Cigarette smoking is a major cause of death worldwide resulting in over six million deaths per year. Cigarette smoke contains complex mixtures of chemicals that are harmful to nearly all organs of the human body, especially the lungs. Cigarette smoking is considered the major risk factor for many lung diseases, particularly chronic obstructive pulmonary diseases (COPD) and lung cancer. However, the underlying molecular mechanisms of smoking-induced lung injury associated with these lung diseases still remain largely unknown. Expression microarray techniques have been widely applied to detect the effects of smoking on gene expression in different human cells in the lungs. These projects have provided a lot of useful information for researchers to understand the potential molecular mechanism(s) of smoke-induced pathogenesis. However, a user-friendly web server that would allow scientists to fast query these data sets and compare the smoking effects on gene expression across different cells had not yet been established. For that reason, we have integrated eight public expression microarray data sets from trachea epithelial cells, large airway epithelial cells, small airway epithelial cells, and alveolar macrophage into an online web server called SEGEL (Smoking Effects on Gene Expression of Lung). Users can query gene expression patterns across these cells from smokers and nonsmokers by gene symbols, and find the effects of smoking on the gene expression of lungs from this web server. Sex difference in response to smoking is also shown. The relationship between the gene expression and cigarette smoking consumption were calculated and are shown in the server. The current version of SEGEL web server contains 42,400 annotated gene probe sets represented on the Affymetrix Human Genome U133 Plus 2.0 platform. SEGEL will be an invaluable resource for researchers interested in the effects of smoking on gene expression in the lungs. The server also provides useful information for drug development against smoking-related diseases. The SEGEL web server is available online at http://www.chengfeng.info/smoking_database.html.
The p16INK4a is an important tumor suppressor gene (TSG) and aberrant methylation of promoter is known to be a major inactivation mechanism of the tumor suppressor and tumor-related genes. Aberrant TSG methylation was considered an important epigenetic silencing mechanism in the progression of head and neck squamous cell carcinoma (HNSCC). However, some studies have reported differences in the methylation frequencies of P16INK4a promoter between cancer and the corresponding control group. Therefore, we conducted a meta-analysis to better identify the association.
PubMed, Ovid, ISI Web of Science, and EMBASE were searched to identify eligible studies to evaluate the association of p16INK4a promoter methylation and HNSCC. Odds ratio (ORs) and 95% confidence intervals (95%CI) were calculated to evaluate the strength of association between p16INK4a promoter methylation and HNSCC.
A total of twenty-one studies with 1155 cases and 1017 controls were included in the meta-analysis. The frequencies of p16INK4a promoter methylation in the cancer group were significantly higher than those in the control group (cancer group: median: 46.67%, range = 7.84%-95.12%; control group: median: 18.37%, range = 0–83.33%; respectively). The pooled odds ratio was 3.37 (95%CI = 2.32–4.90) in the cancer group versus the corresponding control group under the random-effects model.
This meta-analysis of 21 published studies identified that aberrant methylation of p16INK4a promoter was found to be significantly associated with HNSCC.
This article explores Bayesian joint models of event times and longitudinal measures with an attempt to overcome departures from normality of the longitudinal response, measurement errors, and shortages of confidence in specifying a parametric time-to-event model. We allow the longitudinal response to have a skew distribution in the presence of measurement errors, and assume the time-to-event variable to have a nonparametric prior distribution. Posterior distributions of the parameters are attained simultaneously for inference based on Bayesian approach. An example from a recent AIDS clinical trial illustrates the methodology by jointly modeling the viral dynamics and the time to decrease in CD4/CD8 ratio in the presence of CD4 counts with measurement errors and to compare potential models with various scenarios and different distribution specifications. The analysis outcome indicates that the time-varying CD4 covariate is closely related to the first-phase viral decay rate, but the time to CD4/CD8 decrease is not highly associated with either the two viral decay rates or the CD4 changing rate over time. These findings may provide some quantitative guidance to better understand the relationship of the virological and immunological responses to antiretroviral treatments.
Accelerated failure time model; Dirichlet process; Semiparametric linear/nonlinear mixed-effects model; Skew-elliptical distribution; Time-to-event
We propose a new method for family-based tests of association and linkage called transmission/disequilibrium tests incorporating unaffected offspring (TDTU). This new approach, constructed based on transmission/disequilibrium tests for quantitative traits (QTDT), provides a natural extension of the transmission/disequilibrium test (TDT) to utilize transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. TDTU can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. When the study sample contains only case-parent trios, the TDTU is equivalent to TDT. Informative-transmission disequilibrium test (i-TDT) and generalized disequilibrium test(GDT) are another two methods that can use information of both unaffected offspring and affected offspring. In contract to i-TDT and GDT, the test statistic of TDTU is simpler and more explicit, and can be implemented more easily. Through computer simulations, we demonstrate that power of the TDTU is slightly higher compared to i-TDT and GDT. All the three methods are more powerful than method that uses affected offspring only, suggesting that unaffected siblings also provide information about linkage and association.
