Statistics and Probability Commons^™

Cox Models With Nonlinear Effect Of Covariates Measured With Error: A Case Study Of Chronic Kidney Disease Incidence, Ciprian M. Crainiceanu, David Ruppert, Josef Coresh

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose, develop and implement the simulation extrapolation (SIMEX) methodology for Cox regression models when the log hazard function is linear in the model parameters but nonlinear in the variables measured with error (LPNE). The class of LPNE functions contains but is not limited to strata indicators, splines, quadratic and interaction terms. The first order bias correction method proposed here has the advantage that it remains computationally feasible even when the number of observations is very large and multiple models need to be explored. Theoretical and simulation results show that the SIMEX method outperforms the naive method even with small …

Adjustment Uncertainty In Effect Estimation, Ciprian M. Crainiceanu, Francesca Dominici, Giovanni Parmigiani

Johns Hopkins University, Dept. of Biostatistics Working Papers

The selection of confounders and their functional relationship with the out- come affects exposure effect estimates. In practice, there is often substantial uncertainty about this selection, which we define here as “adjustment uncertainty.” We address the problem of estimating the effect of exposure on an outcome with focus on quantifying the effect of unknown confounders from a large set of potential confounders. We propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation, a specific implementation called "Structured Estimation under Adjustment Uncertainty (STEADy)", and associated visualization tools. Theoretical results and simulation studies show that STEADy consistently estimates …

A Flexible General Class Of Marginal And Conditional Random Intercept Models For Binary Outcomes Using Mixtures Of Normals, Brian Caffo, Ming-Wen An, Charles A. Rohde

Johns Hopkins University, Dept. of Biostatistics Working Papers

Random intercept models for binary data are useful tools for addressing between subject heterogeneity. Unlike linear models, the non-linearity of link functions used for binary data force a distinction between marginal and conditional interpretations. This distinction is blurred in probit models with a normally distributed random intercept because the resulting model implies a probit marginal link as well. That is, this model is closed in the sense that the distribution associated with the marginal and conditional link functions and the random effect distribution are all of the same family. In this manuscript we explore another family of random intercept models …

On The Potential For Ill-Logic With Logically Defined Outcomes, Xianbin Li, Brian S. Caffo, Daniel O. Scharfstein

Johns Hopkins University, Dept. of Biostatistics Working Papers

Logically defined outcomes are commonly used in medical diagnoses and epidemiological research. When missing values in the original outcomes exist, the method of handling the missingness can have unintended consequences, even if the original outcomes are missing completely at random. Complicating the issue is that the default behavior of standard statistical packages yields different results. In this paper, we consider two binary original outcomes, which are missing completely at random. For estimating the prevalence of a logically defined "or" outcome, we discuss the properties of four estimators: complete case estimator, all-available case estimator, maximum likelihood estimator (MLE), and moment-based estimator. …

Principal Stratification Designs To Estimate Input Data Missing Due To Death, Constantine E. Frangakis, Donald B. Rubin, Ming-Wen An, Ellen Mackenzie

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider studies of cohorts of individuals after a critical event, such as an injury, with the following characteristics. First, the studies are designed to measure “input” variables, which describe the period before the critical event, and to characterize the distribution of the input variables in the cohort. Second, the studies are designed to measure “output” variables, primarily mortality after the critical event, and to characterize the predictive (conditional) distribution of mortality given the input variables in the cohort. Such studies often possess the complication that the input data are missing for those who die shortly after the critical event …

Recurrent Event Models In The Presence Of A Terminal Event: Comparison, Inference And Data Analysis, Xianghua Luo, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

This article focuses on statistical implications of proportional rate models for recurrent event data in the presence of a terminal event. In such circumstances, various definitions of the recurrent rate function have been adopted in the proportional rate models. Although these rate functions have quite different interpretations, recognition of the differences has been lacking theoretically and practically. We compare three types of rate functions from both conceptual and quantitative perspectives; conclude that the inappropriate choice of a rate function may lead to misleading scientific conclusions. Simulations are conducted for comparisons of the focused models. Analysis of data from an AIDS …

On The Equivalence Of Case-Crossover And Time Series Methods In Environmental Epidemiology, Yun Lu, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series and case-crossover methods are often viewed as competing alternatives in environmental epidemiologic studies. Several recent studies have compared the time series and case-crossover methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for over-dispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using …

On The Use Of Non-Euclidean Isotropy In Geostatistics, Frank C. Curriero

Johns Hopkins University, Dept. of Biostatistics Working Papers

This paper investigates the use of non-Euclidean distances to characterize isotropic spatial dependence for geostatistical related applications. A simple example is provided to demonstrate there are no guarantees that existing covariogram and variogram functions remain valid (i.e.\ positive definite or conditionally negative definite) when used with a non-Euclidean distance measure. Furthermore, satisfying the conditions of a metric is not sufficient to ensure the distance measure can be used with existing functions. Current literature is not clear on these topics. There are certain distance measures that when used with existing covariogram and variogram functions remain valid, an issue that is explored. …

