Power and sample size calculations for the Wilcoxon-Mann-Whitney test in the presence of death-censored observations

Protocol for a Randomized Controlled Trial to Evaluate a Permissive Blood Pressure Target Versus Usual Care in Critically Ill Children with Hypotension (PRESSURE)

OBJECTIVES

Management of hypotension is a fundamental part of pediatric critical care, with cardiovascular support in the form of fluids or vasoactive drugs offered to every hypotensive child. However, optimal blood pressure (BP) targets are unknown. The PRotocolised Evaluation of PermiSSive BP Targets Versus Usual CaRE (PRESSURE) trial aims to evaluate the clinical and cost-effectiveness of a permissive mean arterial pressure (MAP) target of greater than a fifth centile for age compared with usual care.

DESIGN

Pragmatic, open, multicenter, parallel-group randomized control trial (RCT) with integrated economic evaluation.

SETTING

Eighteen PICUs across the United Kingdom.

PATIENTS

Infants and children older than 37 weeks corrected gestational age to 16 years accepted to a participating PICU, on mechanical ventilation and receiving vasoactive drugs for hypotension.

INTERVENTIONS

Adjustment of hemodynamic support to achieve a permissive MAP target greater than fifth centile for age during invasive mechanical ventilation.

MEASUREMENTS AND MAIN RESULTS

Randomization is 1:1 to a permissive MAP target or usual care, stratified by site and age group. Due to the emergency nature of the treatment, approaching patients for written informed consent will be deferred until after randomization. The primary clinical outcome is a composite of death and days of ventilatory support at 30 days. Baseline demographics and clinical status will be recorded as well as daily measures of BP and organ support, and discharge outcomes. This RCT received Health Research Authority approval (reference 289545), and a favorable ethical opinion from the East of England-Cambridge South Research Ethics Committee on May 10, 2021 (reference number 21/EE/0084). The trial is registered and has an International Standard RCT Number (reference 20609635).

CONCLUSIONS

Trial findings will be disseminated in U.K. national and international conferences and in peer-reviewed journals.

Sample size formula for general win ratio analysis

Originally proposed for the analysis of prioritized composite endpoints, the win ratio has now expanded into a broad class of methodology based on general pairwise comparisons. Complicated by the non-i.i.d. structure of the test statistic, however, sample size estimation for the win ratio has lagged behind. In this article, we develop general and easy-to-use formulas to calculate sample size for win ratio analysis of different outcome types. In a nonparametric setting, the null variance of the test statistic is derived using U-statistic theory in terms of a dispersion parameter called the standard rank deviation, an intrinsic characteristic of the null outcome distribution and the user-defined rule of comparison. The effect size can be hypothesized either on the original scale of the population win ratio, or on the scale of a "usual" effect size suited to the outcome type. The latter approach allows one to measure the effect size by, for example, odds/continuation ratio for totally/partially ordered outcomes and hazard ratios for composite time-to-event outcomes. Simulation studies show that the derived formulas provide accurate estimates for the required sample size across different settings. As illustration, real data from two clinical studies of hepatic and cardiovascular diseases are used as pilot data to calculate sample sizes for future trials.

Robust statistical inference for matched win statistics

As alternatives to the time-to-first-event analysis of composite endpoints, the win statistics, that is, the net benefit, the win ratio, and the win odds have been proposed to assess treatment effects, using a hierarchy of prioritized component outcomes based on clinical relevance or severity. Whether we are using paired organs of a human body or pair-matching patients by risk profiles or propensity scores, we can leverage the level of granularity of matched win statistics to assess the treatment effect. However, inference for the matched win statistics (net benefit, win ratio, and win odds)-quantities related to proportions-is either not available or unsatisfactory, especially in samples of small to moderate size or when the proportion of wins (or losses) is near 0 or 1. In this paper, we present methods to address these limitations. First, we introduce a different statistic to test for the null hypothesis of no treatment effect and provided a sample size formula. Then, we use the method of variance estimates recovery to derive reliable, boundary-respecting confidence intervals for the matched net benefit, win ratio, and win odds. Finally, a simulation study demonstrates the performance of the proposed methods. We illustrate the proposed methods with two data examples.

