The statistical significance of randomized controlled trial results is frequently fragile: A case for a Fragility Index

Objectives

A P-value <0.05 is one metric used to evaluate the results of a randomized controlled trial (RCT). We wondered how often statistically significant results in RCTs may be lost with small changes in the numbers of outcomes.

Study Design and Setting

A review of RCTs in high-impact medical journals that reported a statistically significant result for at least one dichotomous or time-to-event outcome in the abstract. In the group with the smallest number of events, we changed the status of patients without an event to an event until the P-value exceeded 0.05. We labeled this number the Fragility Index; smaller numbers indicated a more fragile result.

Results

The 399 eligible trials had a median sample size of 682 patients (range: 15-112,604) and a median of 112 events (range: 8-5,142); 53% reported a P-value <0.01. The median Fragility Index was 8 (range: 0-109); 25% had a Fragility Index of 3 or less. In 53% of trials, the Fragility Index was less than the number of patients lost to follow-up.

Conclusion

The statistically significant results of many RCTs hinge on small numbers of events. The Fragility Index complements the P-value and helps identify less robust results. 

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrodinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Effect of cataract extraction on the Glaucoma Progression Index (GPI) in glaucoma patients

PURPOSE: To determine the effect of cataract extraction on the glaucoma progression index (GPI) in glaucoma patients with coexisting cataract.

PATIENTS AND METHODS: This is a retrospective noncomparative study. Consecutive eligible patients with glaucoma who underwent phacoemulsification alone or in combination with augmented trabeculectomy were included. All patients had Swedish Interactive Threshold Algorithm-standard 24-2 visual fields within 10 months of surgery. Exclusion criteria included other ocular morbidity, intraoperative complications, and perimetric reliability indices greater than 33%. Comparison was made between the immediate visual fields before and after surgery. The main outcome measure was the change in GPI. Changes in the pattern standard deviation (PSD) and mean deviation (MD) were also assessed. Comparison of means was performed with the paired t test.

RESULTS: Thirty-three eyes of 33 patients (all Whites) were analyzed. The mean age at surgery was 77.0+/-8.7 years. Visual field tests were performed 3.3+/-3.0 months SD before surgery and 5.4+/-2.6 months after surgery. There was a statistically significant increase in the GPI after cataract surgery (from 71.5+/-18.5% to 74.6+/-17.1%; P=0.02). The improvement in MD was also statistically significant (from -11.8+/-5.3 to -10.2+/-5.3 dB; P <0.01), but the change in PSD did not reach statistical significance.

CONCLUSIONS: Uncomplicated cataract extraction resulted in a statistically significant improvement in the 24-2 Swedish Interactive Threshold Algorithm-standard GPI and MD, but not in PSD. Both the MD and the GPI may be influenced by lens opacities, which could make detection of glaucoma visual field progression more difficult for clinicians in glaucoma patients with concurrent cataract.

Lung Clearance Index Is a Repeatable and Sensitive Indicator of Radiological Changes in Bronchiectasis

RATIONALE: In bronchiectasis there is a need for improved markers of lung function to determine disease severity and response to therapy.

OBJECTIVES: To assess whether the lung clearance index is a repeatable and more sensitive indicator of computed tomography (CT) scan abnormalities than spirometry in bronchiectasis.

METHODS: Thirty patients with stable bronchiectasis were recruited and lung clearance index, spirometry, and health-related quality of life measures were assessed on two occasions, 2 weeks apart when stable (study 1). A separate group of 60 patients with stable bronchiectasis was studied on a single visit with the same measurements and a CT scan (study 2).

MEASUREMENTS AND MAIN RESULTS: In study 1, the intervisit intraclass correlation coefficient for the lung clearance index was 0.94 (95% confidence interval, 0.89 to 0.97; P < 0.001). In study 2, the mean age was 62 (10) years, FEV1 76.5% predicted (18.9), lung clearance index 9.1 (2.0), and total CT score 14.1 (10.2)%. The lung clearance index was abnormal in 53 of 60 patients (88%) and FEV1 was abnormal in 37 of 60 patients (62%). FEV1 negatively correlated with the lung clearance index (r = -0.51, P < 0.0001). Across CT scores, there was a relationship with the lung clearance index, with little evidence of an effect of FEV1. There were no significant associations between the lung clearance index or FEV1 and health-related quality of life.

CONCLUSIONS: The lung clearance index is repeatable and a more sensitive measure than FEV1 in the detection of abnormalities demonstrated on CT scan. The lung clearance index has the potential to be a useful clinical and research tool in patients with bronchiectasis.