Nonparametric Estimation Of Bivariate Failure Time Associations In The Presence Of A Competing Risk, Karen Bandeen-Roche, Jing Ning

Johns Hopkins University, Dept. of Biostatistics Working Papers

There has been much research on the study of associations among paired failure times. Most has either assumed time invariance of association or been based on complex measures or estimators. Little has accommodated failures arising amid competing risks. This paper targets the conditional cause specific hazard ratio, a recent modification of the conditional hazard ratio to accommodate competing risks data. Estimation is accomplished by an intuitive, nonparametric method that localizes Kendall’s tau. Time variance is accommodated through a partitioning of space into “bins” between which the strength of association may differ. Inferential procedures are researched, small sample performance evaluated, and …

Modeling Differentiated Treatment Effects For Multiple Outcomes Data, Hongfei Guo, Karen Bandeen-Roche

Johns Hopkins University, Dept. of Biostatistics Working Papers

Multiple outcomes data are commonly used to characterize treatment effects in medical research, for instance, multiple symptoms to characterize potential remission of a psychiatric disorder. Often either a global, i.e. symptom-invariant, treatment effect is evaluated. Such a treatment effect may over generalize the effect across the outcomes. On the other hand individual treatment effects, varying across all outcomes, are complicated to interpret, and their estimation may lose precision relative to a global summary. An effective compromise to summarize the treatment effect may be through patterns of the treatment effects, i.e. "differentiated effects." In this paper we propose a two-category model …

Analyzing Panel Count Data With Informative Observation Times, Chiung-Yu Huang, Mei-Cheng Wang, Ying Zhang

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying recurrent event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the recurrent event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximizing a conditional …

Comparison Of Affymetrix Genechip Expression Measures, Rafael A. Irizarry, Zhijin Wu, Harris A. Jaffee

Johns Hopkins University, Dept. of Biostatistics Working Papers

Affymetrix GeneChip expression array technology has become a standard tool in medical science and basic biology research. In this system, preprocessing occurs before one obtains expression level measurements. Because the number of competing preprocessing methods was large and growing, in the summer of 2003 we developed a benchmark to help users of the technology identify the best method for their application. In conjunction with the release of a Bioconductor R package (affycomp), a webtool was made available for developers of preprocessing methods to submit them to a benchmark for comparison. There have now been over 30 methods compared via the …

A User-Friendly Introduction To Link-Probit-Normal Models, Brian S. Caffo, Michael Griswold

Johns Hopkins University, Dept. of Biostatistics Working Papers

Probit-normal models have attractive properties compared to logit-normal models. In particular, they allow for easy specification of marginal links of interest while permitting a conditional random effects structure. Moreover, programming fitting algorithms for probit-normal models can be trivial with the use of well-developed algorithms for approximating multivariate normal quantiles. In typical settings, the data cannot distinguish between probit and logit conditional link functions. Therefore, if marginal interpretations are desired, the default conditional link should be the most convenient one. We refer to models with a probit conditional link an arbitrary marginal link and a normal random effect distribution as link-probit-normal …

When Should One Substract Background Fluorescence In Two Color Microarrays?, Robert B. Scharpf, Christine A. Iacobuzio-Donahue, Julie B. Sneddon, Giovanni Parmigiani

Johns Hopkins University, Dept. of Biostatistics Working Papers

Two color microarrays are a powerful tool for genomic analysis, but have noise components that make inferences regarding gene expression inefficient and potentially misleading. Background fluorescence,whether attributable to non-specific binding or other sources,is an important component of noise. The decision to subtract fluorescence surrounding spots of hybridization from spot fluorescence has been controversial, with no clear criteria for determining circumstances that may favor, or disfavor, background subtraction. While it is generally accepted that subtracting background reduces bias but increases variance in the estimates of the ratios of interest, no formal analysis of the bias-variance trade off of background subtraction has …

Does The Effect Of Micronutrient Supplementation On Neonatal Survival Vary With Respect To The Percentiles Of The Birth Weight Distribution?, Francesca Dominici, Scott L. Zeger, Giovanni Parmigiani, Joanne Katz, Parul Christian

Johns Hopkins University, Dept. of Biostatistics Working Papers

Scientific Background: 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) (less than or equal to 2500 grams), an effective intervention might be needed to increase 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 …

Spatio-Temporal Point Processes: Methods And Applications, Peter J. Diggle

Johns Hopkins University, Dept. of Biostatistics Working Papers

No abstract provided.

