A Methodology for Assessing the Probability of Occurrence of Undesired Events in the Tietê–Paraná Inland Waterway Based on Expert Opinion

The market share of Tietê–Paraná inland waterway (TPIW) in the transport matrix of the São Paulo state, Brazil, is currently only 0.6%, but it is expected to increase to 6% over the next 20 years. In this scenario, to identify and explore potential undesired events a risk assessment is necessary. Part of this involves assigning the probability of occurrence of events, which usually is accomplished by a frequentist approach. However, in many cases, this approach is not possible due to unavailable or nonrepresentative data. This is the case of the TPIW that even though an expressive accident history is available, a frequentist approach is not suitable due to differences between current operational conditions and those met in the past. Therefore, a subjective assessment is an option as allows for working independently of the historical data, thus delivering more reliable results. In this context, this article proposes a methodology for assessing the probability of occurrence of undesired events based on expert opinion combined with fuzzy analysis. This methodology defines a criterion to weighting the experts and, using the fuzzy logic, evaluates the similarities among the experts’ beliefs to be used in the aggregation process before the defuzzification that quantifies the probability of occurrence of the events based on the experts’ opinion. Moreover, the proposed methodology is applied to the real case of the TPIW and the results obtained from the elicited experts are compared with a frequentist approach evidencing the impact on the results when considering different interpretations of the probability.     

Some improved tail bounds for the sum of variables with geometric distribution

Abstract

In this paper, compared with the results in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.[Crossref] , [Google Scholar]), we provide some improved explicit bounds for the tail probabilities of the sum of independent geometric variables with their expectations and variances. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.[Crossref] , [Google Scholar]).     

Augmented inverse probability weighted fractional imputation in quantile regression

By employing all the observed information and the optimal augmentation term, we propose an augmented inverse probability weighted fractional imputation method (AFI) to handle covariates missing at random in quantile regression. Compared with the existing completely case analysis, inverse probability weighting, multiple imputation and fractional imputation based on quantile regression model with missing covarites, we carry out simulation study to investigate its performance in estimation accuracy and efficiency, computational efficiency and estimation robustness. We also talk about the influence of imputation replicates in our AFI. Finally, we apply our methodology to part of the National Health and Nutrition Examination Survey data.     

Generalized confidence limits for the performance index of the exponentially distributed lifetime

Under a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index C_L based on type-II right-censored data. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. Confidence limits of C_L computed under the generalized paradigm are compared with those of C_L computed under the classical paradigm, citing an illustrative example with real data and two examples with simulated data, to demonstrate the merits and advantages of the proposed generalized variable method over the classical method.     

Test for independence between time to failure and cause of failure in competing risks with k causes

In this paper, we develop a simple nonparametric test for testing the independence of time to failure and cause of failure in competing risks set up. We generalise the test to the situation where failure data is right censored. We obtain the asymptotic distribution of the test statistics for complete and censored data. The efficiency loss due to censoring is studied using Pitman efficiency. The performance of the proposed test is evaluated through simulations. Finally we illustrate our test procedure using three real data sets.     

Inferences on the common mean of several heterogeneous log-normal distributions

We consider the problem of making inferences on the common mean of several heterogeneous log-normal populations. We apply the parametric bootstrap (PB) approach and the method of variance estimate recovery (MOVER) to construct confidence intervals for the log-normal common mean. We then compare the performances of the proposed confidence intervals with the existing confidence intervals via an extensive simulation study. Simulation results show that our proposed MOVER and PB confidence intervals can be recommended generally for different sample sizes and number of populations.     

Inverse probability of censoring weighting for visual predictive checks of time-to-event models with time-varying covariates

When constructing models to summarize clinical data to be used for simulations, it is good practice to evaluate the models for their capacity to reproduce the data. This can be done by means of Visual Predictive Checks (VPC), which consist of several reproductions of the original study by simulation from the model under evaluation, calculating estimates of interest for each simulated study and comparing the distribution of those estimates with the estimate from the original study. This procedure is a generic method that is straightforward to apply, in general. Here we consider the application of the method to time-to-event data and consider the special case when a time-varying covariate is not known or cannot be approximated after event time. In this case, simulations cannot be conducted beyond the end of the follow-up time (event or censoring time) in the original study. Thus, the simulations must be censored at the end of the follow-up time. Since this censoring is not random, the standard KM estimates from the simulated studies and the resulting VPC will be biased. We propose to use inverse probability of censoring weighting (IPoC) method to correct the KM estimator for the simulated studies and obtain unbiased VPCs. For analyzing the Cantos study, the IPoC weighting as described here proved valuable and enabled the generation of VPCs to qualify PKPD models for simulations. Here, we use a generated data set, which allows illustration of the different situations and evaluation against the known truth.     

Estimating Desired Sample Size for Simple Random Sampling of a Skewed Population

A simulation study was conducted to assess how well the necessary sample size to achieve a stipulated margin of error can be estimated prior to sampling. Our concern was particularly focused on performance when sampling from a very skewed distribution, which is a common feature of many biological, economic, and other populations. We examined two approaches for estimating sample size—one being the commonly used strategy aimed at regulating the average magnitude of the stipulated margin of error and the second being a previously proposed strategy to control the tolerance probability with which the stipulated margin of error is exceeded. Results of the simulation revealed that (1) skewness does not much affect the average estimated sample size but can greatly extend the range of estimated sample sizes; and (2) skewness does reduce the effectiveness of Kupper and Hafner's sample size estimator, yet its effectiveness is negatively impacted less by skewness directly, and to a much greater degree by the common practice of estimating the population variance via a pilot sampling from the skewed population. Nonetheless, the simulations suggest that estimating sample size to control the probability with which the desired margin of error is achieved is a worthwhile alternative to the usual sample size formula that controls the average width of the confidence interval only.     

Approximate one-sided tolerance limits in random effects model and in some mixed models and comparisons

An approximate closed-form one-sided tolerance limit (TL) in a general mixed model is proposed. One-sided TLs for the distribution of observable random variable and for the distribution of unobservable random variable in one-way random model are obtained as special cases from the one for the general mixed model. Applications to a two-way nested random model are also given. The merits of the TLs are evaluated using Monte Carlo simulation and compared with the existing ones. Our comparison studies indicate that the approximate TLs are quite satisfactory for all parameter and sample size configurations, and better than the existing ones in some cases. Approximate confidence intervals for exceedance probabilities in one-way random effects model are also proposed. The procedures are illustrated using three examples.     

Confidence intervals for the difference of marginal probabilities in clustered matched-pair binary data

Although there are several available test statistics to assess the difference of marginal probabilities in clustered matched‐pair binary data, associated confidence intervals (CIs) are not readily available. Herein, the construction of corresponding CIs is proposed, and the performance of each CI is investigated. The results from Monte Carlo simulation study indicate that the proposed CIs perform well in maintaining the nominal coverage probability: for small to medium numbers of clusters, the intracluster correlation coefficient‐adjusted McNemar statistic and its associated Wald or Score CIs are preferred; however, this statistic becomes conservative when the number of clusters is larger so that alternative statistics and their associated CIs are preferred. In practice, a combination of the intracluster correlation coefficient‐adjusted McNemar statistic with an alternative statistic is recommended. To illustrate the practical application, a real clustered matched‐pair collection of data is used to illustrate testing the difference of marginal probabilities and constructing the associated CIs. Copyright © 2012 John Wiley & Sons, Ltd.