Abberant inverted U-shaped brain pattern and trait-related retinal impairment in schizophrenia patients with combined auditory and visual hallucinations: a pilot study

Schizophrenic patients often experience auditory hallucinations (AHs) and visual hallucinations (VHs). However, brain and retinal alterations associated with combined AHs and VHs in schizophrenic patients are unknown. This study aimed o investigate brain and retinal alterations in first episode un-treated schizophrenic patients with combined AHs and VHs (FUSCHAV). FUSCHAV patients (n = 120), divided into four groups according to severity of AH and VH symptoms, were compared to healthy controls (n = 30). Gray matter volume (GMV) and global functional connectivity density (gFCD) were recorded to reflect brain structure and functional alterations. Total retinal thickness was acquired by optical coherence tomography to assess retinal impairment. The majority of FUSCHAV patients (85.8%) demonstrated both GMV reduction and gFCD increases along with retinal thinning compared to healthy controls. The severity of GMV reduction and gFCD increase differed between patient groups, ranked from highest to lowest severity as follows: severe AHs combined with severe VHs (FUSCHSASV, 20 patients), moderate AHs combined with severe VHs (FUSCHMASV, 23 patients), severe AHs combined with moderate VHs (FUSCHSAMV, 28 patients), and moderate AHs combined with moderate VHs (FUSCHMAMV, 26). Retinal impairment was similar among the four FUSCHAV groups. GMV reduction and gFCD increases in the frontal-parietal lobule show an inverted U-shaped pattern among FUSCHAV patients according to AH and VH severity, while retinal impairment remains stable among FUSCHAV groups. These findings indicate a reciprocal deterioration in auditory and visual disturbances among FUSCHAV patients.

Reciprocal deterioration of visual and auditory hallucinations in schizophrenia presents V-shaped cognition impairment and widespread reduction in brain gray matter-A pilot study

Schizophrenic patients often experience visual hallucinations (VHs) and auditory hallucinations (AHs); however, brain aberrations associated with combined VH and AH in schizophrenic patients remains poorly documented. Changes to the brain and cognition during the first episode of untreated schizophrenic patients (FUSCH) with both VHs and AHs (FUSCHVA) were evaluated. One-hundred and fifty-seven patients were enrolled that had FUSCH (1) with VHs but not AHs (FUSCHV), and (2) with AHs but not VHs (FUSCHA), plus FUSCHVA and healthy controls (n = 30). Gray matter volume (GMV) and MATRICS Consensus Cognitive Battery (MCCB) was measured to reflect impairments to the brain and cognition, respectively. FUSCHVA patients had the severest cognitive impairment for all components of the MCCB, followed by FUSCHV and FUSCHA patients. Compared to healthy patients, FUSCHVA patients had reduced GMV in the occipital, parietal, frontal, and temporal cortex, and increased GMV in the hippocampus and striatum. Compared to FUSCHV patients, FUSCHVA patients had reduced GMV in the occipital cortex and postcentral gyrus, and increased GMV in the posterio-parietal lobe. Compared to patients with FUSCHA, the GMV in patients with FUSCHVV was reduced in the occipital cortex and posterio parietal lobe. In conclusion, visual and auditory hallucinations appear to deteriorate reciprocally in FUSCHVA patients, accompanied with sever cognitive impairments. Compared to AHs, VHs might be accompanied with severe GMV impairment in the brain, especially in the primary visual cortex and higher perception integration cortex (posterio parietal lobe) in patients with FUSCH.

Antipsychotic agents deteriorate brain and retinal function in schizophrenia patients with combined auditory and visual hallucinations: A pilot study and secondary follow-up study

INTRODUCTION

Schizophrenia patients often experience auditory hallucinations (AHs) and visual hallucinations (VHs). However, the degree and type of brain and retinal alterations associated with combined AHs and VHs in schizophrenia patients remain unknown. There is an urgent need for a study that investigates the trajectory of brain and retinal alterations in patients with first-episode untreated schizophrenia accompanied by combined AHs and VHs (FUSCHAV).

