Applying a data duplication technique in linear regression analysis of waiting time to pregnancy

This analysis demonstrates the application of a data duplication technique in linear regression with censored observations of the waiting time to third pregnancy ending in two outcome types, using data from Malaysia. The linear model not only confirmed the results obtained by the Cox proportional hazards model, but also identified two additional significant factors. The method provides a useful alternative when Cox proportionality assumption of the hazards is violated.     

Determinants and effects of waiting time to coitus.

Nonuse of contraception at first intercourse among adolescents is well documented in the adolescent sexuality research literature. This study provides a formal test of the hypothesis that an increase in the courtship period (i.e., waiting time to intercourse) increases the likelihood that a couple will discuss contraception and use it at first intercourse. The data analyzed are from personal interviews with 1,314 women aged 20-29 in the 1983 National Survey of Unmarried Women. The results are mixed about the effect of waiting time on contraceptive behavior, providing weak support for the hypothesis, but also elucidating individual and relative characteristics of the couples, such as age and education of the respective partners, that affected contraceptive behavior at first intercourse. Support for the hypothesis may prove more robust in data with different characteristics from the survey used here.     

A simple linear regression method for quantitative trait loci linkage analysis with censored observations

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.     

Linear regression analysis of censored medical costs

This paper deals with the problem of linear regression for medical cost data when some study subjects are not followed for the full duration of interest so that their total costs are unknown. Standard survival analysis techniques are ill-suited to this type of censoring. The familiar normal equations for the least-squares estimation are modified in several ways to properly account for the incompleteness of the data. The resulting estimators are shown to be consistent and asymptotically normal with easily estimated variance-covariance matrices. The proposed methodology can be used when the cost database contains only the total costs for those with complete follow-up. More efficient estimators are available when the cost data are recorded in multiple time intervals. A study on the medical cost for ovarian cancer is presented.     

Prediction in censored survival data: a comparison of the proportional hazards and linear regression models.

Although the analysis of censored survival data using the proportional hazards and linear regression models is common, there has been little work examining the ability of these estimators to predict time to failure. This is unfortunate, since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a Kaplan-Meier plot obtained by discretizing the variable. In this paper the predictive power of the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-202) proportional hazards estimator and the Buckley-James (1979, Biometrika 66, 429-436) censored regression estimator are compared. Using computer simulations and heuristic arguments, it is shown that the choice of method depends on the censoring proportion, strength of the regression, the form of the censoring distribution, and the form of the failure distribution. Several examples are provided to illustrate the usefulness of the methods.     

Applications of multiple imputation to the analysis of censored regression data.

The first part of the article reviews the Data Augmentation algorithm and presents two approximations to the Data Augmentation algorithm for the analysis of missing-data problems: the Poor Man's Data Augmentation algorithm and the Asymptotic Data Augmentation algorithm. These two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology. The performances of the censored regression algorithms are examined in a simulation study. It is found, up to the precision of the study, that the bias of both the Poor Man's and Asymptotic Data Augmentation estimators, as well as the Buckley-James estimator, does not appear to differ from zero. However, with regard to mean squared error, over a wide range of settings examined in this simulation study, the two Data Augmentation estimators have a smaller mean squared error than does the Buckley-James estimator. In addition, associated with the two Data Augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters. It is shown how this device can be used to estimate the standard error of either Data Augmentation estimate of any parameter (e.g., the correlation coefficient) associated with the model. In the simulation study, the estimated standard error of the Asymptotic Data Augmentation estimate of the regression parameter is found to be congruent with the Monte Carlo standard deviation of the corresponding parameter estimate. The algorithms are illustrated using the updated Stanford heart transplant data set.     

EPMLR: sequence-based linear B-cell epitope prediction method using multiple linear regression

Background

B-cell epitopes have been studied extensively due to their immunological applications, such as peptide-based vaccine development, antibody production, and disease diagnosis and therapy. Despite several decades of research, the accurate prediction of linear B-cell epitopes has remained a challenging task.

Results

In this work, based on the antigen’s primary sequence information, a novel linear B-cell epitope prediction model was developed using the multiple linear regression (MLR). A 10-fold cross-validation test on a large non-redundant dataset was performed to evaluate the performance of our model. To alleviate the problem caused by the noise of negative dataset, 300 experiments utilizing 300 sub-datasets were performed. We achieved overall sensitivity of 81.8%, precision of 64.1% and area under the receiver operating characteristic curve (AUC) of 0.728.

Conclusions

We have presented a reliable method for the identification of linear B cell epitope using antigen’s primary sequence information. Moreover, a web server EPMLR has been developed for linear B-cell epitope prediction: http://www.bioinfo.tsinghua.edu.cn/epitope/EPMLR/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0414-y) contains supplementary material, which is available to authorized users.     

