Covariate adjustment for randomized controlled trials revisited

Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well‐investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis‐specification, in particular, regarding the Neyman‐Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation.     

Asymptotically efficient estimation in response adaptive trials

We examine the issue of asymptotic efficiency of estimation for response adaptive designs of clinical trials, from which the collected data set contains a dependency structure. We establish the asymptotic lower bound of exponential rates for consistent estimators. Under certain regularity conditions, we show that the maximum likelihood estimator achieves the asymptotic lower bound for response adaptive trials with dichotomous responses. Furthermore, it is shown that the maximum likelihood estimator of the treatment effect is asymptotically efficient in the Bahadur sense for response adaptive clinical trials.     

An improved randomized response model: estimation of mean

In this paper, we suggest a new randomized response model useful for collecting information on quantitative sensitive variables such as drug use and income. The resultant estimator has been found to be better than the usual additive randomized response model. An interesting feature of the proposed model is that it is free from the known parameters of the scrambling variable unlike the additive model due to Himmelfarb and Edgell [S. Himmelfarb and S.E. Edgell, Additive constant model: a randomized response technique for eliminating evasiveness to quantitative response questions, Psychol. Bull. 87(1980), 525–530]. Relative efficiency of the proposed model has also been studied with the corresponding competitors. At the end, an application of the proposed model has been discussed.     

Equivariant estimation of a normal mean using a normal concomitant variable for covariance adjustment

Equivariant point estimators of one component of a bivariate normal mean vector are considered when the second component is known. Equivariant point estimators are characterized and compared in terms of their risk functions with respect to a normalized squared-error loss function. Specific point estimators that dominate the usual estimator when the squared correlation coefficient is sufficiently large are provided.     

Self‐consistent estimation of mean response functions and their derivatives

Many methods have been developed for the nonparametric estimation of a mean response function, but most of these methods do not lend themselves to simultaneous estimation of the mean response function and its derivatives. Recovering derivatives is important for analyzing human growth data, studying physical systems described by differential equations, and characterizing nanoparticles from scattering data. In this article the authors propose a new compound estimator that synthesizes information from numerous pointwise estimators indexed by a discrete set. Unlike spline and kernel smooths, the compound estimator is infinitely differentiable; unlike local regression smooths, the compound estimator is self‐consistent in that its derivatives estimate the derivatives of the mean response function. The authors show that the compound estimator and its derivatives can attain essentially optimal convergence rates in consistency. The authors also provide a filtration and extrapolation enhancement for finite samples, and the authors assess the empirical performance of the compound estimator and its derivatives via a simulation study and an application to real data. The Canadian Journal of Statistics 39: 280–299; 2011 © 2011 Statistical Society of Canada     

Joint influence of measurement error and non response on estimation of population mean

In this paper, we propose a method to jointly incorporate measurement error and non response in the estimators of population mean using auxiliary information in simple random sampling. We have not only studied some available estimators but also suggested three new estimators in the presence of two types of non sampling errors occurring jointly: the measurement error and the non response. The expressions for the bias and mean square errors of proposed estimator have been derived. A comparative study is made among the proposed estimators, the Hansen and Hurwitz (1946 Hansen, M.H., Hurwitz, W.N. (1946). The problem of non-response in sample surveys. J. Am. Stat. Assoc. 41:517–529.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator, the Cochran's (1977 Cochran, W.G. (1977). Sampling Techniques, 3rd Edn. New York: John Wiley &; Sons, Inc. [Google Scholar]) estimator, and the Singh and Kumar (2008 Singh, H.P., Karpe, N. (2008). Estimation of population variance using auxiliary information in the presence of measurement errors. Stat. Trans. New Ser. 9(3):443–470. [Google Scholar]) estimator.     

A note on non-negative mean square error estimation of regression estimators in randomized response surveys

Generalized regression estimators are considered for the survey population total of a quantitative sensitive variable based on randomized responses. Formulae are presented for ‘non-negative’ estimators of approximate mean square errors of these biased estimators when population and sample sizes are large.     