METHODS

FUSCHAV patients (n = 120), divided into four groups according to AH and VH symptom severity (severe AHs combined with severe VHs [FUSCHSASV, 20 patients]; middle-to-moderate AHs combined with severe VHs [FUSCHMASV, 23 patients]; severe AHs combined with middle-to-moderate VHs [FUSCHSAMV, 28 patients]; and middle-to-moderate AHs combined with middle-to-moderate VHs [FUSCHMAMV, 26 patients]), were compared to healthy controls (n = 30). Gray matter volume (GMV) was adopted for brain structural alteration assessment. Total retinal thickness was adopted as a measure of retinal thickness impairment.

RESULTS

In the pilot study, the rate of GMV reduction showed an inverted U-shaped pattern across the different FUSCHAV patient groups according to AH and VH severity. The degree of retinal impairment remained stable across the groups. More notably, in the secondary follow-up study, we observed that, after 6 months of treatment with antipsychotic agents, all the GMV reduction-related differences across the different patient groups disappeared, and both GMV and retinal thickness demonstrated a tendency to deteriorate.

CONCLUSIONS

These findings indicate the need for heightened alertness on brain and retinal impairments in patients with FUSCHAV. Further deteriorations induced by antipsychotic agent treatment should be monitored in clinical practice.

Membrane-potential compensation reveals mitochondrial volume expansion during HSC commitment

Proper control of mitochondrial function is a key factor in the maintenance of hematopoietic stem cells (HSCs). Mitochondrial content is commonly measured by staining with fluorescent cationic dyes. However, dye staining can be affected, not only by xenobiotic efflux pumps, but also by dye intake, which is dependent on the negative charge of mitochondria. Therefore, mitochondrial membrane potential (ΔΨ_mt) must be considered in these measurements because a high ΔΨ_mt due to respiratory chain activity can enhance dye intake, leading to the overestimation of mitochondrial volume. Here, we show that HSCs exhibit the highest ΔΨ_mt of the hematopoietic lineages and, as a result, ΔΨ_mt-independent methods most accurately assess the relatively low mitochondrial volumes and DNA amounts of HSC mitochondria. Multipotent progenitor stage or active HSCs display expanded mitochondrial volumes, which decline again with further maturation. Further characterization of the controlled remodeling of the mitochondrial landscape at each hematopoietic stage will contribute to a deeper understanding of the mitochondrial role in HSC homeostasis.

Power of the Wilcoxon-Mann-Whitney test for non-inferiority in the presence of death-censored observations

In clinical trials with patients in a critical state, death may preclude measurement of a quantitative endpoint of interest, and even early measurements, for example for intention-to-treat analysis, may not be available. For example, a non-negligible proportion of patients with acute pulmonary embolism will die before 30 day measurements on the efficacy of thrombolysis can be obtained. As excluding such patients may introduce bias, alternative analyses, and corresponding means for sample size calculation are needed. We specifically consider power analysis in a randomized clinical trial setting in which the goal is to demonstrate noninferiority of a new treatment as compared to a reference treatment. Also, a nonparametric approach may be needed due to the distribution of the quantitative endpoint of interest. While some approaches have been developed in a composite endpoint setting, our focus is on the continuous endpoint affected by death-related censoring, for which no approach for noninferiority is available. We propose a solution based on ranking the quantitative outcome and assigning worst rank scores to the patients without quantitative outcome because of death. Based on this, we derive power formulae for a noninferiority test in the presence of death-censored observations, considering settings with and without ties. The approach is illustrated for an exemplary clinical trial in pulmonary embolism. The results there show a substantial effect of death on power, also depending on differential effects in the two trial arms. Therefore, use of the proposed formulae is advisable whenever there is death to be expected before measurement of a quantitative primary outcome of interest.

Effect of In-Bed Leg Cycling and Electrical Stimulation of the Quadriceps on Global Muscle Strength in Critically Ill Adults: A Randomized Clinical Trial

IMPORTANCE

Early in-bed cycling and electrical muscle stimulation may improve the benefits of rehabilitation in patients in the intensive care unit (ICU).

OBJECTIVE

To investigate whether early in-bed leg cycling plus electrical stimulation of the quadriceps muscles added to standardized early rehabilitation would result in greater muscle strength at discharge from the ICU.

