Correcting for measurement error in individual-level covariates in nonlinear mixed effects models

The nonlinear mixed effects model is used to represent data in pharmacokinetics, viral dynamics, and other areas where an objective is to elucidate associations among individual-specific model parameters and covariates; however, covariates may be measured with error. For additive measurement error, we show substitution of mismeasured covariates for true covariates may lead to biased estimators for fixed effects and random effects covariance parameters, while regression calibration may eliminate bias in fixed effects but fail to correct that in covariance parameters. We develop methods to take account of measurement error that correct this bias and may be implemented with standard software, and we demonstrate their utility via simulation and application to data from a study of HIV dynamics.     

Experimental evaluation of the relationship between lethal or non-lethal virulence and transmission success in malaria parasite infections

Background

Theoretical studies suggest that direct and indirect selection have the potential to cause substantial evolutionary change in female mate choice. Similarly, sexual selection is considered a strong force in the evolution of male attractiveness and the exaggeration of secondary sexual traits. Few studies have, however, directly tested how female mate choice and male attractiveness respond to selection. Here we report the results of a selection experiment in which we selected directly on female mating preference for attractive males and, independently, on male attractiveness in the guppy, Poecilia reticulata. We measured the direct and correlated responses of female mate choice and male attractiveness to selection and the correlated responses of male ornamental traits, female fecundity and adult male and female survival.

Results

Surprisingly, neither female mate choice nor male attractiveness responded significantly to direct or to indirect selection. Fecundity did differ significantly among lines in a way that suggests a possible sexually-antagonistic cost to male attractiveness.

Conclusions

The opportunity for evolutionary change in female mate choice and male attractiveness may be much smaller than predicted by current theory, and may thus have important consequences for how we understand the evolution of female mate choice and male attractiveness. We discuss a number of factors that may have constrained the response of female choice and male attractiveness to selection, including low heritabilities, low levels of genetic (co)variation in the multivariate direction of selection, sexually-antagonistic constraint on sexual selection and the "environmental covariance hypothesis".

     

Structural and functional analysis of the C-terminal STAS (sulfate transporter and anti-sigma antagonist) domain of the Arabidopsis thaliana sulfate transporter SULTR1.2

The C-terminal region of sulfate transporters from plants and animals belonging to the SLC26 family members shares a weak but significant similarity with the Bacillus sp. anti-anti-sigma protein SpoIIAA, thus defining the STAS domain (sulfate transporter and anti-sigma antagonist). The present study is a structure/function analysis of the STAS domain of SULTR1.2, an Arabidopsis thaliana sulfate transporter. A three-dimensional model of the SULTR1.2 STAS domain was built which indicated that it shares the SpoIIAA folds. Moreover, the phosphorylation site, which is necessary for SpoIIAA activity, is conserved in the SULTR1.2 STAS domain. The model was used to direct mutagenesis studies using a yeast mutant defective for sulfate transport. Truncation of the whole SULTR1.2 STAS domain resulted in the loss of sulfate transport function. Analyses of small deletions and mutations showed that the C-terminal tail of the SULTR1.2 STAS domain and particularly two cysteine residues plays an important role in sulfate transport by SULTR1.2. All the substitutions made at the putative phosphorylation site Thr-587 led to a complete loss of the sulfate transport function of SULTR1.2. The reduction or suppression of sulfate transport of the SULTR1.2 mutants in yeast was not due to an incorrect targeting to the plasma membrane. Both our three-dimensional modeling and mutational analyses strengthen the hypothesis that the SULTR1.2 STAS domain is involved in protein-protein interactions that could control sulfate transport.     

An estimator for the proportional hazards model with multiple longitudinal covariates measured with error

In many longitudinal studies, it is of interest to characterize the relationship between a time-to-event (e.g. survival) and several time-dependent and time-independent covariates. Time-dependent covariates are generally observed intermittently and with error. For a single time-dependent covariate, a popular approach is to assume a joint longitudinal data-survival model, where the time-dependent covariate follows a linear mixed effects model and the hazard of failure depends on random effects and time-independent covariates via a proportional hazards relationship. Regression calibration and likelihood or Bayesian methods have been advocated for implementation; however, generalization to more than one time-dependent covariate may become prohibitive. For a single time-dependent covariate, Tsiatis and Davidian (2001) have proposed an approach that is easily implemented and does not require an assumption on the distribution of the random effects. This technique may be generalized to multiple, possibly correlated, time-dependent covariates, as we demonstrate. We illustrate the approach via simulation and by application to data from an HIV clinical trial.     

