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When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited. Because it is well known that an interval estimator using Wald's statistic is generally not likely to perform well especially when the sample size is small, the goal of this paper is to find ways to improve the finite-sample performance of this estimator. This paper develops five asymptotic interval estimators of the gamma by employing various methods that are commonly used to improve the normal approximation of the maximum likelihood estimator (MLE). Using Monte Carlo simulation, this paper notes that the coverage probability of the interval estimator using Wald's statistic can be much less than the desired confidence level, especially when the underlying gamma is large. Further, except for the extreme case, in which the underlying gamma is large and the sample size is small, the interval estimator using a logarithmic transformation together with a monotonic function proposed here not only performs well with respect to the coverage probability, but is also more efficient than all the other estimators considered here. Finally, this paper notes that applying an ad hoc adjustment procedure--whenever any observed frequency equals 0, we add 0.5 to all cells in calculation of the cell proportions--can substantially improve the traditional interval estimator. This paper includes two examples to illustrate the practical use of interval estimators considered here.

Claims a simple, reliable, and comparable measure for suicide mapping and other health problems is needed. Proposes an empirical Bayes approach whereby information from other areas is borrowed to improve the precision of the estimates of local-age specific rates in calculating directly adjusted rates, especially in areas with small population sizes. (Author/ABL)

Because one excludes in the sequential parallel comparison design (SPCD) both placebo responders and patients assigned to the experimental treatment in period 1 from comparison in period 2, test procedures for the SPCD may lose efficiency. Assuming a random effects logistic regression model, we evaluate the loss of efficiency by comparing power of the SPCD with those for the parallel groups design with repeated measurements (PGDRM), simple crossover design (SCD), and parallel group design (PGD). Based on Monte Carlo simulations, we find that the increase in efficiency of the SPCD by use of the PGDRM and SCD can be significant, especially when the variation of responses between patients is large. The SPCD can be, however, of use if the relative treatment effect on placebo non-responders is of our primary interest. [ABSTRACT FROM AUTHOR]

To increase power or reduce the number of patients needed for a parallel groups design, the crossover design has been often used to study treatments for noncurable chronic diseases. However, in the presence of carry‐over effect caused by treatments, the commonly‐used estimator which ignores the carry‐over effect leads to a biased estimator for estimating the treatment effect difference. A two‐stage test approach aimed to address carry‐over effect proposed was found to be potentially misleading. In this paper, we propose a weighted average of the commonly‐used estimator and an unbiased estimator that uses only the first period of the data. We derive an optimal weight that minimizes the mean squared error (MSE) and its modified estimator. We apply Monte Carlo simulation to evaluate the performance of the proposed estimators in a variety of situations. In the simulations, we examine the estimated MSE (EMSE), percentile interval length, and coverage probability calculated from the percentile intervals among considered estimators. Simulation results show that our proposed weighted average estimator and its modified estimator lead to smaller EMSEs on average comparing to the two commonly used estimators. The coverage probabilities using our proposed estimators are reasonably close to the nominal confidence level and the interval lengths are shorter comparing to the use of the unbiased estimator that uses only the first period of the data. We apply an example that was to evaluate the efficacy of two type of bronchodilators for asthma treatment to demonstrate the use of the proposed estimators. [ABSTRACT FROM AUTHOR]

We develop exact interval estimators for some commonly used classical measures of agreement in binary responses. We apply Monte Carlo simulation to evaluate the performance of these estimators. When the measure of agreement is homogeneous, we note that extending the results presented here to accommodate stratified analysis is straightforward. We use the data taken from a survey studying the agreement of religious identifications and the data taken from a study assessing the diagnostic performance of Whooley questions for major depression disorder to illustrate the use of these interval estimators. [ABSTRACT FROM AUTHOR]

This article discusses use of the composite estimator with the optimal weight to reduce the variance (or the mean-squared-error, MSE) of the ratio estimator. To study the practical usefulness of the proposed composite estimator, a Monte Carlo simulation is performed comparing the bias and MSE of composite estimators (with estimated optimal weight and with known optimal weight) with those of the simple expansion and the ratio estimators. Two examples, one regarding the estimation of dead fir trees via an aerial photo and the other regarding the estimation of the average sugarcane acres per county, are included to illustrate the use of the composite estimator developed here. [ABSTRACT FROM AUTHOR]

When patient responses are dichotomous under an AB/BA design, we commonly assume the normal random effects logistic regression model. This normality assumption for random effects is, however, unlikely to hold. Based on the maximum likelihood estimator, we apply Monte Carlo simulations to investigate the impact of misspecification on hypothesis testing and estimation because of the incorrect normal assumption for random effects. We find that Type I error is not affected by misspecifying the normal random effects distributions. We further find that the influence due to misspecifying distributions of random effects on power, bias and mean-squared-error, the coverage probability and the average length of the confidence interval is generally minimal when the variation of responses between patients is small and the number of patients per group is large. This influence can be substantial when the variation of responses between patients is large and the number of patients per group is small. Thus, the estimate of the required sample size or the accuracy of an interval estimator under the normal random effects assumption can be liberal. We use the data comparing a drug with placebo in treating cerebrovascular deficiency to illustrate the potential difference in inference between various random effects distributions considered here. [ABSTRACT FROM AUTHOR]

When studying treatments for psychiatric or mental diseases in a placebo-controlled trial, we may consider use of the sequential parallel comparison design to reduce the number of patients needed through the reduction of the high placebo response rate. Under the assumption that the odds ratio of responses is constant between phases in the sequential parallel comparison design, we derive the conditional maximum likelihood estimator for the odds ratio. On the basis of the conditional likelihood, we further derive three asymptotic interval and an exact interval estimators for the odds ratio of responses. We employ Monte Carlo simulation to evaluate the performance of these interval estimators in a variety of situations. We find that the asymptotic interval and exact interval estimators developed here can all perform well. We use the double-blind, placebo-controlled study assessing the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy for treating patients with major depressive disorder to illustrate the use of these estimators. [ABSTRACT FROM AUTHOR]

Under an incomplete block crossover design with two periods, we derive the least-squares estimators for the period effect, treatment effects and carry-over effects in explicit formulae based on within-patient differences. Using the commonly-used strategy of searching a base model for making inferences in regression analysis, we define a two-stage test procedure in studying treatment effects. On the basis of Monte Carlo simulation, we evaluate the performance of the two-stage procedure for hypothesis testing, point and interval estimation of treatment effects in a variety of situations. We note that use of the two-stage procedure can be potentially misleading and hence one should not apply a test procedure to exclusively determine whether he/she needs to account for the carry-over effect in studying treatment effects. We use the double-blind crossover trial comparing two different doses of formoterol with placebo on the forced expiratory volume in 1 second (FEV1) readings to illustrate the use of the two-stage procedure, as well as the distinction between use of two-stage procedure and the approach with assuming no carry-over effects based on one's subjective knowledge. [ABSTRACT FROM AUTHOR]