arXiv subjects

Paul S. Albert

Publications and source records attributed to Paul S. Albert.

14 recordsLinked to original sources

arXiv2026

Comparing Tobit and Two-Part Hurdle Models for Semi-Continuous Longitudinal Data with an Application to Clonal Hematopoiesis

Zero-inflated nonnegative continuous longitudinal data frequently arise in biomedical studies where outcomes consist of a mixture of excess zeros and positive continuous measurements. Two widely used approaches for analyzing such data are mixed-model versions of Tobit and the two-part hurdle models. The Tobit assumes a latent regression model that is censored below a specified threshold, while the hurdle separately models the continuous positive outcomes and the binary indicator of being positive. The choice between these models has rarely been systematically discussed, and inappropriate model choice may lead to biased estimation and misleading scientific interpretations. In this paper, we derive rigorous mathematical conditions under which the two models are equivalent and show that the Tobit can be viewed as a special case of the hurdle model when the link function for the binary process is probit. Based on simulation studies, we found that the hurdle is more flexible and robust than the Tobit model. On the other hand, if the assumptions of the Tobit are met, this model is easier to interpret since it does not require distinct inferences on both the continuous and binary processes. We therefore recommend that the Tobit model only be used when these assumptions are scientifically plausible and empirically supported; otherwise, the hurdle model is preferable. We applied both models to study the dynamics of somatic mosaicism using longitudinal clonal fraction measurements from the Prostate, Lung, Colorectal, and Ovarian study data while accounting for excess zero values. Estimates obtained from the Tobit and hurdle models were broadly consistent with those from a standard linear model that ignored zero inflation. These findings provide additional support for previously reported associations in studies of clonal hematopoiesis across different types of mosaic chromosomal alterations.

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arXiv2026

Using Importance Sampling to Estimate $p$-values in All-Subset Meta-Analysis, with Applications to Single-Cell eQTL Mapping

Pooling genome-wide association studies of multiple related traits can substantially increase power for detecting genetic variants with pleiotropic effects. ASSET, which exhaustively searches all subsets of studies for association signals, has been widely used to detect modest effects and improve interpretability. Under a normality assumption, ASSET computes p-values via an analytic approximation that accounts for multiple testing. However, this approximation has been evaluated only in limited scenarios and for p-values no smaller than $10^{-3}$. A systematic assessment in the extreme tail is therefore needed, yet naïve Monte Carlo methods would require prohibitively many simulations. We develop a computationally efficient importance-sampling (IS) algorithm that provides accurate ASSET p-value estimates for both independent and overlapping studies, achieving substantial efficiency gains over naïve Monte Carlo, particularly for very small p-values. Using IS, we show that ASSET's analytic approximation is highly accurate across nearly the entire p-value range when normality holds. In contrast, when normality is violated (due to small sample sizes, low-frequency variants, or non-normal traits), ASSET p-values can be inflated or deflated by orders of magnitude, whereas our IS approach remains accurate. We illustrate the method through applications to single-cell eQTL mapping using peripheral blood mononuclear cells from the OneK1K cohort and lung cells from a Korean population.

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arXiv2025

Estimating the Heritability of Longitudinal Rate-of-Change: Genetic Insights into PSA Velocity in Prostate Cancer-Free Individuals

Serum prostate-specific antigen (PSA) is widely used for prostate cancer screening. While the genetics of PSA levels has been studied to enhance screening accuracy, the genetic basis of PSA velocity, the rate of PSA change over time, remains unclear. The Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial, a large, randomized study with longitudinal PSA data (15,260 cancer-free males, averaging 5.34 samples per subject) and genome-wide genotype data, provides a unique opportunity to estimate PSA velocity heritability. We developed a mixed model to jointly estimate heritability of PSA levels at age 54 and PSA velocity. To accommodate the large dataset, we implemented two efficient computational approaches: a partitioning and meta-analysis strategy using average information restricted maximum likelihood (AI-REML), and a fast restricted Haseman-Elston (REHE) regression method. Simulations showed that both methods yield unbiased estimates of both heritability metrics, with AI-REML providing smaller variability in the estimation of velocity heritability than REHE. Applying AI-REML to PLCO data, we estimated heritability at 0.32 (s.e. = 0.07) for baseline PSA and 0.45 (s.e. = 0.18) for PSA velocity. These findings reveal a substantial genetic contribution to PSA velocity, supporting future genome-wide studies to identify variants affecting PSA dynamics and improve PSA-based screening.

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arXiv2022

A hidden Markov modeling approach combining objective measure of activity and subjective measure of self-reported sleep to estimate the sleep-wake cycle

Characterizing the sleep-wake cycle in adolescents is an important prerequisite to better understand the association of abnormal sleep patterns with subsequent clinical and behavioral outcomes. The aim of this research was to develop hidden Markov models (HMM) that incorporate both objective (actigraphy) and subjective (sleep log) measures to estimate the sleep-wake cycle using data from the NEXT longitudinal study, a large population-based cohort study. The model was estimated with a negative binomial distribution for the activity counts (1-minute epochs) to account for overdispersion relative to a Poisson process. Furthermore, self-reported measures were dichotomized (for each one-minute interval) and subject to misclassification. We assumed that the unobserved sleep-wake cycle follows a two-state Markov chain with transitional probabilities varying according to a circadian rhythm. Maximum-likelihood estimation using a backward-forward algorithm was applied to fit the longitudinal data on a subject by subject basis. The algorithm was used to reconstruct the sleep-wake cycle from sequences of self-reported sleep and activity data. Furthermore, we conduct simulations to examine the properties of this approach under different observational patterns including both complete and partially observed measurements on each individual.

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arXiv2021

Is Group Testing Ready for Prime-time in Disease Identification?