Common problems to many longitudinal HIV/AIDS, cancer, vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection (LOD) may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models which can account for a high proportion of censored data should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left-censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left-censoring, skewness and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study.
measurement error; mixed-effects models; mixture Tobit models; skew distributions
To examine the association between early adolescent anxiety disorders and self-esteem development from early adolescence to young adulthood.
Self-esteem was measured at mean ages 13, 16 and 22 for 821 participants from the Children in the Community Study, a population-based longitudinal cohort. Anxiety disorders were measured at mean age 13 years. Multilevel growth models were employed to analyze the change in self-esteem from early adolescence to young adulthood and to evaluate whether adolescent anxiety disorders predict both average and slope of self-esteem development.
Self-esteem increased during adolescence and continued to increase in young adulthood. Girls had lower average self-esteem than boys, but this difference disappeared when examining the effect of anxiety. Adolescents with anxiety disorder had lower self-esteem, on average, compared with healthy adolescents (effect size (ES) =−0.35, p<0.01). Social phobia was found to have the greatest relative impact on average self-esteem (ES=−0.30, p<0.01), followed by overanxious disorder (ES=−0.17, p<0.05), and simple phobia (ES=−0.17, p<0.05). Obsessive compulsive-disorder (OCD) predicted a significant decline in self-esteem from adolescence to young-adulthood (
=−0.1, p<0.05). Separation anxiety disorder was not found to have any significant impact on self-esteem development.
All but one of the assessed adolescent anxiety disorders were related to lower self-esteem, with social phobia having the greatest impact. OCD predicted a decline in self-esteem trajectory with age. The importance of raising self-esteem in adolescents with anxiety and other mental disorders is discussed.
Anxiety disorder; Self-esteem development; Adolescence; Multilevel growth modeling; Longitudinal
The RAS association domain family protein 1a gene (RASSF1A) is one of the tumor suppressor genes (TSG). Inactivation of RASSF1A is critical to the pathogenesis of cancer. Aberrant TSG methylation was considered an important epigenetic silencing mechanism in the progression of ovarian cancer. A number of studies have discussed association between RASSF1A promoter methylation and ovarian cancer. However, they were mostly based on a small number of samples and showed inconsist results, Therefore, we conducted a meta-analysis to better identify the association.
Eligible studies were identified by searching the PubMed, EMBASE, Web of Science, and CNKI databases using a systematic searching strategy. We pooled the odds ratio (ORs) from individual studies using a fixed-effects model. We performed heterogeneity and publication bias analysis simultaneously.
Thirteen studies, with 763 ovarian cancer patients and 438 controls were included in the meta-analysis. The frequencies of RASSF1A promoter methylation ranged from 30% to 58% (median is 48%) in the cancer group and 0 to 21% (median is 0) in the control group. The frequencies of RASSF1A promoter methylation in the cancer group were significantly higher than those in the control group. The pooled odds ratio was 11.17 (95% CI = 7.51–16.61) in the cancer group versus the corresponding control group under the fixed-effects model.
The results suggested that RASSF1A promoter methylation had a strong association with ovarian cancer.
O6-methylguanine-DNA methyltransferase (MGMT) is one of most important DNA repair enzyme against common carcinogens such as alkylate and tobacco. Aberrant promoter methylation of the gene is frequently observed in non-small cell lung cancer (NSCLC). However, the importance of epigenetic inactivation of the gene in NSCLC published in the literature showed inconsistence. We quantified the association between MGMT promoter methylation and NSCLC using a meta-analysis method.
We systematically reviewed studies of MGMT promoter methylation and NSCLC in PubMed, EMBASE, Ovid, ISI Web of Science, Elsevier and CNKI databases and quantified the association between MGMT promoter methylation and NSCLC using meta-analysis method. Odds ratio (OR) and corresponding 95% confidence interval (CI) were calculated to evaluate the strength of association. Potential sources of heterogeneity were assessed by subgroup analysis and meta-regression.
