Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding.

Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research.

Assessing the impact of autologous neutralizing antibodies on viral rebound in postnatally SHIV-infected ART-treated infant rhesus macaques.

While the benefits of early antiretroviral therapy (ART) initiation in perinatally infected infants are well documented, early ART initiation is not always possible in postnatal pediatric HIV infections, which account for the majority of pediatric HIV cases worldwide. The timing of onset of ART initiation is likely to affect the size of the latent viral reservoir established, as well as the development of adaptive immune responses, such as the generation of neutralizing antibody responses against the virus. How these parameters impact the ability of infants to control viremia and the time to viral rebound after ART interruption is unclear. To gain insight into the dynamics, we utilized mathematical models to investigate the effect of time of ART initiation via latent reservoir size and autologous virus neutralizing antibody responses in delaying viral rebound when treatment is interrupted. We used an infant nonhuman primate Simian/Human Immunodeficiency Virus (SHIV) infection model that mimics breast milk HIV transmission in human infants. Infant Rhesus macaques (RMs) were orally challenged with SHIV.C.CH505 375H dCT and either given ART at 4-7 days post-infection (early ART condition), at 2 weeks post-infection (intermediate ART condition), or at 8 weeks post-infection (late ART condition). These infants were then monitored for up to 60 months post-infection with serial viral load and immune measurements. We develop a stochastic mathematical model to investigate the joint effect of latent reservoir size, the autologous neutralizing antibody potency, and CD4+ T cell levels on the time to viral rebound and control of post-rebound viral loads. We find that the latent reservoir size is an important determinant in explaining time to viral rebound by affecting the growth rate of the virus. The presence of neutralizing antibodies also can delay rebound, but we find this effect for high potency antibody responses only.

A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques.

The dynamics of HIV viral load following the initiation of antiretroviral therapy is not well-described by simple, single-phase exponential decay. Several mathematical models have been proposed to describe its more complex behavior, the most popular of which is two-phase exponential decay. The underlying assumption in two-phase exponential decay is that there are two classes of infected cells with different lifespans. However, with the exception of CD4+ T cells, there is not a consensus on all of the cell types that can become productively infected, and the fit of the two-phase exponential decay to observed data from SHIV.C.CH505 infected infant rhesus macaques was relatively poor. Therefore, we propose a new model for viral decay, inspired by the Gompertz model where the decay rate itself is a dynamic variable. We modify the Gompertz model to include a linear term that modulates the decay rate. We show that this simple model performs as well as the two-phase exponential decay model on HIV and SIV data sets, and outperforms it for the infant rhesus macaque SHIV.C.CH505 infection data set. We also show that by using a stochastic differential equation formulation, the modified Gompertz model can be interpreted as being driven by a population of infected cells with a continuous distribution of cell lifespans, and estimate this distribution for the SHIV.C.CH505-infected infant rhesus macaques. Thus, we find that the dynamics of viral decay in this model of infant HIV infection and treatment may be explained by a distribution of cell lifespans, rather than two distinct cell types.

Focused goodness of fit tests for gene set analyses.

Gene set-based signal detection analyses are used to detect an association between a trait and a set of genes by accumulating signals across the genes in the gene set. Since signal detection is concerned with identifying whether any of the genes in the gene set are non-null, a goodness-of-fit (GOF) test can be used to compare whether the observed distribution of gene-level tests within the gene set agrees with the theoretical null distribution. Here, we present a flexible gene set-based signal detection framework based on tail-focused GOF statistics. We show that the power of the various statistics in this framework depends critically on two parameters: the proportion of genes within the gene set that are non-null and the degree of separation between the null and alternative distributions of the gene-level tests. We give guidance on which statistic to choose for a given situation and implement the methods in a fast and user-friendly R package, wHC (https://github.com/mqzhanglab/wHC). Finally, we apply these methods to a whole exome sequencing study of amyotrophic lateral sclerosis.

Incorporating external information to improve sparse signal detection in rare-variant gene-set-based analyses.

Gene-set analyses are used to assess whether there is any evidence of association with disease among a set of biologically related genes. Such an analysis typically treats all genes within the sets similarly, even though there is substantial, external, information concerning the likely importance of each gene within each set. For example, for traits that are under purifying selection, we would expect genes showing extensive genic constraint to be more likely to be trait associated than unconstrained genes. Here we improve gene-set analyses by incorporating such external information into a higher-criticism-based signal detection analysis. We show that when this external information is predictive of whether a gene is associated with disease, our approach can lead to a significant increase in power. Further, our approach is particularly powerful when the signal is sparse, that is when only a small number of genes within the set are associated with the trait. We illustrate our approach with a gene-set analysis of amyotrophic lateral sclerosis (ALS) and implicate a number of gene-sets containing SOD1 and NEK1 as well as showing enrichment of small p values for gene-sets containing known ALS genes. We implement our approach in the R package wHC.