A general framework for subgroup detection via one-step value difference estimation

Recent statistical methodology for precision medicine has focused on either identification of subgroups with enhanced treatment effects or estimating optimal treatment decision rules so that treatment is allocated in a way that maximizes, on average, predefined patient outcomes. Less attention has been given to subgroup testing, which involves evaluation of whether at least a subgroup of the population benefits from an investigative treatment, compared to some control or standard of care. In this work, we propose a general framework for testing for the existence of a subgroup with enhanced treatment effects based on the difference of the estimated value functions under an estimated optimal treatment regime and a fixed regime that assigns everyone to the same treatment. Our proposed test does not require specification of the parametric form of the subgroup and allows heterogeneous treatment effects within the subgroup. The test applies to cases when the outcome of interest is either a time-to-event or a (uncensored) scalar, and is valid at the exceptional law. To demonstrate the empirical performance of the proposed test, we study the type I error and power of the test statistics in simulations and also apply our test to data from a Phase III trial in patients with hematological malignancies.     

Linear mixed models with flexible distributions of random effects for longitudinal data

Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics 55, 363-390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.     

Estimation and Prediction With HIV-Treatment Interruption Data

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.     

Unequal functional redundancy between the two Arabidopsis thaliana high-affinity sulphate transporters SULTR1;1 and SULTR1;2

* In Arabidopsis, SULTR1;1 and SULTR1;2 are two genes proposed to be involved in high-affinity sulphate uptake from the soil solution. We address here the specific issue of their functional redundancy for the uptake of sulphate and for the accumulation of its toxic analogue selenate with regard to plant growth and selenate tolerance. * Using the complete set of genotypes, including the wild-type, each one of the single sultr1;1 and sultr1;2 mutants and the resulting double sultr1;1-sultr1;2 mutant, we performed a detailed phenotypic analysis of root length, shoot biomass, sulphate uptake, sulphate and selenate accumulation and selenate tolerance. * The results all ordered the four different genotypes according to the same functional hierarchy. Wild-type and sultr1;1 mutant plants displayed similar phenotypes. By contrast, sultr1;1-sultr1;2 double-mutant plants showed the most extreme phenotype and the sultr1;2 mutant displayed intermediate performances. Additionally, the degree of selenate tolerance was directly related to the seedling selenate content according to a single sigmoid regression curve common to all the genotypes. * The SULTR1;1 and SULTR1;2 genes display unequal functional redundancy, which leaves open for SULTR1;1 the possibility of displaying an additional function besides its role in sulphate membrane transport.     

Pseudomonas aeruginosa diaminopimelate decarboxylase: evolutionary relationship with other amino acid decarboxylases

The lysA gene encodes meso-diaminopimelate (DAP) decarboxylase (E.C.4.1.1.20), the last enzyme of the lysine biosynthetic pathway in bacteria. We have determined the nucleotide sequence of the lysA gene from Pseudomonas aeruginosa. Comparison of the deduced amino acid sequence of the lysA gene product revealed extensive similarity with the sequences of the functionally equivalent enzymes from Escherichia coli and Corynebacterium glutamicum. Even though both P. aeruginosa and E. coli are Gram-negative bacteria, sequence comparisons indicate a greater similarity between enzymes of P. aeruginosa and the Gram- positive bacterium C. glutamicum than between those of P. aeruginosa and E. coli enzymes. Comparison of DAP decarboxylase with protein sequences present in data bases revealed that bacterial DAP decarboxylases are homologous to mouse (Mus musculus) ornithine decarboxylase (E.C.4.1.1.17), the key enzyme in polyamine biosynthesis in mammals. On the other hand, no similarity was detected between DAP decarboxylases and other bacterial amino acid decarboxylases.