Beta regression models have been widely used to model rates and proportions. We obtain a matrix formula of order $n^{-1/2},$ where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators of the linear parameters in varying dispersion beta regression models. The formula can be used to verify whether inference based on the asymptotic distribution of the maximum likelihood estimators should be performed. A simulation study and two applications are presented to illustrate the results.

Background: Laparoscopic surgery for rectal cancer is associated with improved postoperative outcomes compared to open surgery; however, economic studies have yielded contradictory results. The aim of this study was to compare the clinical and economic outcomes of laparoscopic versus open surgery for patients with rectal cancer. Methods: Propensity score matching analysis was performed in a retrospective cohort of patients who underwent elective low anterior resection for rectal cancer treatment by laparoscopic and open surgery in a single Brazilian cancer center. Matched covariates included age, gender, body mass index, pTNM stage, American Society of Anesthesiologists score, type of anesthesia, neoadjuvant chemoradiotherapy, and interval between neoadjuvant chemoradiotherapy and index surgery. The clinical and economic outcomes were evaluated. The follow-up period was within 30 days of the index procedure. The clinical outcomes were reoperation, postoperative complications, operative time, length of stay in the intensive care unit, and postoperative hospital stay. For economic outcomes, a cost analysis was used to compare the costs. Results: Initially, 220 patients were evaluated. After propensity score matching, 100 patients were included in the analysis (50 patients in the open surgery group and 50 patients in the laparoscopic surgery group). There were no differences in patients’ baseline characteristics. Operative time was longer for laparoscopic surgery (247 minutes vs 285 minutes, P=0.006). There were no significant differences in other clinical outcomes. The hospital costs were similar between the two groups (Brazilian reais 21,233.15 vs Brazilian reais 21,529.28, P=0.115), although the intraoperative costs were higher for laparoscopic surgery, mainly owing to the surgical devices and the theater-related costs. The postoperative costs were lower for laparoscopic surgery, owing to lower intensive care unit, ward, and reoperation costs. Conclusion: Laparoscopic surgery for rectal cancer is not costlier than open surgery from the health care provider’s perspective, since the intraoperative costs were offset by lower postoperative costs. Open surgery tends to have a longer length of stay.

The Marshall-Olkin extended family of distributions is an alternative for modeling lifetimes, and considers more or less asymmetry than its parent model, achieved by incorporating just one extra parameter. We investigate the bias of maximum likelihood estimators and use it to develop an estimator with less bias than traditional estimators, by a modification of the score function. Unlike other proposals, in this paper, we consider a bias reduction methodology that can be applied to any member of the family and not necessarily to any particular distribution. We conduct a Monte Carlo simulation in order to study the performance of the corrected estimators in finite samples. This simulation shows that the maximum likelihood estimator is quite biased and the proposed estimator is much less biased; in small sample sizes, the bias is reduced by around 50 percent. Two applications, related to the air conditioning system of an airplane and precipitations, are presented to illustrate the results. In those applications, the bias reduction for the shape parameters is close to 25% and the bias reduction also reduces, among others things, the width of the 95% confidence intervals for quantiles lower than 0.594.

In this paper, we obtain a matrix formula of order $n^{-1/2},$ where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.

In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-th quantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented.