arXiv subjects

Bryan E. Shepherd

Publications and source records attributed to Bryan E. Shepherd.

32 records · Page 2Linked to original sources

arXiv2023

Asymptotic Properties for Cumulative Probability Models for Continuous Outcomes

Regression models for continuous outcomes often require a transformation of the outcome, which the user either specify {\it a priori} or estimate from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation and are thus a flexible analysis approach for continuous outcomes. However, it is difficult to establish asymptotic properties for CPMs due to the potentially unbounded range of the transformation. Here we show asymptotic properties for CPMs when applied to slightly modified data where the outcomes are censored at the ends. We prove uniform consistency of the estimated regression coefficients and the estimated transformation function over the non-censored region, and describe their joint asymptotic distribution. We show with simulations that results from this censored approach and those from the CPM on the original data are similar when a small fraction of data are censored. We reanalyze a dataset of HIV-positive patients with CPMs to illustrate and compare the approaches.

stat.ME↗

arXiv2022

Optimal Multi-Wave Validation of Secondary Use Data with Outcome and Exposure Misclassification

The growing availability of observational databases like electronic health records (EHR) provides unprecedented opportunities for secondary use of such data in biomedical research. However, these data can be error-prone and need to be validated before use. It is usually unrealistic to validate the whole database due to resource constraints. A cost-effective alternative is to implement a two-phase design that validates a subset of patient records that are enriched for information about the research question of interest. Herein, we consider odds ratio estimation under differential outcome and exposure misclassification. We propose optimal designs that minimize the variance of the maximum likelihood odds ratio estimator. We develop a novel adaptive grid search algorithm that can locate the optimal design in a computationally feasible and numerically accurate manner. Because the optimal design requires specification of unknown parameters at the outset and thus is unattainable without prior information, we introduce a multi-wave sampling strategy to approximate it in practice. We demonstrate the efficiency gains of the proposed designs over existing ones through extensive simulations and two large observational studies. We provide an R package and Shiny app to facilitate the use of the optimal designs.

stat.ME↗

arXiv2022

Analyzing Clustered Continuous Response Variables with Ordinal Regression Models

Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous response variable is measured repeatedly for a subject or the continuous responses arise from clusters, it is more challenging to model the continuous response data due to correlation within clusters. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered continuous response variables based on generalized estimating equation (GEE) methods for ordinal responses. With our approach, estimates of marginal parameters, cumulative distribution functions (CDFs), expectations, and quantiles conditional on covariates can be obtained without pre-transformation of the potentially skewed continuous response data. Computational challenges arise with large numbers of distinct values of the continuous response variable, and we propose two feasible and computationally efficient approaches to fit CPMs for clustered continuous response variables with different working correlation structures. We study finite sample operating characteristics of the estimators via simulation, and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in an HIV study. The other uses data from The Lung Health Study to investigate the contribution of a single nucleotide polymorphism to lung function decline.

stat.ME↗

arXiv2022

Fitting Semiparametric Cumulative Probability Models for Big Data

Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size, the number of predictors, and the number of distinct outcomes. We describe three approaches to address this problem. In the divide-and-combine approach, we divide the data into subsets, fit a CPM to each subset, and then aggregate the information. In the binning and rounding approaches, the outcome variable is redefined to have a greatly reduced number of distinct values. We consider rounding to a decimal place and rounding to significant digits, both with a refinement step to help achieve the desired number of distinct outcomes. We show with simulations that these approaches perform well and their parameter estimates are consistent. We investigate how running time and peak memory usage are influenced by the sample size, the number of distinct outcomes, and the number of predictors. As an illustration, we apply the approaches to a large publicly available dataset investigating matrix multiplication runtime with nearly one million observations.

stat.CO↗

arXiv2022

Addressing Detection Limits with Semiparametric Cumulative Probability Models

Detection limits (DLs), where a variable is unable to be measured outside of a certain range, are common in research. Most approaches to handle DLs in the response variable implicitly make parametric assumptions on the distribution of data outside DLs. We propose a new approach to deal with DLs based on a widely used ordinal regression model, the cumulative probability model (CPM). The CPM is a type of semiparametric linear transformation model. CPMs are rank-based and can handle mixed distributions of continuous and discrete outcome variables. These features are key for analyzing data with DLs because while observations inside DLs are typically continuous, those outside DLs are censored and generally put into discrete categories. With a single lower DL, the CPM assigns values below the DL as having the lowest rank. When there are multiple DLs, the CPM likelihood can be modified to appropriately distribute probability mass. We demonstrate the use of CPMs with simulations and two HIV data examples. The first example models a biomarker in which 15% of observations are below a DL. The second uses multi-cohort data to model viral load, where approximately 55% of observations are outside DLs which vary across sites and over time.

stat.ME↗

arXiv2022

Three-phase generalized raking and multiple imputation estimators to address error-prone data

Validation studies are often used to obtain more reliable information in settings with error-prone data. Validated data on a subsample of subjects can be used together with error-prone data on all subjects to improve estimation. In practice, more than one round of data validation may be required, and direct application of standard approaches for combining validation data into analyses may lead to inefficient estimators since the information available from intermediate validation steps is only partially considered or even completely ignored. In this paper, we present two novel extensions of multiple imputation and generalized raking estimators that make full use of all available data. We show through simulations that incorporating information from intermediate steps can lead to substantial gains in efficiency. This work is motivated by and illustrated in a study of contraceptive effectiveness among 82,957 women living with HIV whose data were originally extracted from electronic medical records, of whom 4855 had their charts reviewed, and a subsequent 1203 also had a telephone interview to validate key study variables.

stat.ME↗

arXiv2022

Bayesian Cumulative Probability Models for Continuous and Mixed Outcomes

Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed discrete/continuous outcomes since these are also ordered. Recent papers describe ordinal CPMs in this setting using non-parametric maximum likelihood estimation. We formulate a Bayesian CPM for continuous or mixed outcome data. Bayesian CPMs inherit many of the benefits of frequentist CPMs and have advantages with regard to interpretation, flexibility, and exact inference (within simulation error) for parameters and functions of parameters. We explore characteristics of the Bayesian CPM through simulations and a case study using HIV biomarker data. In addition, we provide the package 'bayesCPM' which implements Bayesian CPM models using the R interface to the Stan probabilistic programing language. The Bayesian CPM for continuous outcomes can be implemented with only minor modifications to the prior specification and, despite some limitations, has generally good statistical performance with moderate or large sample sizes.

stat.ME↗

arXiv2021

Analysis of Error-prone Electronic Health Records with Multi-wave Validation Sampling: Association of Maternal Weight Gain during Pregnancy with Childhood Outcomes

Electronic health record (EHR) data are increasingly used for biomedical research, but these data have recognized data quality challenges. Data validation is necessary to use EHR data with confidence, but limited resources typically make complete data validation impossible. Using EHR data, we illustrate prospective, multi-wave, two-phase validation sampling to estimate the association between maternal weight gain during pregnancy and the risks of her child developing obesity or asthma. The optimal validation sampling design depends on the unknown efficient influence functions of regression coefficients of interest. In the first wave of our multi-wave validation design, we estimate the influence function using the unvalidated (phase 1) data to determine our validation sample; then in subsequent waves, we re-estimate the influence function using validated (phase 2) data and update our sampling. For efficiency, estimation combines obesity and asthma sampling frames while calibrating sampling weights using generalized raking. We validated 996 of 10,335 mother-child EHR dyads in 6 sampling waves. Estimated associations between childhood obesity/asthma and maternal weight gain, as well as other covariates, are compared to naive estimates that only use unvalidated data. In some cases, estimates markedly differ, underscoring the importance of efficient validation sampling to obtain accurate estimates incorporating validated data.

stat.AP↗

arXiv2021

Optimum Allocation for Adaptive Multi-Wave Sampling in R: The R Package optimall

The R package optimall offers a collection of functions that efficiently streamline the design process of sampling in surveys ranging from simple to complex. The package's main functions allow users to interactively define and adjust strata cut points based on values or quantiles of auxiliary covariates, adaptively calculate the optimum number of samples to allocate to each stratum using Neyman or Wright allocation, and select specific IDs to sample based on a stratified sampling design. Using real-life epidemiological study examples, we demonstrate how optimall facilitates an efficient workflow for the design and implementation of surveys in R. Although tailored towards multi-wave sampling under two- or three-phase designs, the R package optimall may be useful for any sampling survey.

stat.ME↗

arXiv2020

Improved Generalized Raking Estimators to Address Dependent Covariate and Failure-Time Outcome Error

Biomedical studies that use electronic health records (EHR) data for inference are often subject to bias due to measurement error. The measurement error present in EHR data is typically complex, consisting of errors of unknown functional form in covariates and the outcome, which can be dependent. To address the bias resulting from such errors, generalized raking has recently been proposed as a robust method that yields consistent estimates without the need to model the error structure. We provide rationale for why these previously proposed raking estimators can be expected to be inefficient in failure-time outcome settings involving misclassification of the event indicator. We propose raking estimators that utilize multiple imputation, to impute either the target variables or auxiliary variables, to improve the efficiency. We also consider outcome-dependent sampling designs and investigate their impact on the efficiency of the raking estimators, either with or without multiple imputation. We present an extensive numerical study to examine the performance of the proposed estimators across various measurement error settings. We then apply the proposed methods to our motivating setting, in which we seek to analyze HIV outcomes in an observational cohort with electronic health records data from the Vanderbilt Comprehensive Care Clinic.

