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People living with HIV on antiretroviral therapy often have undetectable virus levels by standard assays, but "latent" HIV still persists in viral reservoirs. Eliminating these reservoirs is the goal of HIV cure research. The quantitative viral outgrowth assay (QVOA) is commonly used to estimate the reservoir size, that is, the infectious units per million (IUPM) of HIV-persistent resting CD4+ T cells. A new variation of the QVOA, the ultra deep sequencing assay of the outgrowth virus (UDSA), was recently developed that further quantifies the number of viral lineages within a subset of infected wells. Performing the UDSA on a subset of wells provides additional information that can improve IUPM estimation. This paper considers statistical inference about the IUPM from combined dilution assay (QVOA) and deep viral sequencing (UDSA) data, even when some deep sequencing data are missing. Methods are proposed to accommodate assays with wells sequenced at multiple dilution levels and with imperfect sensitivity and specificity, and a novel bias-corrected estimator is included for small samples. The proposed methods are evaluated in a simulation study, applied to data from the University of North Carolina HIV Cure Center, and implemented in the open-source R package SLDeepAssay. [ABSTRACT FROM AUTHOR]

Motivated by an analysis of single molecular experiments in the study of T‐cell signaling, a new model called varying coefficient frailty model with local linear estimation is proposed. Frailty models have been extensively studied, but extensions to nonconstant coefficients are limited to spline‐based methods that tend to produce estimation bias near the boundary. To address this problem, we introduce a local polynomial kernel smoothing technique with a modified expectation‐maximization algorithm to estimate the unknown parameters. Theoretical properties of the estimators, including their unbiased property near the boundary, are derived along with discussions on the asymptotic bias‐variance trade‐off. The finite sample performance is examined by simulation studies, and comparisons with existing spline‐based approaches are conducted to show the potential advantages of the proposed approach. The proposed method is implemented for the analysis of T‐cell signaling. The fitted varying coefficient model provides a rigorous quantification of an early and rapid impact on T‐cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses. [ABSTRACT FROM AUTHOR]