Physical Sciences and Mathematics Commons^™

Estimating Percentile-Specific Causal Effects: A Case Study Of Micronutrient Supplementation, Birth Weight, And Infant Mortality, Francesca Dominici, Scott L. Zeger, Giovanni Parmigiani, Joanne Katz, Parul Christian

Johns Hopkins University, Dept. of Biostatistics Working Papers

In developing countries, higher infant mortality is partially caused by poor maternal and fetal nutrition. Clinical trials of micronutrient supplementation are aimed at reducing the risk of infant mortality by increasing birth weight. Because infant mortality is greatest among the low birth weight infants (LBW) (• 2500 grams), an effective intervention may need to increase the birth weight among the smallest babies. Although it has been demonstrated that supplementation increases the birth weight in a trial conducted in Nepal, there is inconclusive evidence that the supplementation improves their survival. It has been hypothesized that a potential benefit of the treatment …

A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan

The University of Michigan Department of Biostatistics Working Paper Series

Case-cohort designs are increasingly commonly used in large epidemiological cohort studies. Nan, Yu, and Kalbeisch (2004) provided the asymptotic results for censored linear regression models in case-cohort studies. In this article, we consider computational aspects of their proposed rank based estimating methods. We show that the rank based discontinuous estimating functions for case-cohort studies are monotone, a property established for cohort data in the literature, when generalized Gehan type of weights are used. Though the estimating problem can be formulated to a linear programming problem as that for cohort data, due to its easily uncontrollable large scale even for a …

Ranking Usrds Provider-Specific Smrs From 1998-2001, Rongheng Lin, Thomas A. Louis, Susan M. Paddock, Greg Ridgeway

Johns Hopkins University, Dept. of Biostatistics Working Papers

Provider profiling (ranking, "league tables") is prevalent in health services research. Similarly, comparing educational institutions and identifying differentially expressed genes depend on ranking. Effective ranking procedures must be structured by a hierarchical (Bayesian) model and guided by a ranking-specific loss function, however even optimal methods can perform poorly and estimates must be accompanied by uncertainty assessments. We use the 1998-2001 Standardized Mortality Ratio (SMR) data from United States Renal Data System (USRDS) as a platform to identify issues and approaches. Our analyses extend Liu et al. (2004) by combining evidence over multiple years via an AR(1) model; by considering estimates …

Referent Selection Strategies In Case-Crossover Analyses Of Air Pollution Exposure Data: Implications For Bias, Holly Janes, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

The case-crossover design has been widely used to study the association between short term air pollution exposure and the risk of an acute adverse health event. The design uses cases only, and, for each individual, compares exposure just prior to the event with exposure at other control, or “referent” times. By making within-subject comparisons, time invariant confounders are controlled by design. Even more important in the air pollution setting is that, by matching referents to the index time, time varying confounders can also be controlled by design. Yet, the referent selection strategy is important for reasons other than control of …

Semi-Parametric Single-Index Two-Part Regression Models, Xiao-Hua Zhou, Hua Liang

UW Biostatistics Working Paper Series

In this paper, we proposed a semi-parametric single-index two-part regression model to weaken assumptions in parametric regression methods that were frequently used in the analysis of skewed data with additional zero values. The estimation procedure for the parameters of interest in the model was easily implemented. The proposed estimators were shown to be consistent and asymptotically normal. Through a simulation study, we showed that the proposed estimators have reasonable finite-sample performance. We illustrated the application of the proposed method in one real study on the analysis of health care costs.

Bayesian Hierarchical Distributed Lag Models For Summer Ozone Exposure And Cardio-Respiratory Mortality, Yi Huang, Francesca Dominici, Michelle L. Bell

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994.

At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by …

Multiple Testing And Data Adaptive Regression: An Application To Hiv-1 Sequence Data, Merrill D. Birkner, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Analysis of viral strand sequence data and viral replication capacity could potentially lead to biological insights regarding the replication ability of HIV-1. Determining specific target codons on the viral strand will facilitate the manufacturing of target specific antiretrovirals. Various algorithmic and analysis techniques can be applied to this application. We propose using multiple testing to find codons which have significant univariate associations with replication capacity of the virus. We also propose using a data adaptive multiple regression algorithm to obtain multiple predictions of viral replication capacity based on an entire mutant/non-mutant sequence profile. The data set to which these techniques …

Data Adaptive Estimation Of The Treatment Specific Mean, Yue Wang, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

An important problem in epidemiology and medical research is the estimation of the causal effect of a treatment action at a single point in time on the mean of an outcome, possibly within strata of the target population defined by a subset of the baseline covariates. Current approaches to this problem are based on marginal structural models, i.e., parametric models for the marginal distribution of counterfactural outcomes as a function of treatment and effect modifiers. The various estimators developed in this context furthermore each depend on a high-dimensional nuisance parameter whose estimation currently also relies on parametric models. Since misspecification …

Semiparametric Methods For The Binormal Model With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Abstract: In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We also discuss adjustment for covariates in this class of models and provide a simple …

Estimating The Retransformed Mean In A Heteroscedastic Two-Part Model, Alan H. Welsh, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Two distribution free estimators are proposed to estimate the mean of a dependent variable after fitting a semiparametric two-part heteroscedastic regression model to a transformation of the dependent variable. We show that the proposed estimators are consistent and have asymptotic normal distributions. We also compare their finite-sample performance in a simulation study. Finally, we illustrate the proposed methods in a real-world example of predicting in-patient health care costs.