A total of 18 studies from 2001 to 2011, with 1, 160 tumor tissues and 970 controls, were involved in the meta-analysis. The frequencies of MGMT promote methylation ranged from 1.5% to 70.0% (median, 26.1%) in NSCLC tissue and 0.0% to 55.0% (median, 2.4%) in non-cancerous control, respectively. The summary of OR was 4.43 (95% CI: 2.85, 6.89) in the random-effects model. With stratification by potential source of heterogeneity, the OR was 20.45 (95% CI: 5.83, 71.73) in heterogeneous control subgroup, while it was 4.16 (95% CI: 3.02, 5.72) in the autologous control subgroup. The OR was 5.31 (95% CI: 3.00, 9.41) in MSP subgroup and 3.06 (95% CI: 1.75, 5.33) in Q-MSP subgroup.
This meta-analysis identified a strong association between methylation of MGMT gene and NSCLC. Prospective studies should be required to confirm the results in the future.
Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models which enable us to account for between-subject and within-subject variations. To partially explain the variations, covariates are usually introduced to these models. Some covariates, however, may be often measured with substantial errors. It is often the case that model random error is assumed to be distributed normally, but the normality assumption may not always give robust and reliable results, particularly if the data exhibit skewness. Although there has been considerable interest in accommodating either skewness or covariate measurement error in the literature, there is relatively little work that considers both features simultaneously. In this article, our objectives are to address simultaneous impact of skewness and covariate measurement error by jointly modeling the response and covariate processes under a general framework of Bayesian semiparametric nonlinear mixed-effects models. The method is illustrated in an AIDS data example to compare potential models which have different distributional specifications. The findings from this study suggest that the models with a skew-normal distribution may provide more reasonable results if the data exhibit skewness and/or have measurement errors in covariates.
Bayesian approach; Covariate measurement errors; HIV/AIDS; Joint models; Longitudinal data; Semiparametric nonlinear mixed-effects models; Skew-normal distribution
Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiretroviral (ARV) treatment. Viral dynamic models can be formulated through a system of nonlinear ordinary differential equations (ODE), but there has been only limited development of statistical methodologies for inference. This paper, motivated by an AIDS clinical study, discusses a hierarchical Bayesian nonlinear mixed-effects modeling approach to dynamic ODE models without a closed-form solution. In this model we fully integrate viral load, medication adherence, drug resistance, pharmacokinetics, baseline covariates and time-dependent drug efficacy into the data analysis for characterizing long-term virologic responses. Our method is implemented by a data set from an AIDS clinical study. The results suggest that modeling HIV dynamics and virologic responses with consideration of time-varying clinical factors as well as baseline characteristics may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to ARV treatment and to help evaluation of clinical trial design in response to existing therapies.
Baseline characteristics; Bayesian nonlinear mixed-effects models; Long-term HIV dynamics; Longitudinal data; Time-varying drug efficacy; Treatment factors
HIV dynamic studies have contributed significantly to the understanding of HIV pathogenesis and antiviral treatment strategies for AIDS patients. Establishing the relationship of virologic responses with clinical factors and covariates during long-term antiretroviral (ARV) therapy is important to the development of effective treatments. Medication adherence is an important predictor of the effectiveness of ARV treatment, but an appropriate determinant of adherence rate based on medication event monitoring system (MEMS) data is critical to predict virologic outcomes. The primary objective of this paper is to investigate the effects of a number of summary determinants of MEMS adherence rates on virologic response measured repeatedly over time in HIV-infected patients. We developed a mechanism-based differential equation model with consideration of drug adherence, interacted by virus susceptibility to drug and baseline characteristics, to characterize the long-term virologic responses after initiation of therapy. This model fully integrates viral load, MEMS adherence, drug resistance and baseline covariates into the data analysis. In this study we employed the proposed model and associated Bayesian nonlinear mixed-effects modeling approach to assess how to efficiently use the MEMS adherence data for prediction of virologic response, and to evaluate the predicting power of each summary metric of the MEMS adherence rates. In particular, we intend to address the questions: (i) how to summarize the MEMS adherence data for efficient prediction of virologic response after accounting for potential confounding factors such as drug resistance and covariates, and (ii) how to evaluate treatment effect of baseline characteristics interacted with adherence and other clinical factors. The approach is applied to an AIDS clinical trial involving 31 patients who had available data as required for the proposed model. Results demonstrate that the appropriate determinants of MEMS adherence rates are important in order to more efficiently predict virologic response, and investigations of adherence to ARV treatment would benefit from measuring not only adherence rate but also its summary metric assessment. Our study also shows that the mechanism-based dynamic model is powerful and effective to establish a relationship of virologic responses with medication adherence, virus resistance to drug and baseline covariates.