Bridging the gaps: using an NHP model to predict single dose radiation absorption in humans.

Purpose: Design and characterization of a radiation biodosimetry device are complicated by the fact that the requisite data are not available in the intended use population, namely humans exposed to a single, whole-body radiation dose. Instead, one must turn to model systems. We discuss our studies utilizing healthy, unexposed humans, human bone marrow transplant patients undergoing total body irradiation (TBI), non-human primates subjected to the same irradiation regimen received by the human TBI patients and NHPs given a single, whole-body dose of ionizing radiation.Materials and Methods: We use Bayesian linear mixed models to characterize the association between NHP and human expression patterns in radiation response genes when exposed to a common exposure regimen and across exposure regimens within the same species.Results: We show that population average differences in expression of our radiation response genes from one to another model system are comparable to typical differences between two randomly sampled members of a given model system and that these differences are smaller, on average, for linear combinations of the probe data and for the model-based combinations employed for dose prediction as part of a radiation biodosimetry device.Conclusions: Our analysis suggests that dose estimates based on our gene list will be accurate when applied to humans who have received a single, whole-body exposure to ionizing radiation.

Efficient estimation of grouped survival models.

BACKGROUND: Time- and dose-to-event phenotypes used in basic science and translational studies are commonly measured imprecisely or incompletely due to limitations of the experimental design or data collection schema. For example, drug-induced toxicities are not reported by the actual time or dose triggering the event, but rather are inferred from the cycle or dose to which the event is attributed. This exemplifies a prevalent type of imprecise measurement called grouped failure time, where times or doses are restricted to discrete increments. Failure to appropriately account for the grouped nature of the data, when present, may lead to biased analyses. RESULTS: We present groupedSurv, an R package which implements a statistically rigorous and computationally efficient approach for conducting genome-wide analyses based on grouped failure time phenotypes. Our approach accommodates adjustments for baseline covariates, and analysis at the variant or gene level. We illustrate the statistical properties of the approach and computational performance of the package by simulation. We present the results of a reanalysis of a published genome-wide study to identify common germline variants associated with the risk of taxane-induced peripheral neuropathy in breast cancer patients. CONCLUSIONS: groupedSurv enables fast and rigorous genome-wide analysis on the basis of grouped failure time phenotypes at the variant, gene or pathway level. The package is freely available under a public license through the Comprehensive R Archive Network.

Operative outcomes of conventional specimen radiography versus in-operating room specimen radiography in radioactive seed-localized segmental mastectomies.

INTRODUCTION: In-operating room specimen radiography (ORSR) has not been studied among women undergoing radioactive seed localization (RSL) for breast cancer surgery and had the potential to decrease operative time and perhaps improve intraoperative margin management. METHODS: One hundred consecutive RSL segmental mastectomies among 98 patients using ORSR were compared to 100 consecutive segmental mastectomies among 98 patients utilizing conventional radiography (CSR) prior to the initiation of ORSR from December 2013 to January 2015 after radioactive seed localization. Final pathologic margins were considered to be 10 mm for all cases of no residual disease after biopsy or neoadjuvant therapy, but such patients were excluded from analyses involving tumor size. All patients' specimens were subjected to intraoperative pathologic consultation in addition to ORSR or CSR. RESULTS: The median age of the cohort was 65 years (range 36-97), and the median tumor size was 1 cm. There were no differences between the ORSR and CSR groups in age, tumor size, percentage of cases with only DCIS, and percentage of cases with microcalcifications. The ORSR group had a statistically significant lower BMI. Mean operative time from cut-to-close was not significantly different (ORSR 77 min, SD 24.8 vs CSR 76 min, SD 24.8, p = 0.75). There was no statistical difference in mean closest final pathologic margin (4.99 mm, SD 3.3 vs 4.88 mm, SD 3.5, p = 0.9). The percentage undergoing intraoperative margin re-excision (ORSR 40%, CR 47%, p = 0.31) and the mean total number of margins excised intraoperatively (ORSR 0.9, CR 1.0 p = 0.65) were similar. The rate of any margin <2 mm was 14% vs 12% for ORSR and CR, respectively (p = 0.64). The mean specimen volume for ORSR was 76cm3 (SD 101.8) vs 90cm3 (SD 61.2) for CSR; this difference was not statistically significant (p = 0.25). The mean ratio of segmental mastectomy volume to maximum tumor diameter was less for ORSR (82.7cm2 vs 139.4cm2, p = 0.014). CONCLUSION: ORSR for RSL breast surgery, in the setting of routine intraoperative pathology consultation, does not significantly impact operative time, the rate or number of additional intraoperative margins excised, the number of reoperations for margins, or the width of final pathological margins. ORSR was associated with a decrease in the volume of segmental mastectomies relative to the tumor diameter.