History-Adjusted Marginal Structural Models And Statically-Optimal Dynamic Treatment Regimes, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at a final time point. However, the utility of these models for some applications has been limited by their inability to incorporate modification of the causal effect of treatment by time-varying covariates. …

A Hypothesis Test For The End Of A Common Source Outbreak, Ron Brookmeyer, Xiaojun You

Johns Hopkins University, Dept. of Biostatistics Working Papers

The objective of this paper is to develop a hypothesis testing procedure to determine whether a common source outbreak has ended. We do not assume that the calendar date of exposure to the pathogen is known. We assume an underlying parametric model for the incubation period distribution of a 2-paramter exponential model with a guarantee time, although the parameters are not assumed to be known. The hypothesis testing procedure is based on the spacings between ordered calendar dates of disease onset of the cases. A simulation study was performed to evaluate the robustness of the methods to a lognormal model …

A Marginal Model Approach For Analysis Of Multi-Reader Multi-Test Receiver Operating Characteristic (Roc) Data, Xiao Song, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve is a popular tool to characterize the capabilities of diagnostic tests with continuous or ordinal responses. One common design for assessing the accuracy of diagnostic tests is to have each patient examined by multiple readers with multiple tests; this design is most commonly used in a radiology setting, where the results of diagnostic tests depend on a radiologist's subjective interpretation. The most widely used approach for analyzing data from such a study is the Dorfman-Berbaum-Metz (DBM) method (Dorfman, Berbaum and Metz, 1992) which utilizes a standard analysis of variance (ANOVA) model for the jackknife …

Nonparametric Confidence Intervals For The One- And Two-Sample Problems, Xiao-Hua Zhou, Phillip Dinh

UW Biostatistics Working Paper Series

Confidence intervals for the mean of one sample and the difference in means of two independent samples based on the ordinary-t statistic suffer deficiencies when samples come from skewed distributions. In this article, we evaluate several existing techniques and propose new methods to improve coverage accuracy. The methods examined include the ordinary-t, the bootstrap-t, the biased-corrected acceleration (BCa) bootstrap, and three new intervals based on transformation of the t-statistic. Our study shows that our new transformation intervals and the bootstrap-t intervals give best coverage accuracy for a variety of skewed distributions; and that our new transformation intervals have shorter interval …

Effect Of Misreported Family History On Mendelian Mutation Prediction Models, Hormuzd A. Katki

Johns Hopkins University, Dept. of Biostatistics Working Papers

People with familial history of disease often consult with genetic counselors about their chance of carrying mutations that increase disease risk. To aid them, genetic counselors use Mendelian models that predict whether the person carries deleterious mutations based on their reported family history. Such models rely on accurate reporting of each member's diagnosis and age of diagnosis, but this information may be inaccurate. Commonly encountered errors in family history can significantly distort predictions, and thus can alter the clinical management of people undergoing counseling, screening, or genetic testing. We derive general results about the distortion in the carrier probability estimate …

Estimation Of Treatment Effects In Randomized Trials With Noncompliance And A Dichotomous Outcome , Mark J. Van Der Laan, Alan E. Hubbard, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non-compliance. Recent articles by Vansteelandt and Goethebeur (2003) and Robins and Rotnitzky (2004) have presented consistent and asymptotically linear estimators of a causal odds ratio, which rely, beyond correct specification of a model for the causal odds ratio, on a correctly specified model for a potentially high dimensional nuisance parameter. In this article we propose consistent, asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter -- …

Studying Effects Of Primary Care Physicians And Patients On The Trade-Off Between Charges For Primary Care And Specialty Care Using A Hierarchical Multivariate Two-Part Model, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan.

Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads.

Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for …

A Hierarchical Multivariate Two-Part Model For Profiling Providers' Effects On Healthcare Charges, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Procedures for analyzing and comparing healthcare providers' effects on health services delivery and outcomes have been referred to as provider profiling. In a typical profiling procedure, patient-level responses are measured for clusters of patients treated by providers that in turn, can be regarded as statistically exchangeable. Thus, a hierarchical model naturally represents the structure of the data. When provider effects on multiple responses are profiled, a multivariate model rather than a series of univariate models, can capture associations among responses at both the provider and patient levels. When responses are in the form of charges for healthcare services and sampled …

Estimation Of Direct And Indirect Causal Effects In Longitudinal Studies, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders, Robins & Greenland (1992) and Pearl (2000), develop two identifiability results for direct and indirect causal effects. They define an …

Non-Parametric Estimation Of Roc Curves In The Absence Of A Gold Standard, Xiao-Hua Zhou, Pete Castelluccio, Chuan Zhou

