Exact unconditional testing procedures for comparing two independent Poisson rates

New Confidence Intervals for Relative Risk of Two Correlated Proportions

Biomedical studies, such as clinical trials, often require the comparison of measurements from two correlated tests in which each unit of observation is associated with a binary outcome of interest via relative risk. The associated confidence interval is crucial because it provides an appreciation of the spectrum of possible values, allowing for a more robust interpretation of relative risk. Of the available confidence interval methods for relative risk, the asymptotic score interval is the most widely recommended for practical use. We propose a modified score interval for relative risk and we also extend an existing nonparametric U-statistic-based confidence interval to relative risk. In addition, we theoretically prove that the original asymptotic score interval is equivalent to the constrained maximum likelihood-based interval proposed by Nam and Blackwelder. Two clinically relevant oncology trials are used to demonstrate the real-world performance of our methods. The finite sample properties of the new approaches, the current standard of practice, and other alternatives are studied via extensive simulation studies. We show that, as the strength of correlation increases, when the sample size is not too large the new score-based intervals outperform the existing intervals in terms of coverage probability. Moreover, our results indicate that the new nonparametric interval provides the coverage that most consistently meets or exceeds the nominal coverage probability.

Utilisation of peripheral vasopressor medications and extravasation events among critically ill patients in Rwanda: A prospective cohort study

Introduction

In high-income settings, vasopressor administration to treat haemodynamic instability through a central venous catheter (CVC) is the preferred standard. However, due to lack of availability and potential for complications, CVCs are not widely used in low- and middle-income countries. This prospective cohort study evaluated the use of peripheral vasopressors and associated incidence of extravasation events in patients with haemodynamic instability at the Centre Hospitalier Universitaire Kigali, Rwanda.

Methods

Patients ≥18 years of age receiving peripheral vasopressors in the emergency centre (EC) or intensive care unit (ICU) for >1 hour were eligible for inclusion. The primary outcome was extravasation events. Patients were followed hourly until extravasation, medication discontinuation, death, or CVC placement. Extravasation incidence with 95% confidence intervals (CI) were calculated using Poisson exact tests.

Results

64 patients were analysed. The median age was 49 (Interquartile Range [IQR]:33-65) and 55% were female. Distributive shock was the most frequent aetiology (47%). Intravenous (IV) location was most commonly antecubital fossa/upper arm (31%) and forearm/hand (43%). IV gauges ≤18 were used in 58% of locations. Most patients were treated with adrenaline (66%) and noradrenaline (41%), and 11% received multiple vasopressors. The median treatment duration was 19 hours (IQR:8.5-37). Treatment discontinuation was predominantly due to mortality (41%) or resolution of instability (36%). There were two extravasation events (2.9%), both limited to soft tissue swelling. Extravasation incidence was 0.8 events per 1000 patient-hours (95% CI:0.2-2.2).

Conclusion

Extravasation incidence with peripheral vasopressors was low, even with long use durations, suggesting peripheral infusions may be an acceptable approach when barriers exist to CVC placement.

On powerful exact nonrandomized tests for the Poisson two-sample setting

In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher’s exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

Exact confidence limits for the probability of response in two-stage designs

In addition to point estimate for the probability of response in a two-stage design (e.g., Simon's two-stage design for a Phase II clinical trial with binary endpoints), confidence limits should be Cute the confidence interval does not guarantee coverage probability in a two-stage setting. The existing exact approach to calculate one-sided limits is based on the overall number of responses to order the sample space. This approach could be conservative because many sample points have the same limits. We propose a new exact one-sided interval based on p-value for the sample space ordering. Exact intervals are computed by using binomial distributions directly, instead of a normal approximation. Both exact intervals preserve the nominal confidence level. The proposed exact interval based on the p-value generally performs better than the other exact interval with regard to expected length and simple average length of confidence intervals. Therefore, the new interval calculation based on p-value is recommended for use in practice.

Accurate unconditional p-values for a two-arm study with binary endpoints

Unconditional exact tests are increasingly used in practice for categorical data to increase the power of a study and to make the data analysis approach being consistent with the study design. In a two-arm study with a binary endpoint, p-value based on the exact unconditional Barnard test is computed by maximizing the tail probability over a nuisance parameter with a range from 0 to 1. The traditional grid search method is able to find an approximate maximum with a partition of the parameter space, but it is not accurate and this approach becomes computationally intensive for a study beyond two groups. We propose using a polynomial method to rewrite the tail probability as a polynomial. The solutions from the derivative of the polynomial contain the solution for the global maximum of the tail probability. We use an example from a double-blind randomized Phase II cancer clinical trial to illustrate the application of the proposed polynomial method to achieve an accurate p-value. We also compare the performance of the proposed method and the traditional grid search method under various conditions. We would recommend using this new polynomial method in computing accurate exact unconditional p-values.

Efficient Noninferiority Testing Procedures for Simultaneously Assessing Sensitivity and Specificity of Two Diagnostic Tests

Sensitivity and specificity are often used to assess the performance of a diagnostic test with binary outcomes. Wald-type test statistics have been proposed for testing sensitivity and specificity individually. In the presence of a gold standard, simultaneous comparison between two diagnostic tests for noninferiority of sensitivity and specificity based on an asymptotic approach has been studied by Chen et al. (2003). However, the asymptotic approach may suffer from unsatisfactory type I error control as observed from many studies, especially in small to medium sample settings. In this paper, we compare three unconditional approaches for simultaneously testing sensitivity and specificity. They are approaches based on estimation, maximization, and a combination of estimation and maximization. Although the estimation approach does not guarantee type I error, it has satisfactory performance with regard to type I error control. The other two unconditional approaches are exact. The approach based on estimation and maximization is generally more powerful than the approach based on maximization.