Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Zero‐inflated Poisson factor model with application to microbiome read counts

Dimension reduction of high‐dimensional microbiome data facilitates subsequent analysis such as regression and clustering. Most existing reduction methods cannot fully accommodate the special features of the data such as count‐valued and excessive zero reads. We propose a zero‐inflated Poisson factor analysis model in this paper. The model assumes that microbiome read counts follow zero‐inflated Poisson distributions with library size as offset and Poisson rates negatively related to the inflated zero occurrences. The latent parameters of the model form a low‐rank matrix consisting of interpretable loadings and low‐dimensional scores that can be used for further analyses. We develop an efficient and robust expectation‐maximization algorithm for parameter estimation. We demonstrate the efficacy of the proposed method using comprehensive simulation studies. The application to the Oral Infections, Glucose Intolerance, and Insulin Resistance Study provides valuable insights into the relation between subgingival microbiome and periodontal disease.     

Biochemical analysis of retroviral structural proteins to identify and quantify retrovirus expressed by an NS0 murine myeloma cell line

A subclone of the NS0 murine myeloma cell line, frequently used to produce recombinant monoclonal antibodies, was found by a transmission electron microscopy method to express a surprisingly high titer of 10(11) retroviral particles per ml of culture supernatant. Infectivity assays showed a very low infectious titer with the restricted host range expected for a murine amphotropic retrovirus. A Western blot assay for the viral capsid protein was developed to confirm the high titer values and provide a means for monitoring batch consistency and virus removal during the purification process. Mass spectrometry of several of the viral Gag proteins demonstrated that the cell line appeared to produce at least two closely related retroviruses. N-terminal sequencing of three of the Gag proteins demonstrated that these retroviruses were members of the murine leukemia retroviral family. Western blot detection with an antibody for the capsid protein gave a linear standard curve over the range of 0.1-3 ng per lane. This allows the detection of viral titers as low as 6x10(7) virions per ml without the need to concentrate the sample. The Western blot method has higher throughput and less variability than transmission electron microscopy methods and has potential for monitoring viral titer and clearance during development of manufacturing processes.     

A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives

Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives.     

Efficacy estimates from parasite count data that include zero counts

Because of the positive skewness of parasite distributions and the greater constancy of percentage of response of therapy in animal populations, parasite count data are conventionally transformed logarithmically before combining results from different animals, either all controls or all treated. Observations of zero counts raise difficulties, since the logarithm of zero is not useful. In this study, several types of zero count adjustments are compared. Two systems for assigning values to zero counts were considered: a fixed system, which assigns the same value to all zero counts regardless of the proportion of such counts in a treatment group, and a variable system, which replaces zero counts with a value based on the proportion of zero counts in the group. The values assigned by either system are then adjusted to reflect aliquot size. An evaluation was performed by using 32 compound Poisson lognormal distributions, three sample sizes, and three representatives of each zero count adjustment system. The Poisson lognormal distribution provides a convenient method with which to provide variability greater than Poisson. Expected values of the sample estimate of the (known) population mean were calculated for each of the 576 combinations of these factors, and the bias associated with each combination was derived. The bias associated with the three representatives of the variable adjustment system was similar. The variable adjustment system had a lower overall bias than any representatives of the fixed adjustment system.     

Marginalized zero‐inflated Poisson models with missing covariates

Unlike zero‐inflated Poisson regression, marginalized zero‐inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school‐based fluoride mouthrinse program.     

Reliable RT-qPCR-based titration of retroviral and lentiviral vectors via quantification of residual vector plasmid DNA in samples

Objectives

To develop a method for reliable quantification of viral vectors, which is necessary for determining the optimal dose of vector particles in clinical trials to obtain the desired effects without severe unwanted immune responses.

Results

A significant level of vector plasmid remained in retroviral and lentiviral vector samples, which led to overestimation of viral titers when using the conventional RT-qPCR-based genomic titration method. To address this problem, we developed a new method in which the residual plasmid was quantified by an additional RT-qPCR step, and standard molecules and primer sets were optimized. The obtained counts were then used to correct the conventionally measured genomic titers of viral samples. While the conventional method produced significantly higher genomic titers for mutant retroviral vectors than for wild-type vectors, our method produced slightly higher or equivalent titers, corresponding with the general idea that mutation of viral components mostly results in reduced or, at best, retained titers.

