Sample size in clinical trials with dichotomous endpoints: use of covariables

Clinical and metabolic response to flaxseed oil omega-3 fatty acids supplementation in patients with diabetic foot ulcer: A randomized, double-blind, placebo-controlled trial

BACKGROUND

Data on the effects of flaxseed oil omega-3 fatty acids supplementation on wound healing and metabolic status in subjects with diabetic foot ulcer (DFU) are scarce.

OBJECTIVE

This study was conducted to evaluate the effects of flaxseed oil omega-3 fatty acids supplementation on wound healing and metabolic status in subjects with DFU.

METHODS

The current randomized, double-blind, placebo-controlled trial was conducted among 60 subjects (aged 40-85years old) with grade 3 DFU. Subjects were randomly allocated into two groups (30 subjects each group) to receive either 1000mg omega-3 fatty acids from flaxseed oil supplements or placebo twice a day for 12weeks.

RESULTS

After the 12-week intervention, compared with the placebo, omega-3 fatty acids supplementation resulted in significant decreases in ulcer length (-2.0±2.3 vs. -1.0±1.1cm, P=0.03), width (-1.8±1.7 vs. -1.0±1.0cm, P=0.02) and depth (-0.8±0.6 vs. -0.5±0.5cm, P=0.01). Additionally, significant reductions in serum insulin concentrations (-4.4±5.5 vs. +1.4±8.3 μIU/mL, P=0.002), homeostasis model of assessment-estimated insulin resistance (-2.1±3.0 vs. +1.0±5.0, P=0.005) and HbA1c (-0.9±1.5 vs. -0.1±0.4%, P=0.01), and a significant rise in the quantitative insulin sensitivity check index (+0.01±0.01 vs. -0.005±0.02, P=0.002) were seen following supplementation with omega-3 fatty acids compared with the placebo. In addition, omega-3 fatty acids supplementation significantly decreased serum high sensitivity C-reactive protein (hs-CRP) (-25.5±31.5 vs. -8.2±18.9μg/mL, P=0.01), and significantly increased plasma total antioxidant capacity (TAC) (+83.5±111.7 vs. -73.4±195.5mmol/L, P<0.001) and glutathione (GSH) concentrations (+60.7±140.2 vs. -15.5±129.7μmol/L, P=0.03) compared with the placebo.

CONCLUSIONS

Overall, omega-3 fatty acids supplementation for 12weeks among subjects with DFU had beneficial effects on parameters of ulcer size, markers of insulin metabolism, serum hs-CRP, plasma TAC and GSH levels. In addition, flaxseed oil omega-3 fatty acids may have played an indirect role in wound healing due to its effects on improved metabolic profiles.

Improving precision by adjusting for prognostic baseline variables in randomized trials with binary outcomes, without regression model assumptions

In randomized clinical trials with baseline variables that are prognostic for the primary outcome, there is potential to improve precision and reduce sample size by appropriately adjusting for these variables. A major challenge is that there are multiple statistical methods to adjust for baseline variables, but little guidance on which is best to use in a given context. The choice of method can have important consequences. For example, one commonly used method leads to uninterpretable estimates if there is any treatment effect heterogeneity, which would jeopardize the validity of trial conclusions. We give practical guidance on how to avoid this problem, while retaining the advantages of covariate adjustment. This can be achieved by using simple (but less well-known) standardization methods from the recent statistics literature. We discuss these methods and give software in R and Stata implementing them. A data example from a recent stroke trial is used to illustrate these methods.

Predicting major outcomes in type 1 diabetes: a model development and validation study

AIMS/HYPOTHESIS

Type 1 diabetes is associated with a higher risk of major vascular complications and death. A reliable method that predicted these outcomes early in the disease process would help in risk classification. We therefore developed such a prognostic model and quantified its performance in independent cohorts.

METHODS

Data were analysed from 1,973 participants with type 1 diabetes followed for 7 years in the EURODIAB Prospective Complications Study. Strong prognostic factors for major outcomes were combined in a Weibull regression model. The performance of the model was tested in three different prospective cohorts: the Pittsburgh Epidemiology of Diabetes Complications study (EDC, n = 554), the Finnish Diabetic Nephropathy study (FinnDiane, n = 2,999) and the Coronary Artery Calcification in Type 1 Diabetes study (CACTI, n = 580). Major outcomes included major CHD, stroke, end-stage renal failure, amputations, blindness and all-cause death.

RESULTS

A total of 95 EURODIAB patients with type 1 diabetes developed major outcomes during follow-up. Prognostic factors were age, HbA1c, WHR, albumin/creatinine ratio and HDL-cholesterol level. The discriminative ability of the model was adequate, with a concordance statistic (C-statistic) of 0.74. Discrimination was similar or even better in the independent cohorts, the C-statistics being: EDC, 0.79; FinnDiane, 0.82; and CACTI, 0.73.

