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Summary: Binary data subject to one type of misclassification exist in various fields. It is collected in a double‐sampling scheme that includes a gold standard test and a fallible test. The main parameter of interest for this type of data is the positive probability p$$ p $$ of the gold standard test. Existing intervals are unreliable because the given nominal level 1−α$$ 1-\alpha $$ is not achieved. In this paper, we construct an exact interval by inverting the E+M score tests and improve it by the general h$$ h $$‐function method. We find that the total length of the improved interval is shorter than the exact intervals that are also the improved intervals when we apply the h$$ h $$‐function to several existing approximate intervals, including the score and Bayesian intervals. Therefore, it is recommended for practice. We are also interested in two other parameters: p∗$$ {p}^{\ast } $$—the difference between the two positive rates for the fallible and gold standard tests—and ξ$$ \xi $$—the false positive rate for the fallible test. To the best of our knowledge, the research on these two parameters is limited. For p∗$$ {p}^{\ast } $$, we find that any interval for p$$ p $$ can be converted to an interval for p∗$$ {p}^{\ast } $$. So, the interval converted from the aforementioned recommended interval for p$$ p $$ is recommended for inferring p∗$$ {p}^{\ast } $$. For ξ$$ \xi $$, the improved interval by the h$$ h $$‐function method over the E+M score interval is derived. We use an example to illustrate how the intervals are computed and provide a real data analysis. [ABSTRACT FROM AUTHOR]

The 2×2$$ 2\times 2 $$ table with a structural zero represents a common scenario in clinical trials and epidemiology, characterized by a specific empty cell. In such cases, the risk ratio serves as a vital parameter for statistical inference. However, existing confidence intervals, such as those constructed through the score test and Bayesian methods, fail to achieve the prescribed nominal level. Our focus is on numerically constructing exact confidence intervals for the risk ratio. We achieve this by optimally combining the modified inferential model method and the h$$ h $$‐function method. The resulting interval is then compared with intervals generated by four existing methods: the score method, the exact score method, the Bayesian tailed‐based method and the inferential model method. This comparison is conducted based on the infimum coverage probability, average interval length and non‐coverage probability criteria. Remarkably, our proposed interval outperforms other exact intervals, being notably shorter. To illustrate the effectiveness of our approach, we discuss two examples in detail. [ABSTRACT FROM AUTHOR]

The relative risk and odds ratio are widely used in many fields, including biomedical research, to compare two treatments. Extensive research has been done to infer the two parameters through approximate or exact confidence intervals. However, these intervals may be liberal or conservative. A natural question is whether the intervals can be further improved in maintaining the correct confidence coefficient of an approximate interval or shortening an exact but conservative interval. In this article, when two independent binomials are observed we offer an effort to improve any of the existing intervals by applying the h$$ h $$‐function method. In particular, if the given interval is approximate, then the improved interval is exact; if the given interval is exact, then the improved interval is a subset of the given interval. This method is also applied multiple times to the improved intervals until the final resultant interval cannot be shortened any further. To demonstrate the effectiveness of the method, we use three real datasets to illustrate in detail how several good intervals in practice are improved. Two exact intervals are then recommended for estimating each of the two parameters in different scenarios. [ABSTRACT FROM AUTHOR]

Mechanical interactions between cells have been shown to play critical roles in regulating cell signaling and communications. However, the precise measurement of intercellular forces is still quite challenging, especially considering the complex environment at cell–cell junctions. In this study, we report a fluorescence lifetime‐based approach to image and quantify intercellular molecular tensions. Using this method, tensile forces among multiple ligand–receptor pairs can be measured simultaneously. We first validated our approach and developed lifetime measurement‐based DNA tension probes to image E‐cadherin‐mediated tension on epithelial cells. These probes were then further applied to quantify the correlations between E‐cadherin and N‐cadherin tensions during an epithelial–mesenchymal transition process. The modular design of these probes can potentially be used to study the mechanical features of various physiological and pathological processes. [ABSTRACT FROM AUTHOR]