Efficient Utilization of Auxiliary Information at Estimation Stage

Modified ratio or product estimators are suggested by making use of a very simple linear transformation on the auxiliary variable, which allows for a wider applicability of the modified estimators than that of customary ratio and product estimators.     

The Utilization of Kurtosis in the Estimation of the Parameters of the One‐Way Random Effects Model

This paper deals with the problem of estimating the components of the variance of one‐way random effects model under non‐normality situation using a prior knowledge of coefficient of kurtosis. We have suggested two classes of estimators and for the within and between variances respectively. Optimum estimators in the classes of and are identified with their mean squared errors formulae and compared with that of usual ANOVA unbiased and Shoukri , Tracy and Mian 's (1990) estimators. It is found that the proposed estimators are more efficient than the ANOVA unbiased estimators and Shoukri , Tracy and Mian (1990) estimators.     

An Alternative Approach to Estimation in Two-Phase Sampling Using two Auxiliary Variables

Using two-phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio-type and regression-type estimators suggested by KIREGYERA (1980, 1984).     

Inequality constrained estimation of genetic parameters

Summary A method is presented for computing estimates of genetic parameters under linear inequality constraints such that solutions are within theoretical limits. The method produces biased estimators, yet a small scale numerical study, also presented, shows that the inequality constrained estimators have a small mean squared error of prediction than the best of unbiased estimators. The increase in efficiency of estimation is particularly useful for traits where heritability is near the boundary values of zero or one.     

The Accelerated Failure Time Model Under Biased Sampling

Summary Chen (2009, Biometrics) studies the semi‐parametric accelerated failure time model for data that are size biased. Chen considers only the uncensored case and uses hazard‐based estimation methods originally developed for censored observations. However, for uncensored data, a simple linear regression on the log scale is more natural and provides better estimators.     

Alternative implementations of Monte Carlo EM algorithms for likelihood inferences

Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.     

The weighted generalized estimating equations approach for the evaluation of medical diagnostic test at subunit level

Sensitivity and specificity are common measures used to evaluate the performance of a diagnostic test. A diagnostic test is often administrated at a subunit level, e.g. at the level of vessel, ear or eye of a patient so that the treatment can be targeted at the specific subunit. Therefore, it is essential to evaluate the diagnostic test at the subunit level. Often patients with more negative subunit test results are less likely to receive the gold standard tests than patients with more positive subunit test results. To account for this type of missing data and correlation between subunit test results, we proposed a weighted generalized estimating equations (WGEE) approach to evaluate subunit sensitivities and specificities. A simulation study was conducted to evaluate the performance of the WGEE estimators and the weighted least squares (WLS) estimators (Barnhart and Kosinski, 2003) under a missing at random assumption. The results suggested that WGEE estimator is consistent under various scenarios of percentage of missing data and sample size, while the WLS approach could yield biased estimators due to a misspecified missing data mechanism. We illustrate the methodology with a cardiology example.     

Two-sample nonparametric estimation and confidence intervals under truncation.

We consider point estimates and confidence intervals for the difference in location or scale between two populations when the observations are subject to truncation. We suggest procedures analogous to those for the complete-sample case. A rigorous justification is presented to support the proposed confidence interval procedure. Finally, some simulations verify the properties of the estimators and confidence intervals. We illustrate the procedure using data on tumor size.     

Estimating treatment effects in studies of perinatal transmission of HIV

Fetal loss often precludes the ascertainment of infection status in studies of perinatal transmission of HIV. The standard analysis based on liveborn babies can result in biased estimation and invalid inference in the presence of fetal death. This paper focuses on the problem of estimating treatment effects for mother-to-child transmission when infection status is unknown for some babies. Minimal data structures for identifiability of parameters are given. Methods using full likelihood and the inverse probability of selection-weighted estimators are suggested. Simulation studies are used to show that these estimators perform well in finite samples. Methods are applied to the data from a clinical trial in Dar es Salaam, Tanzania. To validly estimate the treatment effect using likelihood methods, investigators should make sure that the design includes a mini-study among uninfected mothers and that efforts are made to ascertain the infection status of as many babies lost as possible. The inverse probability weighting methods need precise estimation of the probability of observing infection status. We can further apply our methodology to the study of other vertically transmissible infections which are potentially fatal pre- and perinatally.     

Bias-reduced estimators of conditional odds ratios in matched case-control studies with unmatched confounding

We study bias-reduced estimators of exponentially transformed parameters in general linear models (GLMs) and show how they can be used to obtain bias-reduced conditional (or unconditional) odds ratios in matched case-control studies. Two options are considered and compared: the explicit approach and the implicit approach. The implicit approach is based on the modified score function where bias-reduced estimates are obtained by using iterative procedures to solve the modified score equations. The explicit approach is shown to be a one-step approximation of this iterative procedure. To apply these approaches for the conditional analysis of matched case-control studies, with potentially unmatched confounding and with several exposures, we utilize the relation between the conditional likelihood and the likelihood of the unconditional logit binomial GLM for matched pairs and Cox partial likelihood for matched sets with appropriately setup data. The properties of the estimators are evaluated by using a large Monte Carlo simulation study and an illustration of a real dataset is shown. Researchers reporting the results on the exponentiated scale should use bias-reduced estimators since otherwise the effects can be under or overestimated, where the magnitude of the bias is especially large in studies with smaller sample sizes.     

Estimation of a common effect parameter from sparse follow-up data

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.     