Bayesian mixed-effects models; confounding factors; HIV dynamics; longitudinal data; MEMS adherence assessment; time-varying drug efficacy; virus resistance
It is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed-effects (SNLME) models with a normal distribution. Normality assumption of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models, but some covariates may often be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. Inferential procedures can be complicated dramatically when data with skewness, missing values, and measurement error are observed. In the literature, there has been considerable interest in accommodating either skewness, incompleteness or covariate measurement error in such models, but there has been relatively little study concerning all three features simultaneously. In this article, our objective is to address the simultaneous impact of skewness, missingness, and covariate measurement error by jointly modeling the response and covariate processes based on a flexible Bayesian SNLME model. The method is illustrated using a real AIDS data set to compare potential models with various scenarios and different distribution specifications.
Bayesian analysis; Covariate measurement errors; Longitudinal data; Missing data; Random-effects models; Skew distributions
In recent years, various mixed-effects models have been suggested for estimating viral decay rates in HIV dynamic models for complex longitudinal data. Among those models are linear mixed-effects (LME), nonlinear mixed-effects (NLME), and semiparametric nonlinear mixed-effects (SNLME) models. However, a critical question is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In addition, one often assumes that a model random error is normally distributed, but the normality assumption may be unrealistic, particularly if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. This paper addresses these issues simultaneously by jointly modeling the response variable with skewness and a covariate process with measurement errors using a Bayesian approach to investigate how estimated parameters are changed or different under these three models. A real data set from an AIDS clinical trial study was used to illustrate the proposed models and methods. It was found that there was a significant incongruity in the estimated decay rates in viral loads based on the three mixed-effects models, suggesting that the decay rates estimated by using Bayesian LME or NLME joint models should be interpreted differently from those estimated by using Bayesian SNLME joint models. The findings also suggest that the Bayesian SNLME joint model is preferred to other models because an arbitrary data truncation is not necessary; and it is also shown that the models with a skew-normal distribution and/or measurement errors in covariate may achieve reliable results when the data exhibit skewness.
Bayesian analysis; covariate measurement errors; HIV dynamics; mixed-effects joint models; skew-normal distribution
The study of HIV dynamics is one of the most important developments in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from AIDS clinical trials have not been addressed. In this paper, we use a simulation-based approach to deal with design problems in Bayesian hierarchical nonlinear (mixed-effects) models. The underlying model characterizes the long-term viral dynamics with antiretroviral treatment where we directly incorporate drug susceptibility and exposure into a function of treatment efficacy. The Bayesian design method is investigated under the framework of hierarchical Bayesian (mixed-effects) models. We compare a finite number of feasible candidate designs numerically, which are currently used in AIDS clinical trials from different perspectives, and provide guidance on how a design might be chosen in practice.
AIDS; Clinical trial simulation; HIV dynamics; Longitudinal data; mixed-effects models; Optimal design
A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiretroviral (ARV) therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but may be easily affected by clinical factors such as drug exposures and drug resistance as well as baseline characteristics during the long-term treatment evaluation process. HIV dynamic studies have significantly contributed to the understanding of HIV pathogenesis and ARV treatment strategies. Viral dynamic models can be formulated through differential equations, but there has been only limited development of statistical methodologies for estimating such models or assessing their agreement with observed data. This paper develops a mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy. In this model we not only incorporate clinical factors (drug exposures and susceptibility), but also baseline covariate (baseline viral load, CD4 count, weight or age) into a function of treatment efficacy. A Bayesian nonlinear mixed-effects modeling approach is investigated with application to an AIDS clinical trial study. The effects of confounding interaction of clinical factors with covariate-based models are compared using the Deviance Information Criteria (DIC), a Bayesian version of the classical deviance for model assessment, designed from complex hierarchical model settings. Relationships between baseline covariate combined with confounding clinical factors and drug efficacy are explored. In addition, we compared models incorporating each of four baseline covariates through DIC and some interesting findings are presented. Our results suggest that modeling HIV dynamics and virologic responses with consideration of time-varying clinical factors as well as baseline characteristics may play an important role in understanding HIV pathogenesis, designing new treatment strategies for long-term care of AIDS patients.
AIDS; Baseline characteristics; Bayesian nonlinear mixed-effects models; long-term HIV dynamics; longitudinal data; time-varying drug efficacy
The replication rate (or fitness) between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV). HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness.
