Journal of Data Science

Vaccine efficacy is a key index to evaluate vaccines in initial clinical trials during the development of vaccines. In particular, it plays a crucial role in authorizing Covid-19 vaccines. It has been reported that Covid-19 vaccine efficacy varies with a number of factors, including demographics of population, time after vaccine administration, and virus strains. By examining clinical trial data of three Covid-19 vaccine studies, we find that current approach to evaluating vaccines with an overall efficacy does not provide desired accuracy. It requires no time frame during which a candidate vaccine is evaluated, and is subject to misuse, resulting in potential misleading information and interpretation. In particular, we illustrate with clinical trial data that the variability of vaccine efficacy is underestimated. We demonstrate that a new method may help to address these caveats. It leads to accurate estimation of the variation of efficacy, provides useful information to define a reasonable time frame to evaluate vaccines, and avoids misuse of vaccine efficacy and misleading information.

Abstract: In this study, we compared various block bootstrap methods in terms of parameter estimation, biases and mean squared errors (MSE) of the bootstrap estimators. Comparison is based on four real-world examples and an extensive simulation study with various sample sizes, parameters and block lengths. Our results reveal that ordered and sufficient ordered non-overlapping block bootstrap methods proposed by Beyaztas et al. (2016) provide better results in terms of parameter estimation and its MSE compared to conventional methods. Also, sufficient non-overlapping block bootstrap method and its ordered version have the smallest MSE for the sample mean among the others.

Abstract: We propose two classes of nonparametric point estimators of θ = P(X < Y ) in the case where (X, Y ) are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of the joint density of (X, Y ) and the distri bution function of Z = Y − X. We explore the use of several density and distribution function estimators and characterise the convergence of the re sulting estimators of θ. We consider the use of bootstrap methods to obtain confidence intervals. The performance of these estimators is illustrated us ing simulated and real data. These examples show that not accounting for pairing and dependence may lead to erroneous conclusions about the rela tionship between X and Y .

The probability that the estimator is equal to the value of the estimated parameter is zero. Hence in practical applications we provide together with the point estimates their estimated standard errors. Given a distribution of random variable which has heavier tails or thinner tails than a normal distribution, then the confidence interval common in the literature will not be applicable. In this study, we obtained some results on the confidence procedure for the parameters of generalized normal distribution which is robust in any case of heavier or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size n. Some simulation studies and applications are also examined.

Abstract: Scientific interest often centers on characterizing the effect of one or more variables on an outcome. While data mining approaches such as random forests are flexible alternatives to conventional parametric models, they suffer from a lack of interpretability because variable effects are not quantified in a substantively meaningful way. In this paper we describe a method for quantifying variable effects using partial dependence, which produces an estimate that can be interpreted as the effect on the response for a one unit change in the predictor, while averaging over the effects of all other variables. Most importantly, the approach avoids problems related to model misspecification and challenges to implementation in high dimensional settings encountered with other approaches (e.g., multiple linear regression). We propose and evaluate through simulation a method for constructing a point estimate of this effect size. We also propose and evaluate interval estimates based on a non-parametric bootstrap. The method is illustrated on data used for the prediction of the age of abalone.