UW Biostatistics Working Paper Series

In evaluation of diagnostic accuracy of tests, a gold standard on the disease status is required. However, in many complex diseases, it is impossible or unethical to obtain such the gold standard. If an imperfect standard is used as if it were a gold standard, the estimated accuracy of the tests would be biased. This type of bias is called imperfect gold standard bias. In this paper we develop a maximum likelihood (ML) method for estimating ROC curves and their areas of ordinal-scale tests in the absence of a gold standard. Our simulation study shows the proposed estimates for the …

Multiple Testing Methods For Chip-Chip High Density Oligonucleotide Array Data, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit, Simon E. Cawley

U.C. Berkeley Division of Biostatistics Working Paper Series

Cawley et al. (2004) have recently mapped the locations of binding sites for three transcription factors along human chromosomes 21 and 22 using ChIP-Chip experiments. ChIP-Chip experiments are a new approach to the genome-wide identification of transcription factor binding sites and consist of chromatin (Ch) immunoprecipitation (IP) of transcription factor-bound genomic DNA followed by high density oligonucleotide hybridization (Chip) of the IP-enriched DNA. We investigate the ChIP-Chip data structure and propose methods for inferring the location of transcription factor binding sites from these data. The proposed methods involve testing for each probe whether it is part of a bound sequence …

Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang

UW Biostatistics Working Paper Series

We compare simple logistic regression with an alternative robust procedure for constructing linear predictors to be used for the two state classification task. Theoritical advantages of the robust procedure over logistic regression are: (i) although it assumes a generalized linear model for the dichotomous outcome variable, it does not require specification of the link function; (ii) it accommodates case-control designs even when the model is not logistic; and (iii) it yields sensible results even when the generalized linear model assumption fails to hold. Surprisingly, we find that the linear predictor derived from the logistic regression likelihood is very robust in …

Seasonal Analyses Of Air Pollution And Mortality In 100 U.S. Cities, Roger D. Peng, Francesca Dominici, Roberto Pastor-Barriuso, Scott L. Zeger, Jonathan M. Samet

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors develop Bayesian semi-parametric hierarchical models for estimating time-varying effects of pollution on mortality in multi-site time series studies. The methods are applied to the updated National Morbidity and Mortality Air Pollution Study database …

Semiparametic Models And Estimation Procedures For Binormal Roc Curves With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used for receiver operating characteristic (ROC) curve modelling when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We show that the Van der Waerden rank score …

Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data …

Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been much work on developing statistical procedures for associating tumor size with the probability of detecting a metastasis. Recently, Ghosh (2004) developed a unified statistical framework in which equivalences with censored data structures and models for tumor size and metastasis were examined. Based on this framework, we consider model checking techniques for semiparametric regression models in this paper. The procedures are for checking the additive hazards model. Goodness of fit methods are described for assessing functional form of covariates as well as the additive hazards assumption. The finite-sample properties of the methods are assessed using simulation studies.

Binary Isotonic Regression Procedures, With Application To Cancer Biomarkers, Debashis Ghosh, Moulinath Banerjee, Pinaki Biswas

The University of Michigan Department of Biostatistics Working Paper Series

There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for …

On Corrected Score Approach For Proportional Hazards Model With Covariate Measurement Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In the presence of covariate measurement error with the proportional hazards model, several functional modeling methods have been proposed. These include the conditional score estimator (Tsiatis and Davidian, 2001), the parametric correction estimator (Nakamura, 1992) and the nonparametric correction estimator (Huang and Wang, 2000, 2003) in the order of weaker assumptions on the error. Although they are all consistent, each suffers from potential difficulties with small samples and substantial measurement error. In this article, upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error, we investigate their relative finite sample performance …

Evaluating Markers For Selecting A Patient's Treatment, Xiao Song, Margaret S. Pepe

UW Biostatistics Working Paper Series

Selecting the best treatment for a patient's disease may be facilitated by evaluating clinical characteristics or biomarker measurements at diagnosis. We consider how to evaluate the potential of such measurements to impact on treatment selection algorithms. For example, magnetic resonance neurographic imaging is potentially useful for deciding whether a patient should be treated surgically for carpal tunnel syndrome or if he/she should receive less invasive conservative therapy. We propose a graphical display, the selection impact (SI) curve, that shows the population response rate as a function of treatment selection criteria based on the marker. The curve can be useful for …

Causal Inference In Hybrid Intervention Trials Involving Treatment Choice, Qi Long, Rod Little, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Randomized allocation of treatments is a cornerstone of experimental design, but has drawbacks when a limited set of individuals are willing to be randomized, or the act of randomization undermines the success of the treatment. Choice-based experimental designs allow a subset of the participants to choose their treatments. We discuss here causal inferences for experimental designs where some participants are randomly allocated to treatments and others receive their treatment preference. This paper was motivated by the “Women Take Pride” (WTP) study (Janevic et al., 2001), a doubly randomized preference trail (DRPT) to assess behavioral interventions for women with heart disease. …