CONCLUSIONS/INTERPRETATION

Our prognostic model, which uses easily accessible clinical features can discriminate between type 1 diabetes patients who have a good or a poor prognosis. Such a prognostic model may be helpful in clinical practice and for risk stratification in clinical trials.

The effect of covariate adjustment for baseline severity in acute stroke clinical trials with responder analysis outcomes

BACKGROUND

Traditionally in acute stroke clinical trials, the primary clinical outcome employed is a dichotomized modified Rankin Scale (mRS). New statistical methods, such as responder analysis, are being used in stroke studies to address the concern that baseline prognostic variables, such as stroke severity, impact the likelihood of a successful outcome. Responder analysis allows the definition of success to vary according to baseline prognostic variables, producing a more clinically relevant insight into the actual effect of investigational treatments. It is unclear whether or not statistical analyses should adjust for prognostic variables when responder analysis is used, as the outcome already takes these prognostic variables into account. This research aims to investigate the effect of covariate adjustment in the responder analysis framework in order to determine the appropriate analytic method.

METHODS

Using a current stroke clinical trial and its pilot studies to guide simulation parameters, 1,000 clinical trials were simulated at varying sample sizes under several treatment effects to assess power and type I error. Covariate-adjusted and unadjusted logistic regressions were used to estimate the treatment effect under each scenario. In the case of covariate-adjusted logistic regression, the trichotomized National Institute of Health Stroke Scale (NIHSS) was used in adjustment.

RESULTS

Under various treatment effect settings, the operating characteristics of the unadjusted and adjusted analyses do not substantially differ. Power and type I error are preserved for both the unadjusted and adjusted analyses.

CONCLUSIONS

Our results suggest that, under the given treatment effect scenarios, the decision whether or not to adjust for baseline severity when using a responder analysis outcome should be guided by the needs of the study, as type I error rates and power do not appear to vary largely between the methods. These findings are applicable to stroke trials which use the mRS for the primary outcome, but also provide a broader insight into the analysis of binary outcomes that are defined based on baseline prognostic variables.

TRIAL REGISTRATION

This research is part of the Stroke Hyperglycemia Insulin Network Effort (SHINE) trial, Identification Number NCT01369069.

Does the sliding dichotomy result in higher powered clinical trials for stroke and traumatic brain injury research?

BACKGROUND

Recent research has proposed a new method for defining a favorable outcome in traumatic brain injury and stroke research.

PURPOSE

This new method is called the sliding dichotomy, and it is suggested as a potential solution to the problem of underpowered clinical trials.

METHODS

We present a brief simulation study and graphical comparison of the power of each method to detect varying treatment effect sizes.

RESULTS

Simulations of a patient population similar to the National Acute Brain Injury Study: Hypothermia (NABISH) study indicate that the sliding dichotomy method does not result in higher power than traditional methods.

CONCLUSIONS

Although the sliding dichotomy may present gains in power in some cases, several aspects of the patient population need to be considered in choosing between sliding dichotomy and traditional definitions of favorable outcomes.

New approaches to increase statistical power in TBI trials: insights from the IMPACT study

INTRODUCTION

None of the multi-centre phase III randomized controlled trials (RCTs) performed in TBI have convincingly demonstrated efficacy. Problems in clinical trial design and analysis may have contributed to these failures. Clinical trials in the TBI population pose several complicated methodological challenges, related especially to the heterogeneity of the population. In this paper we examine the issue of heterogeneity within the IMPACT (International Mission on Prognosis and Clinical Trial design in TBI) database and investigate the application of conventional and innovative methods for the statistical analysis of trials in TBI.

METHODS AND RESULTS

Simulation studies in the IMPACT database (N = 9205) showed substantial gains in efficiency with covariate adjustment. Adjusting for 7 important predictors yielded up to a 28% potential reduction in trial size. Ongoing analyses on the potential benefit of ordinal analysis, such as proportional odds and sliding dichotomy, gave promising results with even larger potential reductions in trial size.

CONCLUSION

The statistical power of RCTs in TBI can be considerably increased by applying covariate adjustment and by ordinal analysis methods of the GOS. These methods need to be considered for optimizing future TBI trials.

Predicting outcome after traumatic brain injury: development and international validation of prognostic scores based on admission characteristics

BACKGROUND

Traumatic brain injury (TBI) is a leading cause of death and disability. A reliable prediction of outcome on admission is of great clinical relevance. We aimed to develop prognostic models with readily available traditional and novel predictors.

