BIOST 2025: Biostatistics Seminar Notices

In this talk we consider functional imaging of the colon to assess the kinetics of a microbicide lubricant. The overarching goal is to understand the penetration of the lubricant after anal coitus. Such information is crucial for understanding the potential  impact of the microbicide on viral transmission. The experiment was conducted by simulating coitus in a subject after injecting a radiolabeled lubricant. After coital simulation, the subject was imaged via Single photon emission computed tomography (SPECT), a  non-invasive, in-vivo functional imaging technique. We use a highly modified version of the principal curve algorithm to construct a three dimensional curve through the colon images. The algorithm is developed on several difficult two dimensional images of familiar curves. The final curve
fit the colon data is compared to experimental sigmoidoscope collection.

Censored quantile regression offers a valuable supplement to Cox proportional hazards model for survival analysis. Existing work in the literature often requires stringent assumptions, such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels. Moreover, some of the work uses recursive algorithms which makes it challenging to derive asymptotic normality. To overcome these drawbacks, we propose a novel locally weighted censored
quantile regression approach. The new approach adopts the redistribution-of-mass idea and employs a local reweighting scheme.  Its validity only requires conditional independence of the survival time and the censoring variable given the covariates, and linearity at the particular quantile level of interest. Our method leads to a simple algorithm that can be conveniently implemented with R software. Applying recent theory of M-estimation with infinite dimensional parameters, we rigorously establish the consistency and asymptotic normality of the proposed estimator. The proposal method is studied via simulations and the analysis of an acute myocardial infarction dataset.

Development of more accurate and effective diagnostic systems is an important problem in many fields. Although systems for detection of presence/absence of the abnormality of interest often provide results on a multi-category scale, the simplest and often a more clinically relevant scale is binary. When a new diagnostic system is being developed, the initial phase of the assessment often aims to substantially increase sensitivity of a binary test even at the acknowledged cost of decreasing specificity below conventional level. This is followed by a tuning phase in which the goal is to remove as many false positive findings as possible with minimal reduction in sensitivity.

If the characteristics of a new binary diagnostic test are in the acceptable range, one can assess the improvements over the conventional diagnostic test with help of expected utilities. Alternatively, if the ROC curve of a new diagnostic system is available, one can evaluate whether by tuning the new system it is possible to achieve an objective improvement over the conventional diagnostic test. However, both expected utility and ROC curve approaches are associated with additional expenses and possible loss of reliability of the inferences. Expected utility approach often requires specification of a typically subjective and difficult-to-deduce utility function. ROC technique requires conducting an ROC study which in some cases may cast doubts on validity and usefulness of the resulting ROC curves.

We discuss the often overlooked scenarios that enable objective comparison of two binary diagnostic tests, one of which has higher sensitivity but lower specificity, without the need to specify a utility function or conduct an ROC study. The presented approach is conveniently formulated in terms of likelihood ratios, and for ROC inferences it exploits the assumption of concavity of the ROC curve which is often justified, particularly in the case when human observer interpretation is an integral part of diagnostic result.

In Cox proportional hazard models with censored survival data, estimates of
treatment effects with some important covariates omitted will be biased
toward zero (Gail et al., 1984). This is especially problematic in meta-analyses to combine estimates of parameters from studies where different covariate adjustments are made. Presently, few constructive solutions have been provided to address this issue. We propose a meta-analytic ramework for combining incomparable Cox models under both aggregated patient data (APD) and individual patient data (IPD) structures. For APD, two meta-regression models with indicators of different covariates in Cox models are proposed to adjust the heterogeneity of treatment effects across studies. Both parametric and nonparametric estimators for the pooled treatment effect and the heterogeneity variance are presented and compared. For IPD, we propose a fully augmented weighted estimator based on frailty models accommodating covariate(s) omission from different studies, and results are compared with estimations from multiple imputations method. We illustrate the advantages of our proposed analytic procedures over existing methodologies by simulation studies.

