Improved estimation in negative binomial regression.

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn affects inference on mean parameters. This article proposes inference for negative binomial regression based on adjustments of the score function aimed at mean or median bias reduction. The resulting estimating equations generalize those available for improved inference in generalized linear models and can be solved using a suitable extension of iterative weighted least squares. Simulation studies confirm the good properties of the new methods, which are also found to solve in many cases numerical problems of maximum likelihood estimation. The methods are illustrated and evaluated using two case studies: an Ames salmonella assay data set and data on epileptic seizures. Inference based on adjusted scores turns out to generally improve on maximum likelihood, and even on explicit bias correction, with median bias reduction being overall preferable.

Median bias reduction in random-effects meta-analysis and meta-regression.

The reduction of the mean or median bias of the maximum likelihood estimator in regular parametric models can be achieved through the additive adjustment of the score equations. In this paper, we derive the adjusted score equations for median bias reduction in random-effects meta-analysis and meta-regression models and derive efficient estimation algorithms. The median bias-reducing adjusted score functions are found to be the derivatives of a penalised likelihood. The penalised likelihood is used to form a penalised likelihood ratio statistic which has known limiting distribution and can be used for carrying out hypothesis tests or for constructing confidence intervals for either the fixed-effect parameters or the variance component. Simulation studies and real data applications are used to assess the performance of estimation and inference based on the median bias-reducing penalised likelihood and compare it to recently proposed alternatives. The results provide evidence on the effectiveness of median bias reduction in improving estimation and likelihood-based inference.

A composite likelihood approach to predict the sex of the baby.

Couples with diseases associated with the sexual chromosomes, as well as families in countries where the desire for a male is extreme, are interested in influencing the sex of the baby. We propose an original composite likelihood approach to analyse the relation between sex of the newborn and timing of the intercourse which leads to conception. Although there exist numerous works on this relation, only few studies have been carried out on independent datasets to validate the existing theories. Since the sex of the newborn is only known in case of conception, the full likelihood of the data is not easily defined without strong assumptions. A composite likelihood is a pseudo likelihood defined as the product of likelihood functions relative to subsets of the data. In particular, we consider two such likelihoods, one modelling the day-specific probabilities of conception and the other modelling the sex of the newborn given a conception has occurred. The methodology is applied to a dataset from a European fecundability study. The results show no significant dependence of the sex of the newborn on the time of intercourse. The method developed may be applied to other situations when data are affected by selective sampling.

Integrated likelihoods in parametric survival models for highly clustered censored data.

In studies that involve censored time-to-event data, stratification is frequently encountered due to different reasons, such as stratified sampling or model adjustment due to violation of model assumptions. Often, the main interest is not in the clustering variables, and the cluster-related parameters are treated as nuisance. When inference is about a parameter of interest in presence of many nuisance parameters, standard likelihood methods often perform very poorly and may lead to severe bias. This problem is particularly evident in models for clustered data with cluster-specific nuisance parameters, when the number of clusters is relatively high with respect to the within-cluster size. However, it is still unclear how the presence of censoring would affect this issue. We consider clustered failure time data with independent censoring, and propose frequentist inference based on an integrated likelihood. We then apply the proposed approach to a stratified Weibull model. Simulation studies show that appropriately defined integrated likelihoods provide very accurate inferential results in all circumstances, such as for highly clustered data or heavy censoring, even in extreme settings where standard likelihood procedures lead to strongly misleading results. We show that the proposed method performs generally as well as the frailty model, but it is superior when the frailty distribution is seriously misspecified. An application, which concerns treatments for a frequent disease in late-stage HIV-infected people, illustrates the proposed inferential method in Weibull regression models, and compares different inferential conclusions from alternative methods.

Detection of microRNAs in archival cytology urine smears.

MicroRNAs' dysregulation and profiling have been demonstrated to be clinically relevant in urothelial carcinoma (UC). Urine cytology is commonly used as the mainstay non-invasive test for secondary prevention and follow-up of UC patients. Ancillary tools are needed to support cytopathologists in the diagnosis of low-grade UC. The feasibility and reliability of microRNAs profiling by qRT-PCR analysis (miR-145 and miR-205) in archival routine urine cytology smears (affected by fixation/staining [Papanicolau] and room temperature storage) was tested in a series of 15 non-neoplastic and 10 UC urine specimens. Only samples with >5,000 urothelial cells and with <50% of inflammatory cells/red blood cells clusters were considered. Overall, a satisfactory amount of total RNA was obtained from all the considered samples (mean 1.27±1.43 µg, range 0.06-4.60 µg). Twenty nanograms of total RNA have been calculated to be the minimal total RNA concentration for reliable and reproducible miRNAs expression profiling analysis of archival cytological smears (slope= -3.4084; R-squared=0.99; efficiency=1.94). miR-145 and miR-205 were significantly downregulated in UC samples in comparison to non-tumor controls. These findings demonstrate that urine archival cytology smears are suitable for obtaining high-quality RNA to be used in microRNAs expression profiling. Further studies should investigate if miRNAs profiling can be successfully translated into clinical practice as diagnostic or prognostic markers.

Practical use of modified maximum likelihoods for stratified data.

Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between-strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum-specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points.

Local influence analysis when interfacing toxicokinetic and proportional hazard models.

We present a local influence analysis to assigned model quantities in the context of a dose-response analysis of cancer mortality in relation to estimated absorbed dose of dioxin. The risk estimation is performed using dioxin dose as a time-dependent explanatory variable in a proportional hazard model. The dioxin dose is computed using a toxicokinetic model, which depends on some factors, such as assigned constants and estimated parameters. We present a local influence analysis to assess the effects on final results of minor perturbations of toxicokinetic model factors. In the present context, there is no evidence of local influence in risk estimates. It is however possible to identify which factors are more influential.