Estimation of Relative Risk in Case Control Studies Through Logistic Regression Analysis

Multiple logistic regression analysis is used to estimate the relative risk in case control studies. The estimators obtained are valid when disease is rare. In this paper an estimator of relative risk in a case control study has been proposed using logistic regression results when the incidence of disease is not small. The bias of the usual estimator through logistic regression as compared to the new estimator has been worked out. The expression of Mean Square Error of proposed estimator has been derived in situations when the incidence of disease is known exactly as well as when estimated through an independent survey. It has been observed that there is a significant bias using the conventional estimator of relative risk when incidence of disease is high. In such situations the proposed estimator can be used with advantage.     

Estimation of Prevalence and Relative Risk in Repetitive Surveys

The Theory of double sampling as proposed by Neyman (1938) and subsequently used for successive sampling by Jesson (1942), Yates (1960), Patterson (1950), Eckler (1955), Kuldroff (1963) and Tikkiwal (1960, 1967) has been explored to develop a general estimator which can be used for estimation of parameters such as mean, ratio or double ratio. A simple case of sampling on two occasions has only been considered but the logic can easily be extended for more than two occasions. The results show that the generalised estimator will be very useful for the applied statisticians.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

On the Estimation of the Nearest Neighbour Distribution,G(t), for Point Processes

A new method is proposed for estimating G(t), the distribution function of the distance from an object to its nearest neighbour in a spatial point process. The new method makes more complete use of the information available and has a smaller mean squared error than that of the existing alternatives. The method appears equally effective with random, clustered and regular patterns.     

Estimation of Odds Ratios from Matched Case-Control Studies with Incomplete Data

Matched case-control studies often include pairs with incomplete exposure information. This work presents and compares two estimators for the odds ratio that can be used when the exposures of some of the cases and controls are missing. A simulation study shows that the estimator that uses the marginal exposure frequencies is usually more efficient than the estimator based on discordant pairs.     

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.     

Monte Carlo Investigations for Relative Efficiency of Stratified Random Sampling Scheme for Estimation of Relative Risk in Case-Control Studies

Monte Carlo Investigations have been widely used in Sample Surveys in Comparing the efficiency of various methods when exact mathematical comparisons are not possible. In this paper the same has been used for comparing the efficiency of Stratified Random Sampling with respect to Simple Random Sampling for estimation of Relative Risk in Case-Control Studies. The data used relate to a Case Control study on peptic ulcer. On the basis of Monte Carlo Investigations on 50 samples of size 10–20 (Cases and Controls), it has been observed that there is considerable gain in efficiency in using Stratified Random Sampling over Simple Random Sampling. The sensitivity of the results with the change in Sample Size has also been investigated.     

Point Estimation on Relative Risk under Inverse Sampling

When the underlying disease is rare, to control the coefficient of variation for the sample proportion of cases, we may wish to apply inverse sampling. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) of relative risk and its variance in closed form under inverse sampling. On the basis of a Monte Carlo simulation, we demonstrate that using the UMVUE of relative risk can substantially reduce the mean-squared-error of using the maximum likelihood estimator, especially when the number of index cases in both comparison samples is small. For a given fixed total cost, we include a program that can be used to find the optimal allocation for the number of index cases to minimize the variance of the UMVUE as well.     

Estimation of Relative Risk Under Variable Multiple Matching

When disease incidence is low, the odds ratio, which closely approximates relative risk, is estimated optimally in a closed form using a variable matching ratio in a retrospective design. The model also enables one to assess the homogeneity of the odds ratio from the same one matched sample. Analogous procedures are shown to hold for the prospective design.     

Comparison of Several Relative Risk Estimators with Interval‐Censored Data

Several simple, intuitive, explicitly computable estimation procedures for relative risk with interval‐censored data are proposed. These procedures are the modified versions of relative risk estimators for right‐censored data developed by Peto, Pike, and Andersen. Simulation study is conducted to demonstrate the performances of the proposed estimators.     

Estimation of Partial Regression Coefficient

A sampling scheme providing unbiased partial regression coefficient has been proposed. The proposed sampling scheme is not only unbiased but also superior to simple random sampling and that due to Singh and Bathla (1990) for estimation of partial regression coefficient.     

Referent sampling,family history and relative risk: the role of length-biased sampling

Familial risk of disease is often assessed using case control studies based on referent databases. A referent database is a collection of family histories of cases typically assembled as a result of one family member being diagnosed with disease. This sampling scheme is equivalent to sampling families proportional to their size. The larger the family, the greater the probability of finding the family in the referent registry. This phenomena is known as length-biased sampling. The consequence of this kind of sampling is to bias the regression estimate associated with family history. The estimate is typically inflated in comparison to what is true for the actual population.     

On blocking rules for the bootstrap with dependent data

We address the issue of optimal block choice in applicationsof the block bootstrap to dependent data. It is shown that optimalblock size depends significantly on context, being equal ton^1/3, n^1/4 and n^1/5 in the cases of variance or bias estimation,estimation of a onesided distribution function, and estimationof a two-sided distribution function, respectively. A clearintuitive explanation of this phenomenon is given, togetherwith outlines of theoretical arguments in specific cases. Itis shown that these orders of magnitude of block sizes can beused to produce a simple, practical rule for selecting blocksize empirically. That technique is explored numerically.     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

Product Cum Difference Method of Estimation Using two Auxiliary Variables

Product method of estimation (MURTHY, 1964) using supplementary information on an auxiliary variable having high negative correlation with the main variable under our study, is well known. In this paper, we propose product-cum-difference method of estimation for the population total and the product of population parameters when supplementary information is available on two auxiliary variables. A comparison of product-cum-difference method of estimation with the usual product method of estimation using single auxiliary character and the estimators by SINGH (1965) for the estimation of product of population parameters has been made along with an empirical study.     

On the Estimation of Population Mean in Stratified Sampling

When stratified random sampling is used for the estimation of population mean, use of ‘Combined ratio estimator’ is well known. Some improved estimators for population mean are proposed which are better than ‘Combined ratio estimator’ and some other well known existing ones, from the point of view of bias and mean square error. An empirical illustration is given.     

Improved Shrinkage Estimation of Relative Potency

This article considers the asymptotic estimation theory for the log relative potency in a symmetric parallel bioassay when uncertain prior information about the true log relative potency is assumed to be a known quantity. Three classes of point estimation, namely, the unrestricted estimator, the shrinkage restricted estimator and shrinkage preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators is presented. Interestingly, proposed shrinkage preliminary test estimator dominates the unrestricted estimator in a range that is wider than that of the usual preliminary test estimator. Most importantly, the size of the preliminary test is much appropriate than the usual preliminary test estimator.     

Risk Assessment for a Flood Control Engineering System Using Fuzzy Theory: A Case in China

Flood control engineering system risk assessment entails fuzziness. An assessment model is developed, based on the improved fuzzy comprehensive assessment method that developed a new index (S_fin ) to judge the assessment class. The model is used to assess the flood control engineering risk of a case in China. The results show that the proposed model in the present article can rationally determine the risk status of a flood control engineering system, and has higher resolution compared to the two conventional methods, fuzzy comprehensive assessment and matter-element model method. The proposed model is flexible and adaptable for determining flood control engineering system risk status.     

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).