Data-adaptive estimation of the treatment-specific mean

An important problem in epidemiology and medical research is the estimation of the causal effect of a treatment action at a single point in time on the mean of an outcome, possibly within strata of the target population defined by a subset of the baseline covariates. Current approaches to this problem are based on marginal structural models, i.e. parametric models for the marginal distribution of counterfactual outcomes as a function of treatment and effect modifiers. The various estimators developed in this context furthermore each depend on a high-dimensional nuisance parameter whose estimation currently also relies on parametric models. Since misspecification of any of these models can lead to severely biased estimates of causal effects, the dependence of current methods on such parametric models represents a major limitation.     

On the estimation of restricted mean

In sampling from a continuous distribution with unknown mean μ and variance σ² the problem of estimation of μ, when it is known that μ∈(a, ∞) (or μ∈(-∞, b)), is considered. The estimators proposed here lie in the interval (a, ∞) (or (-∞, b)) almost surely. The performance of these estimators is compared to that of some known estimators in the case of sampling from a normal, exponential and a weighted difference of two independent chi-square distributions.     

Nonparametric estimation of mean residual functions

Situations frequently arise in practice in which mean residual life (mrl) functions must be ordered. For example, in a clinical trial of three experiments, let e (1), e (2) and e (3) be the mrl functions, respectively, for the disease groups under the standard and experimental treatments, and for the disease-free group. The well-documented mrl functions e (1) and e (3) can be used to generate a better estimate for e (2) under the mrl restriction e (1) < or = e (2) < or = e (3). In this paper we propose nonparametric estimators of the mean residual life function where both upper and lower bounds are given. Small and large sample properties of the estimators are explored. Simulation study shows that the proposed estimators have uniformly smaller mean squared error compared to the unrestricted empirical mrl functions. The proposed estimators are illustrated using a real data set from a cancer clinical trial study.     

Interval estimation of the common mean

Brown and Cohen (1974) considered the problem of interval estimation of the common mean of two normal populations based on independent random samples. They showed that if we take the usual confidence interval using the first sample only and centre it around an appropriate combined estimate of the common mean the resulting interval would contain the true value with higher probability. They also gave a sufficient condition which such a point estimate should satisfy. Bhattacharya and Shah (1978) showed that the estimates satisfying this condition are nearly identical to the mean of the first sample. In this paper we obtain a stronger sufficient condition which is satisfied by many point estimates when the size of the second sample exceeds ten.     

Efficient mean estimation in log-normal linear models

Log-normal linear models are widely used in applications, and many times it is of interest to predict the response variable or to estimate the mean of the response variable at the original scale for a new set of covariate values. In this paper we consider the problem of efficient estimation of the conditional mean of the response variable at the original scale for log-normal linear models. Several existing estimators are reviewed first, including the maximum likelihood (ML) estimator, the restricted ML (REML) estimator, the uniformly minimum variance unbiased (UMVU) estimator, and a bias-corrected REML estimator. We then propose two estimators that minimize the asymptotic mean squared error and the asymptotic bias, respectively. A parametric bootstrap procedure is also described to obtain confidence intervals for the proposed estimators. Both the new estimators and the bootstrap procedure are very easy to implement. Comparisons of the estimators using simulation studies suggest that our estimators perform better than the existing ones, and the bootstrap procedure yields confidence intervals with good coverage properties. A real application of estimating the mean sediment discharge is used to illustrate the methodology.     

Analytical expressions for the average adjustment interval and mean squared deviation for bounded adjustment schemes

This paper presents analytical expressions for the average adjustment interval and the mean squared deviation from target of the “bounded adjustment” schemes of Box and Luceno (1997a) under the assumption that the disturbances are generated from a double-exponential distribution. The solutions obtained are very close to those computed numerically for normally distributed innovations. This not only demonstrates the robustness of the schemes to the distributional assumptions, but also provides new useful expressions for the average adjustment interval and mean squared deviation from target. Expressions for the characteristic and probability mass functions of the adjustment interval are also given.     

Predictive estimation of population mean in two-phase sampling

ABSTRACT

The present investigation deals with the problem of estimation of population mean in two-phase sampling. In the presence of two auxiliary variables, some classes of estimators have been proposed through predictive approach. Properties of the proposed classes of estimators have been studied, and the unbiased versions of these estimators along with their approximate variance expressions are obtained under simple random sampling without replacement scheme. The respective optimum strategies of the proposed estimators are discussed, and their empirical and graphical comparisons with some contemporary estimators of population mean have been made. Suitable recommendations to the survey practitioner are given.     