Conclusion

Subtraction of the number of residual vector plasmid molecules from the conventionally measured genomic titer can yield reliable quantification of retroviral and lentiviral vector samples, a prerequisite to advancing the safety of gene therapy applications.

     

Safety of the production process of SURFACEN® to inactivate and remove virus

SURFACEN^® is a biological product produced from pig lungs. Since these animals can be potential sources of microbial pathogens such as viruses, the manufacturing process of this product should guarantee safety from health hazards. The SURFACEN^® production procedure is capable of effective viral clearance (inactivation/removal) by involving two stages of organic solvent extraction followed by acetone precipitation and heat treatment. In this study, we evaluated the clearance capacity of these four stages for a wide range of viruses by performing spiking experiments. Residual contamination was assessed using a Tissue Culture Infectious Dose assay (log₁₀ TCID₅₀). The validation study demonstrated that, for all viruses tested, the TCID₅₀ titers were reduced by more than 2 log₁₀ in each stage. Total log reduction values achieved were between ≥17.82 log₁₀ and ≥27.93 log₁₀, depending on the virus physical properties, titer, and the number of processing stages applied. Results indicated that the production procedure of SURFACEN^® can inactivate or remove contaminant viruses from the raw material.     

Systematic comparison of a color reporter gene and drug resistance genes for the determination of retroviral titers

Retroviral vectors usually contain drug resistance genes, which are used to select for infected cells and to determine the viral titers. The viral titer is referred to as colony-forming units (CFUs). Color reporter genes, such as thelacZ gene and the green fluorescent protein gene(gfp), have been widely used as markers in retroviral vectors. In this report, a simple and rapid method for the determination of retroviral titers has been developed. The number of viral particles capable of forming individual green cells per unit volume is defined as marker-forming units (MFUs). The MFUs determined by usinggfp as a marker were found to be proportional to the CFUs obtained by using drug selection for five different drug resistance genes. In addition, after adjusting the time factor, the MFUs are higher than CFUs in viruses released from 30 stable helper cell lines. The lower titers determined by CFUs are likely due to the toxicity on transduced cells.     

Distribution of viral abundance in the reef environment of Key Largo, Florida.

The distribution of viral and microbial abundance in the Key Largo, Fla., reef environment was measured. Viral abundance was measured by transmission electron microscope direct counts and plaque titer on specific bacterial hosts in water and sediment samples from Florida Bay (Blackwater Sound) and along a transect from Key Largo to the outer edge of the reef tract in Key Largo Sanctuary. Water column viral direct counts were highest in Blackwater Sound of Florida Bay (1.2 x 10(7) viruses per ml), decreased to the shelf break (1.7 x 10(6) viruses per ml), and were inversely correlated with salinity (r = -0.97). Viral direct counts in sediment samples ranged from 1.35 x 10(8) to 5.3 x 10(8)/cm(3) of sediment and averaged nearly 2 orders of magnitude greater than counts in the water column. Viral direct counts (both sediment and water column measurements) exceeded plaque titers on marine bacterial hosts (Vibrio natriegens and others) by 7 to 8 orders of magnitude. Water column viral abundance did not correlate with bacterial direct counts or chlorophyll a measurements, and sediment viral parameters did not correlate with water column microbial, viral, or salinity data. Coliphage, which are indicators of fecal pollution, were detected in two water column samples and most sediment samples, yet their concentrations were relatively low (<2 to 15/liter for water column samples, and <2 to 108/cm(3) of sediment). Our findings indicate that viruses are abundant in the Key Largo environment, particularly on the Florida Bay side of Key Largo, and that processes governing their distribution in the water column (i.e., salinity and freshwater input) are independent of those governing their distribution in the sediment environment.     

On the generalized poisson regression mixture model for mapping quantitative trait loci with count data

Statistical methods for mapping quantitative trait loci (QTL) have been extensively studied. While most existing methods assume normal distribution of the phenotype, the normality assumption could be easily violated when phenotypes are measured in counts. One natural choice to deal with count traits is to apply the classical Poisson regression model. However, conditional on covariates, the Poisson assumption of mean-variance equality may not be valid when data are potentially under- or overdispersed. In this article, we propose an interval-mapping approach for phenotypes measured in counts. We model the effects of QTL through a generalized Poisson regression model and develop efficient likelihood-based inference procedures. This approach, implemented with the EM algorithm, allows for a genomewide scan for the existence of QTL throughout the entire genome. The performance of the proposed method is evaluated through extensive simulation studies along with comparisons with existing approaches such as the Poisson regression and the generalized estimating equation approach. An application to a rice tiller number data set is given. Our approach provides a standard procedure for mapping QTL involved in the genetic control of complex traits measured in counts.     