stat.ME↗

arXiv2020

Two-phase analysis and study design for survival models with error-prone exposures

Increasingly, medical research is dependent on data collected for non-research purposes, such as electronic health records data (EHR). EHR data and other large databases can be prone to measurement error in key exposures, and unadjusted analyses of error-prone data can bias study results. Validating a subset of records is a cost-effective way of gaining information on the error structure, which in turn can be used to adjust analyses for this error and improve inference. We extend the mean score method for the two-phase analysis of discrete-time survival models, which uses the unvalidated covariates as auxiliary variables that act as surrogates for the unobserved true exposures. This method relies on a two-phase sampling design and an estimation approach that preserves the consistency of complete case regression parameter estimates in the validated subset, with increased precision leveraged from the auxiliary data. Furthermore, we develop optimal sampling strategies which minimize the variance of the mean score estimator for a target exposure under a fixed cost constraint. We consider the setting where an internal pilot is necessary for the optimal design so that the phase two sample is split into a pilot and an adaptive optimal sample. Through simulations and data example, we evaluate efficiency gains of the mean score estimator using the derived optimal validation design compared to balanced and simple random sampling for the phase two sample. We also empirically explore efficiency gains that the proposed discrete optimal design can provide for the Cox proportional hazards model in the setting of a continuous-time survival outcome.

stat.ME↗

arXiv2020

Raking and Regression Calibration: Methods to Address Bias from Correlated Covariate and Time-to-Event Error

Medical studies that depend on electronic health records (EHR) data are often subject to measurement error, as the data are not collected to support research questions under study. These data errors, if not accounted for in study analyses, can obscure or cause spurious associations between patient exposures and disease risk. Methodology to address covariate measurement error has been well developed; however, time-to-event error has also been shown to cause significant bias but methods to address it are relatively underdeveloped. More generally, it is possible to observe errors in both the covariate and the time-to-event outcome that are correlated. We propose regression calibration (RC) estimators to simultaneously address correlated error in the covariates and the censored event time. Although RC can perform well in many settings with covariate measurement error, it is biased for nonlinear regression models, such as the Cox model. Thus, we additionally propose raking estimators which are consistent estimators of the parameter defined by the population estimating equation. Raking can improve upon RC in certain settings with failure-time data, require no explicit modeling of the error structure, and can be utilized under outcome-dependent sampling designs. We discuss features of the underlying estimation problem that affect the degree of improvement the raking estimator has over the RC approach. Detailed simulation studies are presented to examine the performance of the proposed estimators under varying levels of signal, error, and censoring. The methodology is illustrated on observational EHR data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

stat.ME↗

arXiv2018

Post-randomization Biomarker Effect Modification in an HIV Vaccine Clinical Trial

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, previous studies, biological theories, and the finding that immune response markers strongly correlated with infection in vaccine recipients generated the hypothesis that a qualitative interaction occurred. This hypothesis can be assessed with statistical methods for studying treatment effect modification by an intermediate response variable (i.e., principal stratification effect modification (PSEM) methods). However, available PSEM methods make untestable structural risk assumptions, such that assumption-lean versions of PSEM methods are needed in order to surpass the high bar of evidence to demonstrate a qualitative interaction. Fortunately, the survivor average causal effect (SACE) literature is replete with assumption-lean methods that can be readily adapted to the PSEM application for the special case of a binary intermediate response variable. We map this adaptation, opening up a host of new PSEM methods for a binary intermediate variable measured via two-phase sampling, for a dichotomous or failure time final outcome and including or excluding the SACE monotonicity assumption. The new methods support that the vaccine partially protected vaccine recipients with a high polyfunctional CD8+ T cell response, an important new insight for the HIV vaccine field.

stat.AP↗

arXiv2018

Probability-Scale Residuals in HIV/AIDS Research: Diagnostics and Inference

The probability-scale residual (PSR) is well defined across a wide variety of variable types and models, making it useful for studies of HIV/AIDS. In this manuscript, we highlight some of the properties of the PSR and illustrate its application with HIV data. As a residual, it can be useful for model diagnostics; we demonstrate its use with ordered categorical data and semiparametric transformation models. The PSR can also be used to construct tests of residual correlation. In fact, partial Spearman's rank correlation between $X$ and $Y$ while adjusting for covariates $Z$ can be constructed as the correlation between PSRs from models of $Y$ on $Z$ and of $X$ on $Z$. The covariance of PSRs is also useful in some settings. We apply these methods to a variety of HIV datasets including 1) a study examining risk factors for more severe forms of cervical lesions among 145 women living with HIV in Zambia, 2) a study investigating the association between 21 metabolomic biomarkers among 70 HIV-positive patients in the southeastern United States, and 3) a genome wide association study investigating the association between single nucleotide polymorphisms and tenofovir clearance among 501 HIV-positive persons participating in a multi-site randomized clinical trial.

stat.AP↗