Genetic progression and the waiting time to cancer

Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers may evolve through mutations in as many as 20 different cancer-associated genes. We use data published by Sjöblom et al. (2006) to develop a new mathematical model for the somatic evolution of colorectal cancers. We employ the Wright-Fisher process for exploring the basic parameters of this evolutionary process and derive an analytical approximation for the expected waiting time to the cancer phenotype. Our results highlight the relative importance of selection over both the size of the cell population at risk and the mutation rate. The model predicts that the observed genetic diversity of cancer genomes can arise under a normal mutation rate if the average selective advantage per mutation is on the order of 1%. Increased mutation rates due to genetic instability would allow even smaller selective advantages during tumorigenesis. The complexity of cancer progression can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth.     

Using conditional logistic regression to fit proportional odds models to interval censored data

An easily implemented approach to fitting the proportional odds regression model to interval-censored data is presented. The approach is based on using conditional logistic regression routines in standard statistical packages. Using conditional logistic regression allows the practitioner to sidestep complications that attend estimation of the baseline odds ratio function. The approach is applicable both for interval-censored data in settings in which examinations continue regardless of whether the event of interest has occurred and for current status data. The methodology is illustrated through an application to data from an AIDS study of the effect of treatment with ZDV+ddC versus ZDV alone on 50% drop in CD4 cell count from baseline level. Simulations are presented to assess the accuracy of the procedure.     

Regression analysis of doubly censored failure time data using the additive hazards model

Doubly censored failure time data arise when the survival time of interest is the elapsed time between two related events and observations on occurrences of both events could be censored. Regression analysis of doubly censored data has recently attracted considerable attention and for this a few methods have been proposed (Kim et al., 1993, Biometrics 49, 13-22; Sun et al., 1999, Biometrics 55, 909-914; Pan, 2001, Biometrics 57, 1245-1250). However, all of the methods are based on the proportional hazards model and it is well known that the proportional hazards model may not fit failure time data well sometimes. This article investigates regression analysis of such data using the additive hazards model and an estimating equation approach is proposed for inference about regression parameters of interest. The proposed method can be easily implemented and the properties of the proposed estimates of regression parameters are established. The method is applied to a set of doubly censored data from an AIDS cohort study.     

A simplified method to determine binding parameters in a two-site case using linear regression

A program using a simplified method to compute estimates of binding parameters in a system with two independent classes of binding sites is presented. An iterative method is used to approximate step-by-step the two lines describing the binding activities separately, starting from a curvilinear Scatchard or Hofstee plot. This method is designed for use on microcomputers with graphic facilities and on programmable hand-held calculators.     

Fitting piecewise linear regression functions to biological responses

An iterative approach was achieved for fitting piecewise linear functions to nonrectilinear responses of biological variables. This algorithm is used to estimate the parameters of the two (or more) regression functions and the separation point(s) (thresholds, sensitivities) by statistical approximation. Although it is often unknown whether the response of a biological variable is adequately described by one rectilinear regression function or by piecewise linear regression function(s) with separation point(s), an F test is proposed to determine whether one regression line is the optimal fitted function. A FORTRAN-77 program has been developed for estimating the optimal parameters and the coordinates of the separation point(s). A few sets of data illustrating this kind of problem in the analysis of thermoregulation, osmoregulation, and the neuronal responses are discussed.     

Optimization of the production of bacterial cellulose using multivariable linear regression analysis

The biosynthesis of bacterial cellulose by Acetobacter xylinum was optimized by numerically finding the maximum of an arbitrarily chosen second order polynomial model function of several variables (describing the dependence of the cellulose production on the concentrations of the medium components), using multivariable linear regression analysis. The chosen function appeared to describe the analyzed correlation sufficiently well. Consequently, three to six stages of optimization made the determination of the optimum medium compositions possible for 16 days of fermentation at 30°C in a medium based on fructose (wt%: fructose, 3.68; yeast extract, 5.02; (NH₄)₂NO₃, 0.001; KH₂PO₄, 0.3; MgSO₄ × 7 H₂O, 0.05; resulting in a cellulose production equal to 0.505 wt.% – namely 5.6 times higher than before the optimization) and for 7 days fermentations at 30°C in a medium based on sucrose and ethanol (wt.%: sucrose, 5.0; ethanol, 1.36; yeast extract, 1.27; (NH₄)₂SO₄, 0.5; KH₂PO₄, 0.3; MgSO₄ × 7 H₂O, 0.05; resulting in a cellulose production equal to 0.251 wt.% – namely 1.5 times higher than before the optimization).