Exploiting expression patterns across multiple tissues to map expression quantitative trait loci.

BACKGROUND: In order to better understand complex diseases, it is important to understand how genetic variation in the regulatory regions affects gene expression. Genetic variants found in these regulatory regions have been shown to activate transcription in a tissue-specific manner. Therefore, it is important to map the aforementioned expression quantitative trait loci (eQTL) using a statistically disciplined approach that jointly models all the tissues and makes use of all the information available to maximize the power of eQTL mapping. In this context, we are proposing a score test-based approach where we model tissue-specificity as a random effect and investigate an overall shift in the gene expression combined with tissue-specific effects due to genetic variants. RESULTS: Our approach has 1) a distinct computational edge, and 2) comparable performance in terms of statistical power over other currently existing joint modeling approaches such as MetaTissue eQTL and eQTL-BMA. Using simulations, we show that our method increases the power to detect eQTLs when compared to a tissue-by-tissue approach and can exceed the performance, in terms of computational speed, of MetaTissue eQTL and eQTL-BMA. We apply our method to two publicly available expression datasets from normal human brains, one comprised of four brain regions from 150 neuropathologically normal samples and another comprised of ten brain regions from 134 neuropathologically normal samples, and show that by using our method and jointly analyzing multiple brain regions, we identify eQTLs within more genes when compared to three often used existing methods. CONCLUSIONS: Since we employ a score test-based approach, there is no need for parameter estimation under the alternative hypothesis. As a result, model parameters only have to be estimated once per genome, significantly decreasing computation time. Our method also accommodates the analysis of next- generation sequencing data. As an example, by modeling gene transcripts in an analogous fashion to tissues in our current formulation one would be able to test for both a variant overall effect across all isoforms of a gene as well as transcript-specific effects. We implement our approach within the R package JAGUAR, which is now available at the Comprehensive R Archive Network repository.

Robust analysis of secondary phenotypes in case-control genetic association studies.

The case-control study is a common design for assessing the association between genetic exposures and a disease phenotype. Though association with a given (case-control) phenotype is always of primary interest, there is often considerable interest in assessing relationships between genetic exposures and other (secondary) phenotypes. However, the case-control sample represents a biased sample from the general population. As a result, if this sampling framework is not correctly taken into account, analyses estimating the effect of exposures on secondary phenotypes can be biased leading to incorrect inference. In this paper, we address this problem and propose a general approach for estimating and testing the population effect of a genetic variant on a secondary phenotype. Our approach is based on inverse probability weighted estimating equations, where the weights depend on genotype and the secondary phenotype. We show that, though slightly less efficient than a full likelihood-based analysis when the likelihood is correctly specified, it is substantially more robust to model misspecification, and can out-perform likelihood-based analysis, both in terms of validity and power, when the model is misspecified. We illustrate our approach with an application to a case-control study extracted from the Framingham Heart Study. Copyright © 2016 John Wiley & Sons, Ltd.

Ten Years of Routine α- and ß-Globin Gene Sequencing in UK Hemoglobinopathy Referrals Reveals 60 Novel Mutations.