DESIGN, SETTING, AND PARTICIPANTS

Single-center, randomized clinical trial enrolling critically ill adult patients at 1 ICU within an 1100-bed hospital in France. Enrollment lasted from July 2014 to June 2016 and there was a 6-month follow-up, which ended on November 24, 2016.

INTERVENTIONS

Patients were randomized to early in-bed leg cycling plus electrical stimulation of the quadriceps muscles added to standardized early rehabilitation (n = 159) or standardized early rehabilitation alone (usual care) (n = 155).

MAIN OUTCOMES AND MEASURES

The primary outcome was muscle strength at discharge from the ICU assessed by physiotherapists blinded to treatment group using the Medical Research Council grading system (score range, 0-60 points; a higher score reflects better muscle strength; minimal clinically important difference of 4 points). Secondary outcomes at ICU discharge included the number of ventilator-free days and ICU Mobility Scale score (range, 0-10; a higher score reflects better walking capability). Functional autonomy and health-related quality of life were assessed at 6 months.

RESULTS

Among 314 randomized patients, 312 (mean age, 66 years; women, 36%; receiving mechanical ventilation at study inclusion, 78%) completed the study and were included in the analysis. The median global Medical Research Council score at ICU discharge was 48 (interquartile range [IQR], 29 to 58) in the intervention group and 51 (IQR, 37 to 58) in the usual care group (median difference, -3.0 [95% CI, -7.0 to 2.8]; P = .28). The ICU Mobility Scale score at ICU discharge was 6 (IQR, 3 to 9) in both groups (median difference, 0 [95% CI, -1 to 2]; P = .52). The median number of ventilator-free days at day 28 was 21 (IQR, 6 to 25) in the intervention group and 22 (IQR, 10 to 25) in the usual care group (median difference, 1 [95% CI, -2 to 3]; P = .24). Clinically significant events occurred during mobilization sessions in 7 patients (4.4%) in the intervention group and in 9 patients (5.8%) in the usual care group. There were no significant between-group differences in the outcomes assessed at 6 months.

CONCLUSIONS AND RELEVANCE

In this single-center randomized clinical trial involving patients admitted to the ICU, adding early in-bed leg cycling exercises and electrical stimulation of the quadriceps muscles to a standardized early rehabilitation program did not improve global muscle strength at discharge from the ICU.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT02185989.

An optimal Wilcoxon-Mann-Whitney test of mortality and a continuous outcome

We consider a two-group randomized clinical trial, where mortality affects the assessment of a follow-up continuous outcome. Using the worst-rank composite endpoint, we develop a weighted Wilcoxon-Mann-Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon-Mann-Whitney test statistic that maximize its power. We derive a formula for its power and demonstrate its accuracy in simulations. Finally, we apply the method to data from an acute ischemic stroke clinical trial of normobaric oxygen therapy.

Power and sample size calculations for the Wilcoxon-Mann-Whitney test in the presence of death-censored observations

We consider a clinical trial of a potentially lethal disease in which patients are randomly assigned to two treatment groups and are followed for a fixed period of time; a continuous endpoint is measured at the end of follow-up. For some patients; however, death (or severe disease progression) may preclude measurement of the endpoint. A statistical analysis that includes only patients with endpoint measurements may be biased. An alternative analysis includes all randomized patients, with rank scores assigned to the patients who are available for the endpoint measurement on the basis of the magnitude of their responses and with 'worst-rank' scores assigned to those patients whose death precluded the measurement of the continuous endpoint. The worst-rank scores are worse than all observed rank scores. The treatment effect is then evaluated using the Wilcoxon-Mann-Whitney test. In this paper, we derive closed-form formulae for the power and sample size of the Wilcoxon-Mann-Whitney test when missing measurements of the continuous endpoints because of death are replaced by worst-rank scores. We distinguish two approaches for assigning the worst-rank scores. In the tied worst-rank approach, all deaths are weighted equally, and the worst-rank scores are set to a single value that is worse than all measured responses. In the untied worst-rank approach, the worst-rank scores further rank patients according to their time of death, so that an earlier death is considered worse than a later death, which in turn is worse than all measured responses. In addition, we propose four methods for the implementation of the sample size formulae for a trial with expected early death. We conduct Monte Carlo simulation studies to evaluate the accuracy of our power and sample size formulae and to compare the four sample size estimation methods.