METHODS AND FINDINGS

Prospectively collected individual patient data were analyzed from 11 studies. We considered predictors available at admission in logistic regression models to predict mortality and unfavorable outcome according to the Glasgow Outcome Scale at 6 mo after injury. Prognostic models were developed in 8,509 patients with severe or moderate TBI, with cross-validation by omission of each of the 11 studies in turn. External validation was on 6,681 patients from the recent Medical Research Council Corticosteroid Randomisation after Significant Head Injury (MRC CRASH) trial. We found that the strongest predictors of outcome were age, motor score, pupillary reactivity, and CT characteristics, including the presence of traumatic subarachnoid hemorrhage. A prognostic model that combined age, motor score, and pupillary reactivity had an area under the receiver operating characteristic curve (AUC) between 0.66 and 0.84 at cross-validation. This performance could be improved (AUC increased by approximately 0.05) by considering CT characteristics, secondary insults (hypotension and hypoxia), and laboratory parameters (glucose and hemoglobin). External validation confirmed that the discriminative ability of the model was adequate (AUC 0.80). Outcomes were systematically worse than predicted, but less so in 1,588 patients who were from high-income countries in the CRASH trial.

CONCLUSIONS

Prognostic models using baseline characteristics provide adequate discrimination between patients with good and poor 6 mo outcomes after TBI, especially if CT and laboratory findings are considered in addition to traditional predictors. The model predictions may support clinical practice and research, including the design and analysis of randomized controlled trials.

Adjustment for Strong Predictors of Outcome in Traumatic Brain Injury Trials: 25% Reduction in Sample Size Requirements in the IMPACT Study

The aim of this study was to quantify the potential reduction in sample size that can be achieved by adjustment for predictors of outcome in traumatic brain injury (TBI) trials. We used individual patient data from seven therapeutic phase III randomized clinical trials (RCTs; n = 6166) in moderate or severe TBI, and three TBI surveys (n = 2238). The primary outcome was the dichotomized Glasgow Outcome Scale at 6 months (favorable/unfavorable). Baseline predictors of outcome considered were age, motor score, pupillary reactivity, computed tomography (CT) classification, traumatic subarachnoid hemorrhage, hypoxia, hypotension, glycemia, and hemoglobin. We calculated the potential sample size reduction obtained by adjustment of a hypothetical treatment effect for one to seven predictors with logistic regression models. The distribution of predictors was more heterogeneous in surveys than in trials. Adjustment of the treatment effect for the strongest predictors (age, motor score, and pupillary reactivity) yielded a reduction in sample size of 16-23% in RCTs and 28-35% in surveys. Adjustment for seven predictors yielded a reduction of about 25% in most studies: 20-28% in RCTs and 32-39% in surveys. A major reduction in sample size can be obtained with covariate adjustment in TBI trials. Covariate adjustment for strong predictors should be incorporated in the analysis of future TBI trials.

Subgroup analysis and covariate adjustment in randomized clinical trials of traumatic brain injury: a systematic review

OBJECTIVE

Few randomized clinical trials (RCTs) in the field of traumatic brain injury (TBI) have shown a significant treatment benefit. We critically reviewed the use of two types of secondary analyses, covariate adjustment and subgroup analysis, which are common in TBI trials.

METHODS

We performed a systematic review of therapeutic phase III RCTs, including adult patients with acute, moderate-to-severe TBI. Glasgow Outcome Scale (GOS) at > or =3 months as outcome, and > or =50 patients per arm were required. We compared the actual reporting of covariate adjustment and subgroup analyses with the Consolidated Standards of Reporting Trials (CONSORT) recommendations. Likewise, we reviewed six protocols of large multicenter RCTs and compared planned and reported subgroups.

RESULTS

We identified 18 RCTs (n = 6439). Sixteen trials used GOS at 6 months as outcome. Five RCTs reported covariate adjustment. The number of covariates was limited (< or =5), most frequently including age. Many covariates were outcome predictors. Four RCTs reported only adjusted treatment effects as the main efficacy parameter. Eleven RCTs reported subgroup analyses. Several subgroup factors (< or =7, mainly outcome predictors) and outcomes (< or =4) were included. The highest total number of subgroups was 15, and only three RCTs completely pre-specified subgroups. Notably, 10 of 11 RCTs performed inappropriate separate subgroup analyses. Of 11 RCTs, 5 gave subgroups the same emphasis as the overall effect. Reported subgroup analyses were insufficiently described and clearly differed from those planned in the protocol.

CONCLUSION

The reported covariate adjustment and subgroup analyses from TBI trials had several methodological shortcomings. Appropriate performance and reporting of covariate adjustment and subgroup analysis should be considerably improved in future TBI trials because interpretation of treatment benefits may be misleading otherwise.

Predictors of acamprosate efficacy: results from a pooled analysis of seven European trials including 1485 alcohol-dependent patients

RATIONALE

Acamprosate is a proven effective intervention in the treatment of alcohol dependence. However, acamprosate prevents lapses or relapses only in a minority of patients. An important question, therefore, is whether there is a specific subgroup of patients who respond particularly well to acamprosate.

