostic techniques to decide between models. Use of computer to summarize the distributions and make inference and prediction using sample data.
Abstract:
Survival analysis involves the study of time until event data (like time until death) or the study of cost data (cost until death or cost until discharge from a hospital). These analyses are useful in public policy studies to examine whether a new treatment is more cost-effective than a standard treatment, or in insurance studies to investigate the impact of a change in policy deductibles or policy limits. The use of parametric models in analyzing time or cost until event data is advantageous as the models are simple to explain, produce a smooth function, and allow inferences to be made beyond the sample data. We will explore differences between various parametric models used in survival analysis both analytically and in the estimation of parameters for sample data sets.