Variability in Dengue Titer Estimates from Plaque Reduction Neutralization Tests Poses a Challenge to Epidemiological Studies and Vaccine Development

Background

Accurate determination of neutralization antibody titers supports epidemiological studies of dengue virus transmission and vaccine trials. Neutralization titers measured using the plaque reduction neutralization test (PRNT) are believed to provide a key measure of immunity to dengue viruses, however, the assay''s variability is poorly understood, making it difficult to interpret the significance of any assay reading. In addition there is limited standardization of the neutralization evaluation point or statistical model used to estimate titers across laboratories, with little understanding of the optimum approach.

Methodology/Principal Findings

We used repeated assays on the same two pools of serum using five different viruses (2,319 assays) to characterize the variability in the technique under identical experimental conditions. We also assessed the performance of multiple statistical models to interpolate continuous values of neutralization titer from discrete measurements from serial dilutions. We found that the variance in plaque reductions for individual dilutions was 0.016, equivalent to a 95% confidence interval of 0.45–0.95 for an observed plaque reduction of 0.7. We identified PRNT₇₅ as the optimum evaluation point with a variance of 0.025 (log₁₀ scale), indicating a titer reading of 1∶500 had 95% confidence intervals of 1∶240–1∶1000 (2.70±0.31 on a log₁₀ scale). The choice of statistical model was not important for the calculation of relative titers, however, cloglog regression out-performed alternatives where absolute titers are of interest. Finally, we estimated that only 0.7% of assays would falsely detect a four-fold difference in titers between acute and convalescent sera where no true difference exists.

Conclusions

Estimating and reporting assay uncertainty will aid the interpretation of individual titers. Laboratories should perform a small number of repeat assays to generate their own variability estimates. These could be used to calculate confidence intervals for all reported titers and allow benchmarking of assay performance.     

Zero-Inflated Poisson Models and C.A.MAN: A Tutorial Collection of Evidence

Analysis of count data is required in many areas of biometric interest. Often the simple Poisson distribution is not appropriate, since an extra-number of zero counts occur in the count data. Some current approaches for the problem at hand are reviewed. It will be argued that these situations can often be easily modeled using the zero-inflated Poisson distribution. A variety of applications are considered in which this occurs. Possibilities are outlined on how the validity of the zero-inflated Poisson can be validated including a comparison with the nonparametric Poisson mixture maximum likelihood estimator.     

Multiplex RT Q-PCR assay for simultaneous quantification of three viruses used for validation of virus clearance by biopharmaceutical production

Virus removal studies are used to insure the safety of biopharmaceutical products by quantitatively estimating the viral clearance capacity by the manufacturing process. Virus quantification assays are used to measure the log₁₀ clearance factor of individual purification unit operations in spike recovery studies. We have developed a multiplex RT Q-PCR assay that detects and quantifies three commonly used model viruses X-MuLV, SV40, and MMV simultaneously. This RT Q-PCR multiplex assay has a 6 log₁₀ dynamic range with a limit of detection (LOD) of ≈1 genome copy/μL. Amplification profiles are similar to existing singleplex assays. Overall, this RT Q-PCR multiplex assay is highly quantitative, accurately identifies multiple viruses simultaneously, and may prove useful to validate viral clearance of biological products in small scale studies.     

Characterization of ionic strength for X-MuLV inactivation by low pH treatment for monoclonal antibody purification