Large scale disease screening is a complicated process in which high costs must be balanced against pressing public health needs. When the goal is screening for infectious disease, one approach is group testing in which samples are initially tested in pools and individual samples are retested only if the initial pooled test was positive. Intuitively, if the prevalence of infection is small, this could result in a large reduction of the total number of tests required. Despite this, the use of group testing in medical studies has been limited, largely due to skepticism about the impact of pooling on the accuracy of a given assay. While there is a large body of research addressing the issue of testing errors in group testing studies, it is customary to assume that the misclassification parameters are known from an external population and/or that the values do not change with the group size. Both of these assumptions are highly questionable for many medical practitioners considering group testing in their study design. In this article, we explore how the failure of these assumptions might impact the efficacy of a group testing design and, consequently, whether group testing is currently feasible for medical screening. Specifically, we look at how incorrect assumptions about the sensitivity function at the design stage can lead to poor estimation of a procedure's overall sensitivity and expected number of tests. Furthermore, if a validation study is used to estimate the pooled misclassification parameters of a given assay, we show that the sample sizes required are so large as to be prohibitive in all but the largest screening programs

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arXiv2021

Nested Group Testing Procedures for Screening

This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing) to be defective, and the probability $1-p$ to be non-defective independent from the other items. A group test applied to any subset of size $n$ is a binary test with two possible outcomes, positive or negative. The outcome is negative if all $n$ items are non-defective, whereas the outcome is positive if at least one item among the $n$ items is defective. The goal is complete identification of all $N$ items with the minimum expected number of tests.

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arXiv2020

An optimal design for hierarchical generalized group testing

Choosing an optimal strategy for hierarchical group testing is an important problem for practitioners who are interested in disease screening with limited resources. For example, when screening for infectious diseases in large populations, it is important to use algorithms that minimize the cost of potentially expensive assays. Black et al. (2015) described this as an intractable problem unless the number of individuals to screen is small. They proposed an approximation to an optimal strategy that is difficult to implement for large population sizes. In this article, we develop an optimal design with respect to the expected total number of tests that can be obtained using a novel dynamic programming algorithm. We show that this algorithm is substantially more efficient than the approach proposed by Black et al. (2015). In addition, we compare the two designs for imperfect tests. R code is provided for the practitioner.

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arXiv2019

Statistical approaches using longitudinal biomarkers for disease early detection: A comparison of methodologies

Early detection of clinical outcomes such as cancer may be predicted based on longitudinal biomarker measurements. Tracking longitudinal biomarkers as a way to identify early disease onset may help to reduce mortality from diseases like ovarian cancer that are more treatable if detected early. Two general frameworks for disease risk prediction, the shared random effects model (SREM) and the pattern mixture model (PMM) could be used to assess longitudinal biomarkers on disease early detection. In this paper, we studied the predictive performances of SREM and PMM on disease early detection through an application to ovarian cancer, where early detection using the risk of ovarian cancer algorithm (ROCA) has been evaluated. Comparisons of the above three methods were performed via the analyses of the ovarian cancer data from the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial and extensive simulation studies. The time-dependent receiving operating characteristic (ROC) curve and its area (AUC) were used to evaluate the prediction accuracy. The out-of-sample predictive performance was calculated using leave-one-out cross-validation (LOOCV), aiming to minimize the problem of model over-fitting. A careful analysis of the use of the biomarker cancer antigen 125 for ovarian cancer early detection showed improved performance of PMM as compared with SREM and ROCA. More generally, simulation studies showed that PMM outperforms ROCA unless biomarkers are taken at very frequent screening settings.

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arXiv2017

Revisiting nested group testing procedures: new results, comparisons, and robustness

Group testing has its origin in the identification of syphilis in the US army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this paper, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article is available online.

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arXiv2015

A two-state mixed hidden Markov model for risky teenage driving behavior

This paper proposes a joint model for longitudinal binary and count outcomes. We apply the model to a unique longitudinal study of teen driving where risky driving behavior and the occurrence of crashes or near crashes are measured prospectively over the first 18 months of licensure. Of scientific interest is relating the two processes and predicting crash and near crash outcomes. We propose a two-state mixed hidden Markov model whereby the hidden state characterizes the mean for the joint longitudinal crash/near crash outcomes and elevated g-force events which are a proxy for risky driving. Heterogeneity is introduced in both the conditional model for the count outcomes and the hidden process using a shared random effect. An estimation procedure is presented using the forward-backward algorithm along with adaptive Gaussian quadrature to perform numerical integration. The estimation procedure readily yields hidden state probabilities as well as providing for a broad class of predictors.

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arXiv2015

Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian-Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored.

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arXiv2014

A note on the minimax solution for the two-stage group testing problem

Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations the exact value of the probability p of being affected is unknown. We present both minimax and Bayesian solutions for the group size problem when p is unknown. For unbounded p we show that the minimax solution for group size is 8, while using a Bayesian strategy with Jeffreys prior results in a group size of 13. We also present solutions when p is bounded from above. For the practitioner we propose strong justification for using a group size of between eight to thirteen when a constraint on p is not incorporated and provide useable code for computing the minimax group size under a constrained p.

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arXiv2012

Marginal analysis of longitudinal count data in long sequences: Methods and applications to a driving study

Most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small. Motivated by the Naturalistic Teenage Driving Study (NTDS), which represents the exact opposite situation, we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences. We consider standard methods based on generalized estimating equations, under working independence or an appropriate correlation structure, and find them unsatisfactory for dealing with time-dependent covariates when the counts are low. For this situation, we explore a within-cluster resampling (WCR) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples. This leads to a novel WCR method which operates on separated blocks within subjects and which performs better than all of the previously considered methods. The methods are applied to the NTDS data and evaluated in simulation experiments mimicking the NTDS.

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arXiv2010

An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.

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