Transporting stochastic direct and indirect effects to new populations

Transported mediation effects may contribute to understanding how interventions work differently when applied to new populations. However, we are not aware of any estimators for such effects. Thus, we propose two doubly robust, efficient estimators of transported stochastic (also called randomized interventional) direct and indirect effects. We demonstrate their finite sample properties in a simulation study. We then apply the preferred substitution estimator to longitudinal data from the Moving to Opportunity Study, a large‐scale housing voucher experiment, to transport stochastic indirect effect estimates of voucher receipt in childhood on subsequent risk of mental health or substance use disorder mediated through parental employment across sites, thereby gaining understanding of drivers of the site differences.     

Use of the Multinomial Dirichlet Model for Analysis of Subdivided Genetic Populations

The distribution found by compounding the multinomial distribution with the Dirichlet distribution has been suggested as a basis for the estimation of parameters in subdivided populations, in particular of the "correlation between genotypes" within subpopulations. It is shown that the estimators deriving from these procedures perform poorly when the data are generated by the classical Wright drift model of subdivided populations. This conclusion suggests that the compound distribution estimation approach does not provide a good estimation procedure for real populations which are reasonably described by the Wright model.     

Inferring admixture proportions from molecular data

We derive here two new estimators of admixture proportions based on a coalescent approach that explicitly takes into account molecular information as well as gene frequencies. These estimators can be applied to any type of molecular data (such as DNA sequences, restriction fragment length polymorphisms [RFLPs], or microsatellite data) for which the extent of molecular diversity is related to coalescent times. Monte Carlo simulation studies are used to analyze the behavior of our estimators. We show that one of them (mY) appears suitable for estimating admixture from molecular data because of its absence of bias and relatively low variance. We then compare it to two conventional estimators that are based on gene frequencies. mY proves to be less biased than conventional estimators over a wide range of situations and especially for microsatellite data. However, its variance is larger than that of conventional estimators when parental populations are not very differentiated. The variance of mY becomes smaller than that of conventional estimators only if parental populations have been kept separated for about N generations and if the mutation rate is high. Simulations also show that several loci should always be studied to achieve a drastic reduction of variance and that, for microsatellite data, the mean square error of mY rapidly becomes smaller than that of conventional estimators if enough loci are surveyed. We apply our new estimator to the case of admixed wolflike Canid populations tested for microsatellite data.      

Testing Linear Contrasts of Means in Experimental Design Without Assuming Normality and Homogeneity of Variances

We investigate the efficiencies of TIKU'S (1967, 1980) modified maximum likelihood (MML) estimators of location and scale parameters of symmetric distributions and show that they are remarkably efficient (jointly). We develop test statistics (based on MML estimators), analogous to the classical tests based on sample means and variances, for testing the equality of two means (the population variances not necessarily equal). We show that these tests are remarkably robust to distributional assumptions and generally more powerful than the well-known nonparametric tests (WILCOXON , normal-score, KOLMOGOROV -SMIRNOV ). We generalize the results to testing linear contrasts of means in experimental design (the error variances not necessarily equal). We show that the analogous tests based on ‘adaptive’ robust estimators (wave, bisquare, HAMPEL ,) etc., GROSS (1976, and other ‘adaptive’ robust estimators) give misleading Type I errors.     

A comparison of estimators of the population recombination rate

Three new estimators of the population recombination rate C = 4Nr are introduced. These estimators summarize the data using the number of distinct haplotypes and the estimated minimum number of recombination events, then calculate the value of C that maximizes the likelihood of obtaining the summarized data. They are compared with a number of previously proposed estimators of the recombination rate. One of the newly proposed estimators is generally better than the others for the parameter values considered here, while the three programs that calculate maximum-likelihood estimates give conflicting results.     

Estimating the kernel parameters of premises-based stochastic models of farmed animal infectious disease epidemics using limited, incomplete, or ongoing data

Three different estimators are presented for the types of parameters present in mathematical models of animal epidemics. The estimators make use of the data collected during an epidemic, which may be limited, incomplete, or under collection on an ongoing basis. When data are being collected on an ongoing basis, the estimated parameters can be used to evaluate putative control strategies. These estimators were tested using simulated epidemics based on a spatial, discrete-time, gravity-type, stochastic mathematical model containing two parameters. Target epidemics were simulated with the model and the three estimators were implemented using various combinations of collected data to independently determine the two parameters.     

Efficient inference for random-coefficient growth curve models with unbalanced data

Growth and dose-response curve studies often result in incomplete or unbalanced data. Random-effects models together with a variety of computer-intensive iterative techniques have been suggested for the analysis of such data. This paper is concerned with a noniterative method for estimating and comparing location parameters in random-coefficient growth curve models. Consistent and asymptotically efficient estimators of the location parameters are obtained using estimated generalized least squares. Two criteria for testing multivariate general linear hypotheses are introduced and their asymptotic properties are investigated. The results are applied to clinical data obtained on the blood ultrafiltration performance of hemodialyzers used in the treatment of patients with end-stage renal disease.     

An Estimate of the Variance of Estimators for Lead Time and Screening Benefit Time in Randomized Cancer Screening Trials

Variance estimators are derived for estimators of the average lead time and average benefit time due to screening in a randomized screening trial via influence functions. The influence functions demonstrate that these estimators are asymptotically equivalent to the mean difference, between the study and control case groups, in the appropriate survival times. For estimating benefit time, the survival time is measured since start of study; for estimating lead time, the survival time is measured since time of diagnosis. Asymptotic variances of these estimators can be calculated in a straightforward manner from the influence functions, and these variances can be estimated from actual trial data. The performance of the variance estimators is assessed via a simulated screening trial. The situation involving censored data is also discussed.     

Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.