Improved Confidence Intervals for the Difference between Two Proportions

Wald-z asymptotic methods, with and without a continuity correction, have less than nominal coverage probability characteristics but continue to be used. Newcombe\u27s hybrid method and the Agresti-Caffo methods have coverage probabilities that are near nominal for either equal or unequal samples. Newcombe\u27s hybrid and Agresti-Caffo methods demonstrate superior coverage properties

Higher Order C(t, p, s) Crossover Designs

A crossover study is a repeated measures design in which each subject is randomly assigned to a sequence of treatments, including at least two treatments. The most damning characteristic of a crossover study is the potential of a carryover effect of one treatment to the next period. To solve the first-order crossover problem characteristic in the classic AB|BA design, the design must be extended. One alternative uses additional treatment sequences in two periods; a second option is to add a third period and repeat one of the treatments. Assuming a traditional model that specifies a first-order carryover effect, this study investigates the following alternative crossover trial designs: (1) two-treatment two-period four-sequence design (Balaam, 1968) design, (2) two treatments-three period-four sequence design (Ebbutt, 1984), and (3) three treatment-two period-six sequence design (Koch, 1983). Each design has attractive properties and, when properly applied, allows both treatment and carryover effects to be estimated

AB/BA Crossover Trials - Binary Outcome

On occasion, the response to treatment in an AB/BA crossover trial is measured on a binary variable - success or failure. It is assumed that response to treatment is measured on an outcome variable with (+) representing a treatment success and a (-) representing a treatment failure. Traditionally, three tests for comparing treatment effect have been used (McNemar’s, Mainland-Gart, and Prescott’s). An issue arises concerning treatment comparisons when there may be a residual effect (carryover effect) of a previous treatment affecting the current treatment. A general consensus as to which procedure is preferable is debatable. However, if both group and carry-over effects are absent, Prescott’s test is the best one to use. Under a model with residual effects, Prescott’s test is biased. Therefore, a conservative approach includes testing for residual effects. When there is no period effect, McNemar’s test is optimal, while McNemar’s test is biased

JMASM11: Comparing Two Small Binomial Proportions

A large volume of research has focused on comparing the difference between two small binomial proportions. Statisticians recognize that Fisher’s Exact test and Yates chi-square test are excessively conservative. Likewise, many statisticians feel that Pearson’s Chi-square or the likelihood statistic may be inappropriate for small samples. Viable alternatives exist

Extension of Grizzle’s Classic Crossover Design

The crossover design compares treatments A and B over two periods using sequences AB and BA (the AB|BA design) and is the classic design most often illustrated and critiqued in textbooks. Other crossover designs have been used but their use is relatively rare and not always well understood. This article introduces alternatives to a randomized two-treatment, two-period crossover study design. One strategy, which is to extend the classic AB|BA by adding a third period to repeat one of the two treatments, has several attractive advantages; an added treatment period may not imply a large additional cost but will allow carryover effects to be estimated and compared with the within-subject variability. Careful choice of treatment sequences will enable the first two trial periods to constitute a conventional two-period crossover trial if the third treatment period leads to excessive subject drop-outs. Four alternative designs that address the first-order carryover effect are presented. These designs have more statistical power than the classic design and allow the treatment effects to be estimated, even in the presence of a carryover effect

Four Period Crossover Designs

In higher-order four period crossover designs with two treatments, sixteen possible treatment sequences can result: AAAA, AAAB, AABA, AABB, ABAA, ABAB, ABBA, ABBB and their duals. Higher-order crossover designs are useful for several reasons: they allow estimation of a treatment effect even in the presence of a carry-over effect, they provide estimates of intra-subject variability and they draw inference on the carry-over effect. The real question related to a two-treatment four-period crossover design is the real world application of these designs. This article considers four designs: Design I: ABBA and its dual; Design II: ABBA, AABB and their duals, Design III: ABBA, ABAA and their duals, Design IV: ABBA, ABAB and their duals. A traditional model that specifies a first-order carryover effect is assumed and methods for estimating treatment and first-order carryover effects in the set of four period trials are outlined

Closed Form Confidence Intervals for Small Sample Matched Proportions

The behavior of the Wald-z, Wald-c, Quesenberry-Hurst, Wald-m and Agresti-Min methods was investigated for matched proportions confidence intervals. It was concluded that given the widespread use of the repeated-measure design, pretest-posttest design, matched-pairs design, and cross-over design, the textbook Wald-z method should be abandoned in favor of the Agresti-Min alternative

Better Binomial Confidence Intervals

The construction of a confidence interval for a binomial parameter is a basic analysis in statistical inference. Most introductory statistics textbook authors present the binomial confidence interval based on the asymptotic normality of the sample proportion and estimating the standard error - the Wald method. For the one sample binomial confidence interval the Clopper-Pearson exact method has been regarded as definitive as it eliminates both overshoot and zero width intervals. The Clopper-Pearson exact method is the most conservative and is unquestionably a better alternative to the Wald method. Other viable alternatives include Wilson\u27s Score, the Agresti-Coull method, and the Borkowf SAIFS-z

The spectrum of bicyclic antiautomorphisms of directed triple systems

AbstractA transitive triple, (a,b,c), is defined to be the set {(a,b),(b,c),(a,c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D,β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of a directed triple system, (D,β), is a permutation of D which maps β to β−1, where β−1={(c,b,a)|(a,b,c)∈β}. In this paper we complete the necessary and sufficient conditions for the existence of a directed triple system of order v admitting an antiautomorphism consisting of two cycles