OBJECTIVES

To identify predictors of acamprosate efficacy. Based upon the available evidence and hypotheses about the mechanisms underlying acamprosate's effects on drinking behavior, the following variables were considered to be potential positive predictors: high physiological dependence at baseline, negative family history of alcoholism, late age-of-onset, serious anxiety symptomatology at baseline, severe craving at baseline, and female gender.

METHOD

Potential predictors of acamprosate's efficacy were analyzed in a pooled analysis of data from seven randomized placebo-controlled trials involving a total of 1485 patients with alcohol dependence. Outcome is measured in terms of cumulative abstinence duration (CAD), continuous abstinence (ABST), and time to first relapse (TFR).

RESULTS

CAD and ABST were predicted by baseline measures of craving and anxiety, as well as by study and treatment condition. Acamprosate efficacy was not differentially associated with any of the predictor variables. Importantly, the hypotheses were rejected despite the large sample size and sufficient statistical power.

COMMENT

The most straight-forward clinical implication of this study is that acamprosate can be considered as a potentially effective pharmacotherapy for all patients with alcohol dependence. The effect size of acamprosate alone is, however, moderate. Some evidence indicates that the combination of acamprosate with naltrexone or disulfiram leads to substantially better outcomes.

Covariate adjustment in randomized controlled trials with dichotomous outcomes increases statistical power and reduces sample size requirements

OBJECTIVE

Randomized controlled trials (RCTs) with dichotomous outcomes may be analyzed with or without adjustment for baseline characteristics (covariates). We studied type I error, power, and potential reduction in sample size with several covariate adjustment strategies.

STUDY DESIGN AND SETTING

Logistic regression analysis was applied to simulated data sets (n=360) with different treatment effects, covariate effects, outcome incidences, and covariate prevalences. Treatment effects were estimated with or without adjustment for a single dichotomous covariate. Strategies included always adjusting for the covariate ("prespecified"), or only when the covariate was predictive or imbalanced.

RESULTS

We found that the type I error was generally at the nominal level. The power was highest with prespecified adjustment. The potential reduction in sample size was higher with stronger covariate effects (from 3 to 46%, at 50% outcome incidence and covariate prevalence) and independent of the treatment effect. At lower outcome incidences and/or covariate prevalences, the reduction was lower.

CONCLUSION

We conclude that adjustment for a predictive baseline characteristic may lead to a potentially important increase in power of analyses of treatment effect. Adjusted analysis should, hence, be considered more often for RCTs with dichotomous outcomes.

Intercenter variance in clinical trials of head trauma--experience of the National Acute Brain Injury Study: Hypothermia

OBJECT

In a recently conducted trial of hypothermia in patients with severe brain injury, differences were found in the effects of hypothermia treatment among various centers. This analysis explores the reasons for such differences.

METHODS

The authors reviewed data obtained in 392 patients treated for severe brain injury. Prerandomization variables, critical physiological variables, treatment variables, and accrual methodologies were investigated among various centers. Hypothermia was found to be detrimental in patients older than the age of 45 years, beneficial in patients younger than 45 years of age in whom hypothermia was present on admission, and without effect in those in whom normothermia was documented on admission. Marginally significant differences (p < 0.054) in the intercenter outcomes of hypothermia-treated patients were likely the result of wide differences in the percentage of patients older than 45 years of age and in the percentage of patients in whom hypothermia was present on admission among centers. The trial sensitivity was likely diminished by significant differences in the incidence of mean arterial blood pressure (MABP) less than 70 mm Hg (p < 0.001) and cerebral perfusion pressure (CPP) less than 50 mm Hg (p < 0.05) but not intracranial pressure (ICP) greater than 25 mm Hg (not significant) among patients in the various centers. Hours of vasopressor usage (p < 0.03) and morphine dose (p < 0.001) and the percentage of dehydrated patients varied significantly among centers (p < 0.001). The participation of small centers increased intercenter variance and diminished the quality of data.

CONCLUSIONS

For Phase III clinical trials we recommend: 1) a detailed protocol specifying fluid and MABP, ICP, and CPP management: 2) continuous monitoring of protocol compliance; 3) a run-in period for new centers to test accrual and protocol adherence; and 4) inclusion of only centers in which patients are regularly randomized.

Design and statistical issues in multicenter trials of severe head injury

Multicenter clinical trials are the most powerful agent to evaluate new therapies in medicine, but have failed to impact traumatic brain injury, in which at least 20 such trials have been performed, without a positive result. Such trials need to be carefully planned, with a run-in period to ensure center compliance. Stratification, careful monitoring, adequate sample size, interim analysis and adequate numbers of patients per center are all vital requirements for a useful outcome in such trials.