In the production of monoclonal antibodies (mAbs) intended for use in humans, it is a global regulatory requirement that the manufacturing process includes unit operations that are proven to inactivate or remove adventitious agents to ensure viral safety. Viral inactivation by low pH hold (LPH) is typically used to ensure this viral safety in the purification process of mAbs and other biotherapeutics derived from mammalian cell lines. To ascertain the effectiveness of the LPH step, viral clearance studies have evaluated LPH under worst-case conditions of pH above the manufacturing set point and hold duration at or below the manufacturing minimum. Highly acidic conditions (i.e., pH < 3.60) provide robust and effective enveloped virus inactivation but may lead to reduced product quality of the therapeutic protein. However, when viral inactivation is operated above pH 3.60 to ensure product stability, effective (>4 log₁₀ reduction factor) viral inactivation may not be observed under these worst-case pH conditions in viral clearance studies. A multivariate design of experiments was conducted to further characterize the operating space for low pH viral inactivation of a model retrovirus, xenotropic murine leukemia virus (X-MuLV). The statistically designed experiment evaluated the effect of mAb isotype, pH, temperature, acid titrant, sodium chloride (NaCl) concentration, virus spike timing, and post-spike filtration on X-MuLV inactivation. Data from the characterization study were used to generate predictive models to identify conditions that reliably achieve effective viral inactivation at pH ≥ 3.60. Results of the study demonstrated that NaCl concentration has the greatest effect on virus inactivation in the range studied, and pH has a large effect when the load material has no additional NaCl. Overall, robust and effective inactivation of X-MuLV at pH 3.65–3.80 can be achieved by manipulating either the pH or the NaCl concentration of the load material. This study contributes to the understanding of ionic strength as an influential parameter in low pH viral inactivation studies.     

A Bagging‐Based Correction for the Mixture Model Estimator of Population Size

Estimation of a population size by means of capture‐recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero‐truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so‐called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Protection from H1N1 Influenza Virus Infections in Mice by Supplementation with Selenium: A Comparison with Selenium-Deficient Mice

The present paper describes protective effects of supplemental selenium in mice infected with influenza virus. The effects of supplemental selenium on serum selenium levels, mortality, lung virus titers, and cytokine titers were investigated in mice inoculated intranasally with suspensions of influenza virus. Whereas the mortality of the virus-infected Se-deficient mice was 75%, along with a marked reduction in body weight, lower levels of TNF-α and IFN-γ and lower serum selenium concentrations, the mortality of mice maintained on feed containing 0.5 mg Se/kg in the form of sodium selenite was 25%.There were no significantly differences, however, in viral titer between the Se-adequate and the selenium-supplemented groups. The data indicate that selenium supplementation may provide a feasible approach to improving the immune response to viral infections, such as lethal influenza infection.     

抗体几何平均滴度计算中如何处理抗体阴性者？

不同作者在计算抗体几何平均滴度（ＧＭＴ）时，对抗体阴性者的处理方法不完全一致，共有三种：①将抗体阴性者的抗体滴度作为零纳入抗体ＧＭＴ计算；②将抗体阴性者不纳入计算；③用阳性界值的１／２作为阴性者的抗体滴度纳入计算。统计分析国内１１种医学杂志９２篇文献发现，科研机构和医学院校多用第三种方法（５７．１４％），省级和地市县级单位多用第一种方法（４４．８７％）。作者比较分析了三种方法的计算结果及优劣，认为第一种方法较适宜。     

Bayesian time-varying autoregressive models of COVID-19 epidemics

The COVID-19 pandemic has highlighted the importance of reliable statistical models which, based on the available data, can provide accurate forecasts and impact analysis of alternative policy measures. Here we propose Bayesian time-dependent Poisson autoregressive models that include time-varying coefficients to estimate the effect of policy covariates on disease counts. The model is applied to the observed series of new positive cases in Italy and in the United States. The results suggest that our proposed models are capable of capturing nonlinear growth of disease counts. We also find that policy measures and, in particular, closure policies and the distribution of vaccines, lead to a significant reduction in disease counts in both countries.     

An immunological assay for determination of baculovirus titers in 48 hours

Th baculovirus expression system is a system of choice for expressing eukaryotic proteins. Large amounts of biologically active material can be generated using this system by infecting insect cells with a baculovirus expressing the target protein. At several stages during the production of a baculovirus stock, it is necessary to titer the virus. Current methods have long time lines and are either technically difficult or are limited to viruses expressing a reporter gene. The new assay described here yields titers in 48 h, is easy to perform using 96-well plates, and is applicable to any Autographa californica nucleopolyhedrovirus-based recombinant baculovirus. This assay uses an antibody to a viral envelope glycoprotein to detect infected cells via immunostaining. The titer is determined by counting foci of infection under a light microscope. The required incubation period is shortened considerably because infected cells express viral antigens long before the macroscopic signs of infection scored in other assays become apparent. Titers determined using this immunological assay are comparable, both in value and variability, to those obtained using a traditional method, provided that the stocks have titers above 10(4) pfu/ml.