Bayes estimation of a langevin mean direction

A Langevin distribution with two parameters (mean direction and concentration parameter) has been extensively used for modeling and analyzing problems related to directional data. In this article, we examine the estimation problem for the mean direction. Bayes estimators are derived with respect to a conjugate as well as the Jeffreys’ priors. Further in case of unknown concentration parameter, other priors are also chosen. An extensive analysis of risk behavior of Bayes estimators is carried out with the help of simulations.     

Second order minimax estimation of the mean

In this study we consider the problem of the improvement of the sample mean in the second order minimax estimation sense for a mean belonging to an unrestricted mean parameter space R⁺${\mathbb{R}}^{+}$. We solve this problem for the class of natural exponential families (NEF's) whose variance functions (VF's) are regular at zero and at infinity. Such a class of VF's (or NEF's) is huge and contains (among others): Polynomial VF's (e.g., quadratic VF's in the Morris class, cubic VF's in the Letac&Mora class and VF's in the Hinde–Demétrio class); VF's belonging to the Tweedie class with power VF's, VF's belonging to the Babel class and many others. Moreover, we show that if the canonical parameter space of the corresponding NEF is R$\mathbb{R}$ (which is obviously the case if the support of the NEF is bounded), then the sample mean as an estimator of the mean cannot be further improved. This work presents an original constructive methodology and provides with constructive tools enabling to obtain explicit forms of the second order minimax estimators as well as the forms of the related weight functions. Our work establishes a substantial generalization of the results obtained so far in the literature. Illustrations of the resulting methods are provided and a simulation-based analysis is presented for the negative binomial case.     

Partial groups ranked set sampling and mean estimation

Ranked set sampling (RSS) is an advanced sampling method which is very effective for estimating mean of the population when exact measurement of observation is difficult and/or expensive. Balanced Groups RSS (BGRSS) is one of the modification of RSS where only the lowest, the median and the largest ranked units are taken into account. Although BGRSS is advantageous and useful for some specific cases, it has strict restrictions regarding the set size which could be problematic for sampling plans. In this study, we make an improvement on BGRSS and propose a new design called Partial Groups RSS which offers a more flexible sampling plan providing the independence of the set size and sample size. Partial Groups RSS also has a cost advantage over BGRSS. We construct a Monte Carlo simulation study comparing the performance of the mean estimators of the proposed sampling design and BGRSS according to their sampling costs and mean squared errors for various type of distributions. In addition, we give a biometric data application for investigating the efficiency of Partial Groups RSS in real life applications.     

Bayesian estimation of mean and square of mean of normal distribution using linex loss function

In this paper, the Bayes estimators for mean and square of mean ol a normal distribution with mean μ and vaiiance σ r2 (known), relative to LINEX loss function are obtained Comparisons in terms of risk functions and Bayes risks of those under LINEX loss and squared error loss functions with their respective alternative estimators viz, UMVUE and Bayes estimators relative to squared error loss function, are made. It is found that Bayes estimators relative to LINEX loss function dominate the alternative estimators m terms of risk function snd Bayes risk. It is also found that if t2 is unknown the Bayes estimators are still preferable over alternative estimators.     

Use of multiauxiliary variables to cope with non response in estimation of current population mean in two-occasion successive sampling

ABSTRACT

The present work utilizes the information on multiauxiliary variables to neutralize the negative effect of non response in estimation of current population mean in two-occasion successive sampling. Generalized exponential type estimators have been proposed for the situation when non response occurs at both occasion or at first occasion or at current (second) occasion in two-occasion successive sampling. Properties of the proposed estimators have studied and empirical studies are carried out to justify the preposition of estimators. Suitable recommendations have been made.     

Sequential estimation of the mean of NEF-PVF distributions

Let F = {F₀: 0 ϵ Θ} denote the class of natural exponential family of distributions having power variance function, (NEF-PVF). We consider the problem of sequentially estimating the mean μ of F₀ ϵ F, based on i.i.d. observations from F₀. We propose an appropriate sequential estimation procedure under a combined loss of estimation error and sampling cost. We provide expansion for the regret R_a and study its asymptotic properties. We show that R_a = cv²(μ) + o(1) as a → ∞, where c > 0 is a known constant and v(μ) denotes the coefficient of variation of F₀.