Parametric bootstrap and approximate tests for two Poisson variates

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.

Toward a More Robust Prediction of Pulmonary Embolism in Trauma Patients: A Risk Assessment Model Based on 38,000 Patients

OBJECTIVES

Pulmonary embolism (PE) is a rare but sometimes fatal complication of trauma. Risk stratification models identify patients at increased risk of PE; however, they are often complex and difficult to use. This research aims to develop a model, based on a large sample of trauma patients, which can be easily and quickly used at the time of admission to predict PE.

METHODS

This study used trauma registry data from 38,597 trauma patients. Of these, 239 (0.619%) developed a PE. We targeted demographic and injury data, prehospital information, and data on treatments and events during hospitalization. A multivariate binary logistic regression model was developed to predict the odds of developing a PE during hospitalization. The model was developed using a 50% randomly selected development subsample and then tested for accuracy using the remaining 50% validation sample.

RESULTS

We found 7 statistically significant predictors of PE, including (1) age [odds ratio (OR) = 1.01; 95% CI, 1.00-1.02; P = 0.05], (2) obesity (OR = 2.54; 95% CI, 1.29-4.99; P < 0.01), (3) injury from motorcycle accident (OR = 2.01; 95% CI, 1.25-3.22; P < 0.01), (4) arrival by helicopter (OR = 2.91; 95% CI, 1.16-7.27; P = 0.02), (5) emergency department admission pulse rate (OR = 1.01; 95% CI, 1.0-1.02; P = 0.06), (6) admission to intensive care unit (OR = 5.03; 95% CI, 3.12-8.12; P < 0.01), and (7) injury location, including thorax (OR = 1.57; 95% CI, 1.04-2.37; P = 0.03), abdomen (OR = 1.56; 95% CI, 1.04-2.33; P = 0.03), and lower extremity injuries (OR = 2.85; 95% CI, 3.12-8.12; P < 0.01). Our model was able to discriminate between predicted and actual PE events with a receiver operating characteristic area under the curve of 0.87. By identifying the top 25% high-risk patients, we were able to predict 80%-84% of pulmonary emboli.

CONCLUSIONS

This knowledge allows us to focus stronger thromboprophylactic efforts on patients at highest risk. This model can be used to rapidly identify trauma patients at high risk for PE.

LEVEL OF EVIDENCE

Prognostic Level II. See Instructions for Authors for a complete description of levels of evidence.

Stationarity tests for spatial point processes using discrepancies

For testing stationarity of a given spatial point pattern, Guan (2008) proposed a model-free statistic, based on the deviations between observed and expected counts of points in expanding regions within the sampling window. This article extends his method to a general class of statistics by incorporating also such information when points are projected to the axes and by allowing different ways to construct regions in which the deviations are considered. The limiting distributions of the new statistics can be expressed in terms of integrals of a Brownian sheet and hence asymptotic critical values can be approximated. A simulation study shows that the new tests are always more powerful than that of Guan. When applied to the longleaf pine data where Guan's test gave an inconclusive answer, the new tests indicate a clear rejection of the stationarity hypothesis.