Amongst the high-throughput technologies, DNA microarray experiments
provide enormous quantity of genes and arrays with biological information
to disease. Despite advances and the popular usage of microarray, the
microarray experiments frequently produce multiple missing values due to
many flaw factors. Thus, gene expression data contains some missing entries and a large number of genes may be affected. Many downstream algorithms for gene expression analysis require a complete matrix as an input.  For now, there exists no uniformly superior imputation method and the performance depends on the structure and nature of data set.  In addition, imputation methods have been mostly compared in terms of variants of RMSEs (Root Mean Squared Error) which compare true expression values to imputed values. The drawback of RMSE-based evaluation is that the measure does not reflect the true biological effect in down-stream analyses. In this study, we investigate how missing value imputation process affects the biological results of differentially expressed genes discovery, clustering and classification. Quantitative measures reflecting the true biological effects in each down-stream analysis will be used to evaluate imputation methods and compared to RMSE-based evaluation.

We often encounter left-censored biomarker measurements subject to the
limits of detection (LOD). Ignoring or replacing the censored observations
with naive imputation method lead to biased estimates of the parameters in
the regression analysis. Maximum likelihood methods have been developed
when the distribution of the biomarkers are assumed normal. However, the
computation can be very intensive or even prohibitive as the number of
censored biomarkers increases. Motivated by a sepsis study, where a panel of biomarkers were measured to investigate the association between the sepsis and the biomarkers such as cytokines and coagulation markers, we propose a multiple imputation(MI) approach based on Tobit regression and Gibbs sampling. We conduct simulation study to evaluate the performance of our MI approach and use a sepsis dataset for demonstration.

In the Genetic and Inflammatory Marker of Sepsis (GenIMS) study (a large
multicenter cohort study), a number of pro-inflammatory and anti-inflammatory continuous biomarkers associated with sever sepsis and
death have been measured longitudinally. In this work, we are proposing to
extend the theory of the predictiveness curve (PC) that has been developed
by Huang, Pepe and Feng (Bcs2007) for longitudinally measured continuous biomarkers data. We fitted the PC using longitudinally measured GenIMS biomarker data for comparison of their effectiveness in predicting the risk of death. The PC has provided a common scale (zero to one) across various markers for comparing the usefulness of a given marker relative to other potential markers. Using this graphical tool, we have compared population distribution of risk of death for a number of competitive biomarkers associated with the disease. An extensive simulation study has been undertaken to establish the properties of the proposed methods under
differing scenarios.

Determining the lagged effects of ambient air levels of a pollutant on
cardiac distress is important in health effect studies. Standard model
selection procedures where a set of predictor variables is selected ignore
the associated uncertainties and may lead to overestimation of effects.
Bayesian model averaging approach takes account of model uncertainty by
combining information from all possible models. Zellner’s g-prior containing a hyperparameter g can account for model uncertainty and has potential usefulness in this endeavor. We present results from a sensitivity analysis for Bayesian model averaging with different calibrated hyperparameter g, viz., Akaike Information Criterion prior, Bayes Information Criterion prior, and Local Empirical Bayes estimate. Data from Allegheny County Air Pollution Study and the simulated data sets are used.

In two stage randomization designs, patients are randomized to one of the
initial treatments, and at the end of the first stage, they are randomized
to one of the second stage treatments depending on the outcome of the
initial treatment.  Statistical inference for survival data from these trials uses methods such as marginal mean models and weighted risk set estimates.  In this article, we propose a weighted Kaplan-Meier (WKM) estimator based on the method of inverse-probability weighting and compare its properties to that of the standard Kaplan-Meier (SKM) estimator, marginal mean model based (MM) estimator and weighted risk set (WRS) estimator.  Simulation study reveals that the WKM estimator is asymptotically unbiased, and provides coverage rates similar to that of MM and WRS estimators.  The SKM estimator, however, is biased when the second randomization rates are not same for the responders and non-responders to initial treatment.  The methods described are demonstrated by applying to a leukemia dataset.

