An Examination of the Conservative Nature of “Classical” Confidence Limits for a Proportion

The performance of the standard confidence limits for a proportion is studied over the entire range of proportions, and for various prescribed values of the nominal confidence coefficient. In the light of the conservative nature of these limits, modifications are suggested resulting in limits with average confidence coefficients close to the 95% nominal value. A comparison is made with a solution obtained from the application of Bayes's theorem to the problem.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

Confidence bands for cumulative incidence curves under the additive risk model

In the context of competing risks, the cumulative incidence function is often used to summarize the cause-specific failure-time data. As an alternative to the proportional hazards model, the additive risk model is used to investigate covariate effects by specifying that the subject-specific hazard function is the sum of a baseline hazard function and a regression function of covariates. Based on such a formulation, we present an approach to constructing simultaneous confidence intervals for the cause-specific cumulative incidence function of patients with given risk factors. A melanoma data set is used for the purpose of illustration.     

Note on Confidence Regions in Multiple Assays

This note is in continuation of the author's results on ’classical‘ confidence regions for relative potencies in multiple assays (Bennett, 1987). It is shown by the use of a Bonferroni inequality (e.g. Miller, ch. 2, 1980) that approximate confidence regions for the relative potencies {M_i} i = 1, …, p may also be obtained directly. A comparison with the classical regions is made for the case: p = 2 using Finney's example (1978, ch. 2).     

Conditional Inference Following Group Sequential Testing

The work of Fisher (1959) and Buehler (1959) discuss the importance of conditioning on recognizable subsets of the sample space. The stopping time yields an easily identifiable partition of the sample space when considering group sequential testing. We first present confidence intervals that are correct when conditioning on the subset of data for which a trial stopped at a particular analysis. These intervals have very desirable properties for observations that are highly unusual (given any value of the mean). In addition, they provide insight into how information about the mean is distributed between the two sufficient statistics. We then use conditional coverage probabilities to compare the sample mean, stagewise, and repeated confidence intervals. We find that none of these intervals outperforms the others when conditioning on stopping time, and no interval is a uniformly acceptable performer.     

Confidence as an expression of commitment: why misplaced expressions of confidence backfire

Because communication can be abused by senders, it is not inherently stable. One way of stabilizing communication is for senders to commit to their messages. If a sender is committed to a message, she is willing to incur a cost (direct or reputational) if the message is found to be unreliable. This cost provides a reason for receivers to accept messages to which senders are committed. We suggest that expressions of confidence can be used as commitment signals: messages expressed more confidently commit their senders more. On this basis, we make three predictions: that confidently expressed messages are more persuasive (H1’, already well established), that senders whose messages were accepted due to the senders' confidence but were then found to be unreliable should incur costs (H2’), and that if a message is accepted for reasons other than confidence, when it is found to be unreliable the sender should incur lower reputational costs than if the message had been accepted on the basis of the sender's confidence (H3’). A review of the literature revealed broadly supportive but still ambiguous evidence for H2’ and no tests of H3’. In experiments 1, 2, and 3 (testing H2’) participants received the same advice from two senders, one being confident and the other unconfident. Participants were more likely to follow the advice of the confident sender, but once the advice was revealed to have been misguided, participants adjusted their trust so that they trusted the initially unconfident sender more than the confident sender. In experiments 3 and 4 (testing H3’) participants chose between either two senders differing in confidence or two senders differing in competence. Participants followed the advice of the confident sender and of the competent sender. When it was revealed that the advice was misguided, the confident sender suffered from a larger drop in trust than the competent sender. These results are relevant for communicative theories of overconfidence.     

An Alternative Approach for the Assessment of Bioequivalence Between Two Formulations of a Drug

The problem of the assessment of bioequivalence between a test formulation (T) and a reference formulation (R) of a drug using a two-way crossover experiment is considered. To claim bioequivalence between two formulations, it is required by the United States Food and Drug Administration (FDA) to demonstrate that the true ratio of means μT/μR of pharmacokinetic parameters of concern falls within some reasonable limits (e.g., (80%, 120%)) with certain assurance. A commonly used approach is to construct an approximate 90% confidence interval for μT/μR and compare it with (80%, 120%). In this paper, an exact approach according to the FDA's criteria is proposed. The proposed procedure is derived by constructing an exact confidence region (an ellipse) for (μR, μT) and comparing it with the region bounded by μT = 0.8 μR and μT = 1.2 μR. Bioequivalence is concluded if the ellipse is within the critical region.     

自花授粉作物杂交育种组合潜势的预测和比较

在黄花烟草Nicotiana russica中,开花期这一性状用V_5作亲本可能产生较大变异,无论是选择早开花的还是选择迟开花的,都有较大机会得到理想目标株系;对于株高这一性状,含有V(?)的组合可望有较大机会产生高于标准品种的株系。通过组合间育种潜势的比较,能了解各亲本中基因分布的基本情况,进而进行客观评价并对杂交组合做出取舍。试验证明,用一个组合的早期世代的参数m和D来预测高世代或纯系的育种潜势是可行的。     

Lower Confidence Limits for the Positive Linear Combination of two Variances

An alternative method for determining the approximate lower confidence limits for the positive linear combination of two variances based on an approach similar to BULMER (1957) has been proposed. The probability coverage of the proposed alternative limits has been compared with the other existing methods.     

Simultaneous inference for ratios of linear combinations of general linear model parameters

Consider a general linear model with p -dimensional parameter vector beta and i.i.d. normal errors. Let K(1), ..., K(k ), and L be linearly independent vectors of constants such that L(T)beta not equal 0. We describe exact simultaneous tests for hypotheses that Ki(T)beta/L(T)beta equal specified constants using one-sided and two-sided alternatives, and describe exact simultaneous confidence intervals for these ratios. In the case where the confidence set is a single bounded contiguous set, we describe what we claim are the best possible conservative simultaneous confidence intervals for these ratios - best in that they form the minimum k -dimensional hypercube enclosing the exact simultaneous confidence set. We show that in the case of k = 2, this "box" is defined by the minimum and maximum values for the two ratios in the simultaneous confidence set and that these values are obtained via one of two sources: either from the solutions to each of four systems of equations or at points along the boundary of the simultaneous confidence set where the correlation between two t variables is zero. We then verify that these intervals are narrower than those previously presented in the literature.