We review and report here the genotypes and phenotypes of 60 novel thalassemia and abnormal hemoglobin (Hb) mutations discovered following the adoption of routine DNA sequencing of both α- and ß-globin genes for all UK hemoglobinopathy samples referred for molecular investigation. This screening strategy over the last 10 years has revealed a total of 11 new ß chain variants, 15 α chain variants, 19 ß-thalassemia (ß-thal) mutations and 15 α(+)-thalassemia (α(+)-thal) mutations. The large number of new thalassemia alleles confirms the wide racial heterogeneity of mutations in the UK immigrant population. Eleven of the new variants ran with Hb A on high performance liquid chromatography (HPLC), demonstrating the value of routine sequencing of both α- and ß-globin genes for all hemoglobinopathy investigations. The new ß chain variants are: Hb Bury [ß22(B4)Glu → Asp (HBB: c.69A > T)], Hb Fulwood [ß35(C1)Tyr → His (HBB: c.106T > C)], Hb Little Venice [ß42(CD1)Phe → Cys (HBB: c.128T > G)], Hb Cork [ß57(E1)Asn → Ser (HBB: c.173A > G), Hb Basingstoke [ß118(GH1)Phe → Ser (HBB: c.356T > C)], Hb Howden [ß20(B2)Val → Ala (HBB: c.62T > C)], Hb Wilton [ß41(C7)Phe → Leu (HBB: c.126C > A)], Hb Belsize Park [ß120(GH3)Lys → Asn (HBB: c.363A > T)], Hb Hampstead Heath [ß2(NA2)His → Gln;ß26(B8)Glu → Lys (HBB: c.[6C > G;79G > A])], Hb Grantham [ß85(F1)Phe → Cys (HBB: c.257T > G)] and Hb Calgary [ß64(E8)Gly → Val (HBB: c.194G > T). The new α chain variants are: Hb Edinburgh [α70(E19)Val → Gly (HBA2: c.212T > G)], Hb Walsgrave [α116(GH4)Glu → Val (HBA2: c.350A > T)], Hb Wexham [α117(GH5) and 118(H1) insertion Ser (HBA1: c.354-355insTCA)], Hb Coombe Park [α127(H10)Lys → Glu (HBA2: c.382A > G)], Hb Oxford [α17(A15)Val → Asp (HBA2: c.53T > A)], Hb Bridlington [α32(B13)Met → Thr (HBA1: c.98T > C), Hb Wolverhampton [α81(F2)Ser → Tyr (HBA2: c.9245C > A)], Hb Little Waltham [α13(A11)Ala → Asp (HBA2: c.41C > A)], Hb Derby [α61(E10)Lys → Arg (HBA1: c.185A > G)], Hb Uttoxter [α74(EF3)Tyr → Asp (HBA2: c.223G > T)], Hb Harehills [α124(H7)Ser → Cys (HBA1: c.374C > G)], Hb Hekinan II [α27(B8)Glu → Asp (HBA1: c.84G > T)], Hb Manitoba IV [α102(G9)Ser → Arg (HBA1: c.307A > C), Hb Witham [α139(HC1)Lys → Arg (HBA2: c.419A > G) and Hb Farnborough [α9(A7)Asn → Asp (HBA1: c.28A > G). In addition, 10 more paralogous α-globin chain variants have been discovered. The novel ß-thal alleles are: HBB: c.-138C > G, HBB: c.-121C > T, HBB: c.-80T > G, HBB: c.18_19delTG, HBB: c.219_220insT, HBB: c.315 + 2_315 + 13delTGAGTCTATGGG, HBB: c.316-70C > G, HBB: c.345_346insTGTGCTG, HBB: c.354delC, HBB: c.376-381delCCAGTG, HBB: c.393T > A, HBB: c.394_395insA, HBB: c.375_376insA, HBB: c.*+95_*+107delTGGATTCTinsC, HBB: c.* + 111_*+112delAA, HBB: c.*+112A > T, HBB: c.394C > T, HBB: c.271delG and HBB: c.316-3C > T. The novel α (+ )-thal alleles are: HBA1: c.95+1G > C, HBA1: c.315C > G [Hb Donnington, α104(G11)Cys → Trp], HBA1: c.327delC, HBA1: c.333_345del, HBA1: c.*+96G > A, HBA2: c.2T > G, HBA2: c.112delC, HBA2: c.143delA, HBA2: c.143_146delACCT, HBA2: c.156_157insG, HBA2: c.220_223delGTGG, HBA2: c.305T > C [Hb Bishopstown, α101(G8)Leu → His], HBA2: c.169_170delAA, HBA2: c.1A > T and HBA2: c.-3delA.

Testing the effect of rare compound-heterozygous and recessive mutations in case--parent sequencing studies.

Compound heterozygous mutations are mutations that occur on different copies of genes and may completely "knock-out" gene function. Compound heterozygous mutations have been implicated in a large number of diseases, but there are few statistical methods for analyzing their role in disease, especially when such mutations are rare. A major barrier is that phase information is required to determine whether both gene copies are affected and phasing rare variants is difficult. Here, we propose a method to test compound heterozygous and recessive disease models in case-parent trios. We propose a simple algorithm for phasing and show via simulations that tests based on phased trios have almost the same power as tests using true phase information. A further complication in the study of compound heterozygous mutations is that only families where both parents carry mutations are informative. Thus, the informative sample size will be quite small even when the overall sample size is not, making asymptotic approximations of the null distribution of the test statistic inappropriate. To address this, we develop an exact test that will give appropriate P-values regardless of sample size. Using simulation, we show that our method is robust to population stratification and significantly outperforms other methods when the causal model is recessive.