Link to Abtract:

Higher Criticism Thresholding: Optimal Feature Selection when Useful Features are Rare and Weak

We investigated the use of pseudo-values from a jackknife statistic constructed from a simple summary statistic as a way of developing  direct
regression models of survival parameters. These pseudo-values, based on the difference between the complete sample and leave-one-out estimator, are used in a generalized estimating equation to obtain estimates of model
parameters. The approach can be applied to direct regression modeling of
the survival function over time, the cumulative incidence function for competing risk data, the restricted mean survival time, the mean quality of
life, and the probabilities in a multistate model.

In modern clinical neuro-oncology, the diagnosis and classification of malignant gliomas remains problematic and effective therapies are still elusive. As patient prognosis and therapeutic decisions rely on accurate pathological grading or classification of tumor cells, extensive investigation is going on for accurately identifying the types of glioma cancer. Unfortunately, many malignant gliomas are diagnostically challenging; these non-classic lesions are difficult to classify by histological features, thereby resulting in considerable interobserver variability and limited diagnosis reproducibility. In recent years, there has been a move towards the use of cDNA microarrays for tumor classification. These high-throughput assays provide relative mRNA expression measurements simultaneously for thousands of genes. A key statistical task is to perform classification via different expression patterns. Gene expression profiles may offer more information than classical morphology and may provide a better alternative to the classical tumor diagnosis schemes. The classification becomes more difficult when there are more than two cancer types, as with glioma.

This paper considers several Bayesian classification methods for the analysis of the glioma cancer with microarray data based on reproducing kernel Hilbert space under the multiclass setup. We consider the multinomial logit likelihood as well as the likelihood related to the muliclass Support Vector Machine (SVM) model. It is shown that our proposed Bayesian classification models with multiple shrinkage parameters can produce much accurate classification scheme for the glioma cancer compared to the several existing classical methods. We have also proposed a Bayesian variable selection scheme for selecting the differentially expressed genes integrated with our model. This integrated approach improves classifier design by yielding simultaneous gene selection.

Accurate risk prediction is an important step in developing optimal strategies for disease prevention and treatment. Based on the predicted risks, patients can be stratified to different risk categories where each category corresponds to a particular clinical intervention. Incorrect or sub-optimal interventions are likely to result in unnecessary financial and medical consequences. It is thus essential to account for the costs associated with the clinical interventions when developing and evaluating risk stratification rules for clinical use. In this article, we propose to quantify the value of a risk stratification rule based on the total expected cost attributed to incorrect assignment of risk groups due to the rule. For any given set of cost parameters, we develop an optimal stratification rule that minimizes the total expected cost over the entire population of interest. Statistical inference procedures are developed for evaluating and comparing risk stratification rules and examined through simulation studies. When new biomarkers become available, it is crucial to evaluate the incremental value of the new biomarkers in risk stratification. We propose robust procedures for evaluating such incremental values within various sub-populations. The proposed procedures are illustrated with an example from the Cardiovascular Health Study.

The remarkably increasing rate at which genomes are being sequenced has opened a new area of genome research, functional genomics, which is concerned with assigning biological function to DNA sequences. The novel biotechnologies such as cDNA microarrays and oligonucleotide chips are increasingly used to exploit DNA sequence data and yield information on the gene expression levels for entire genomes.

Many statisticians have developed some statistical methods for designing and analyzing microarray gene expression data. However, most of the commercial softwares do not fully cover these statistical methods but only emphasize the visualization tools and user-friendly operating tools. It is still not easy for the biologists to use the appropriate statistical software and interpret the results. Thus, we developed an integrated statistical software system for analyzing DNA chip data, ISSAC. It is as user-friendly as the other commercial softwares and implements many recently proposed statistical methods.