A Partial Likelihood For Spatio-Temporal Point Processes, Peter J. Diggle

Johns Hopkins University, Dept. of Biostatistics Working Papers

Spatio-temporal point process data arise in many fields of application. An intuitively natural way to specify a model for a spatio-temporal point process is through its conditional intensity at location x and time t, given the history of the process up to time t. Typically, this results in an analytically intractable likelihood. Likelihood-based inference therefore relies on Monte Carlo methods which are computationally intensive and require careful tuning to each application. We propose a partial likelihood alternative which is computationally straightforward and can be applied routinely. We apply the method to data from the 2001 foot-and-mouth epidemic in the UK, …

Polydesigns And Causal Inference, Fan Li, Constantine E. Frangakis

Johns Hopkins University, Dept. of Biostatistics Working Papers

In an increasingly common class of studies, the goal is to evaluate causal effects of treatments that are only partially controlled by the investigator. In such studies there are two conflicting features: (1) a model on the full cohort design and data can identify the causal effects of interest, but can be sensitive to extreme regions of that design's data, where model specification can have more impact; and (2) models on a reduced design (i.e., a subset of the full data), e.g., conditional likelihood on matched subsets of data, can avoid such sensitivity, but do not generally identify the causal …

Model Choice In Time Series Studies Of Air Pollution And Mortality, Roger D. Peng, Francesca Dominici, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Multi-city time series studies of particulate matter (PM) and mortality and morbidity have provided evidence that daily variation in air pollution levels is associated with daily variation in mortality counts. These findings served as key epidemiological evidence for the recent review of the United States National Ambient Air Quality Standards (NAAQS) for PM. As a result, methodological issues concerning time series analysis of the relation between air pollution and health have attracted the attention of the scientific community and critics have raised concerns about the adequacy of current model formulations. Time series data on pollution and mortality are generally analyzed …

A Statistical Framework For The Analysis Of Microarray Probe-Level Data, Zhijin Wu, Rafael A. Irizarry

Johns Hopkins University, Dept. of Biostatistics Working Papers

Microarrays are an example of the powerful high through-put genomics tools that are revolutionizing the measurement of biological systems. In this and other technologies, a number of critical steps are required to convert the raw measures into the data relied upon by biologists and clinicians. These data manipulations, referred to as preprocessing, have enormous influence on the quality of the ultimate measurements and studies that rely upon them. Many researchers have previously demonstrated that the use of modern statistical methodology can substantially improve accuracy and precision of gene expression measurements, relative to ad-hoc procedures introduced by designers and manufacturers of …

Fixed-Width Output Analysis For Markov Chain Monte Carlo, Galin L. Jones, Murali Haran, Brian S. Caffo, Ronald Neath

Johns Hopkins University, Dept. of Biostatistics Working Papers

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we …

Designs In Partially Controlled Studies: Messages From A Review, Fan Li, Constantine E. Frangakis

Johns Hopkins University, Dept. of Biostatistics Working Papers

The ability to evaluate effects of factors on outcomes is increasingly important for a class of studies that control some but not all of the factors. Although important advances have been made in methods of analysis for such partially controlled studies,work on designs for such studies has been relatively limited. To help understand why, we review main designs that have been used for such partially controlled studies. Based on the review, we give two complementary reasons that explain the limited work on such designs, and suggest a new direction in this area.

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 …

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 …

Semiparametric Regression In Capture-Recapture Modelling, O. Gimenez, C. Barbraud, Ciprian M. Crainiceanu, S. Jenouvrier, B.T. Morgan

Johns Hopkins University, Dept. of Biostatistics Working Papers

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in the survival process may be explained by incorporating relevant covariates. We develop nonparametric and semiparametric regression models for estimating survival in capture-recapture models. A fully Bayesian approach using MCMC simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adelie.

The Proportional Odds Model For Assessing Rater Agreement With Multiple Modalities, Elizabeth Garrett-Mayer, Steven N. Goodman, Ralph H. Hruban

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop a model for evaluating an ordinal rating systems where we assume that the true underlying disease state is continuous in nature. Our approach in motivated by a dataset with 35 microscopic slides with 35 representative duct lesions of the pancreas. Each of the slides was evaluated by eight raters using two novel rating systems (PanIN illustrations and PanIN nomenclature),where each rater used each systems to rate the slide with slide identity masked between evaluations. We find that the two methods perform equally well but that differentiation of higher grade lesions is more consistent across raters …

Cross-Study Validation And Combined Analysis Of Gene Expression Microarray Data, Elizabeth Garrett-Mayer, Giovanni Parmigiani, Xiaogang Zhong, Leslie Cope, Edward Gabrielson

Johns Hopkins University, Dept. of Biostatistics Working Papers

Investigations of transcript levels on a genomic scale using

hybridization-based arrays led to formidable advances in our

understanding of the biology of many human illnesses. At the same time, these investigations have generated controversy, because of the probabilistic nature of the conclusions, and the surfacing of noticeable discrepancies between the results of studies addressing the same biological question. In this article we present simple and effective data analysis and visualization tools for gauging the degree to which

the finding of one study are reproduced by others, and for integrating multiple studies in a single analysis.

We describe these approaches in …

On Marginalized Multilevel Models And Their Computation, Michael E. Griswold, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and …

Spatially Adaptive Bayesian P-Splines With Heteroscedastic Errors, Ciprian M. Crainiceanu, David Ruppert, Raymond J. Carroll

Johns Hopkins University, Dept. of Biostatistics Working Papers

An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. These extensions have been studied before, but never together and never in the multivariate case. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian \mbox{MCMC}. The variance process controlling the spatially-adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized …

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 …