Testing for risk and protective trends in genetic analyses of HIV acquisition.

Host genetics studies of HIV-1 acquisition are critically important for the identification of new targets for drug and vaccine development. Analyses of such studies typically focus on pairwise comparisons of three different groups: HIV-1 positive individuals, HIV-1 high-risk seronegative individuals, and population controls. Because there is a clear expectation of how gene frequencies of risk or protective alleles would be ordered in the three groups, we are able to construct a statistical framework that offers a consistent increase in power over a wide-range of the magnitude of risk/protective effects. In this paper, we develop tests that constrain the alternative hypothesis to appropriately reflect risk or protective trends jointly across the three groups and show that they lead to a substantial increase in power over the naive pairwise approach. We develop both likelihood-ratio and score statistics that test for genetic effects across the three groups while constraining the alternative hypothesis to reflect biologically motivated trends of risk or protection. The asymptotic distribution of both statistics (likelihood ratio and score) is derived. We investigate the performance of our approach via extensive simulation studies using a biologically motivated model of HIV-1 acquisition, and find that our proposed approach leads to an increase in power of roughly 10-28%. We illustrate our approach with an analysis of the effect of the CCR5Δ32 mutation on HIV acquisition.

Multiplex ligation-dependent probe amplification identification of 17 different beta-globin gene deletions (including four novel mutations) in the UK population.

Large deletions of the beta-globin gene cluster are problematic to diagnose, and consequently the frequency and range of these mutations in the UK is unknown. Here we present a study evaluating the efficacy of the recently available technique of multiplex ligation-dependent prob amplification (MLPA) to determine the range and frequency of these deletions in the UK population. The results revealed a large deletion mutation in 75 of 316 patient samples collected over a 3-year period. Of these, 52 had a common (deltabeta)(0)-thalassemia [(deltabeta)(0)-thal] or hereditary persistence of fetal hemoglobin (HPFH) allele and 23 had rare or novel deletions resulting in (epsilon(G)gamma(A)gammadeltabeta)(0)-thal, (G)gamma(A)gamma(deltabeta)(0)-thal and beta(0)-thal. A total of 17 different deletions were found, 10 of which were rare and four were most likely novel [Asian Indian (epsilon(G)gamma(A)gammadeltabeta)(0)-thal, African (deltabeta)(0)-thal, African beta(0)-thal and Afghanistani beta(0)-thal]. The MLPA technique detected examples from all four categories of beta-globin gene deletions and demonstrated the wide molecular basis of deletional beta-thal/HPFH in UK patients.

Incidence of haemoglobinopathies in various populations - the impact of immigration.

OBJECTIVES: The aim of this study was to update the incidence data of beta thalassaemia mutations in various populations and compare it to the spectrum of mutations in the United Kingdom (UK) population in order to determine the impact of immigration. DESIGN AND METHODS: Published data for the beta-thalassaemia mutation spectrum and allele frequencies for 60 other countries was updated and collated into regional tables. The beta-thalassaemia mutations in the UK population have been characterised in 1712 unrelated carriers referred for antenatal screening. Similarly, the alpha-thalassaemia mutations in the UK population have been characterised in 2500 possible alpha-thalassaemia carriers. RESULTS: A total of 68 different beta-thalassaemia mutations were identified in couples requiring screening for antenatal diagnosis in the UK population. Of these mutations, 59 were found in immigrants to the UK, from all major ethnic groups with a high incidence of haemoglobinopathies. A total of 40 different alpha-thalassaemia mutations were characterised in the UK population. Ten deletion mutations were identified, including all the Southeast Asian and Mediterranean alpha(0)-thalassaemia mutations. In addition, 30 non-deletion alpha(+)-thalassaemia mutations were discovered, accounting for 46% of the worldwide known non-deletion mutations. CONCLUSIONS: The impact of immigration has resulted in the UK population having a higher number of beta-thalassaemia mutations and alpha-thalassaemia mutations than any of the 60 other countries with a published spectrum of mutations, including both endemic countries and the non-endemic countries of Northern Europe. The racial heterogeneity of the immigrant population in a non-endemic country significantly increases the spectrum of haemoglobinopathy mutations and their combinations found in individuals, making the provision of a molecular diagnostic prenatal diagnosis service more challenging.