Based on a mathematical model and several statistical methods (least-squares approach and measurement error models), a Web-based computing tool has been developed for improving estimation of virus fitness in growth competition assays of human immunodeficiency virus type 1 (HIV-1).
Unlike the two-point calculation used in previous studies, the estimation here uses linear regression methods with all observed data in the competition experiment to more accurately estimate relative viral fitness parameters. The dilution factor is introduced for making the computational tool more flexible to accommodate various experimental conditions. This Web-based tool is implemented in C# language with Microsoft ASP.NET, and is publicly available on the Web at http://bis.urmc.rochester.edu/vFitness/.
In this paper, the mechanism-based ordinary differential equation (ODE) model and the flexible semiparametric regression model are employed to identify the significant covariates for antiretroviral response in AIDS clinical trials. We consider the treatment effect as a function of three factors (or covariates) including pharmacokinetics, drug adherence and susceptibility. Both clinical and simulated data examples are given to illustrate these two different kinds of modeling approaches. We found that the ODE model is more powerful to model the mechanism-based nonlinear relationship between treatment effects and virological response biomarkers. The ODE model is also better in identifying the significant factors for virological response, although it is a little bit liberal and there is a trend to include more factors (or covariates) in the model. The semiparametric mixed-effects regression model is very flexible to fit the virological response data, but it is too liberal to identify correct factors for virological response; sometimes it may miss the correct factors. The ODE model is also biologically justifiable and good for predictions and simulations for various biological scenarios. The limitations of the ODE models include the high cost of computation and the requirement of biological assumptions that sometimes may not be easy to validate. The methodologies reviewed in this paper are also generally applicable to studies of other viruses such as hepatitis B virus (HBV) or hepatitis C virus (HCV).
Adherence; AIDS; antiretroviral therapy; Bayesian mixed-effects models; drug resistance; nonlinear mixed-effects models; pharmacodynamics; regression spline; semiparametric regression; viral dynamic models
HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.
Antiretroviral drug therapy; Bayesian mixed-effects models; Drug exposures; Drug resistance; HIV dynamics; MCMC; Parameter estimation
Human immunodeficiency virus type 1 (HIV-1) replication efficiency or fitness, as measured in cell culture, has been postulated to correlate with clinical outcome of HIV infection, although this is still controversial. One limitation is the lack of high-throughput assays that can measure replication efficiency over multiple rounds of replication. We have developed a multiple-cycle growth competition assay to measure HIV-1 replication efficiency that uses flow cytometry to determine the relative proportions of test and reference viruses, each of which expresses a different reporter gene in place of nef. The reporter genes are expressed on the surface of infected cells and are detected by commercially available fluorescence-labeled antibodies. This method is less labor-intensive than those that require isolation and amplification of nucleic acids. The two reporter gene products are detected with similar specificity and sensitivity, and the proportion of infected cells in culture correlates with the amount of viral p24 antigen produced in the culture supernatant. HIV replication efficiencies of six different drug-resistant site-directed mutants were reproducibly quantified and were similar to those obtained with a growth competition assay in which the relative proportion of each variant was measured by sequence analysis, indicating that recombination between the pol and reporter genes was negligible. This assay also reproducibly quantified the relative fitness conferred by protease and reverse transcriptase sequences containing multiple drug resistance mutations, amplified from patient plasma. This flow cytometry-based growth competition assay offers advantages over current assays for HIV replication efficiency and should prove useful for the evaluation of patient samples in clinical trials.
Growth competition assays have been developed to quantify the relative fitnesses of human immunodeficiency virus (HIV-1) mutants. In this article we develop mathematical models to describe viral/cellular dynamic interactions in the assay experiment, from which new competitive fitness indices or parameters are defined. These indices include the log fitness ratio (LFR), the log relative fitness (LRF), and the production rate ratio (PRR). From the population genetics perspective, we clarify the confusion and correct the inconsistency in the definition of relative fitness in the literature of HIV-1 viral fitness. The LFR and LRF are easier to estimate from the experimental data than the PRR, which was misleadingly defined as the relative fitness in recent HIV-1 research literature. Calculation and estimation methods based on two data points and multiple data points were proposed and were carefully studied. In particular, we suggest using both standard linear regression (method of least squares) and a measurement error model approach for more-accurate estimates of competitive fitness parameters from multiple data points. The developed methodologies are generally applicable to any growth competition assays. A user-friendly computational tool also has been developed and is publicly available on the World Wide Web at http://www.urmc.rochester.edu/bstools/vfitness/virusfitness.htm.