Dichotomising continuous data while retaining statistical power using a distributional approach

Unifying the analysis of continuous and categorical measures of weight loss and incorporating group effect: a secondary re-analysis of a large cluster randomized clinical trial using Bayesian approach

Background

Although frequentist paradigm has been the predominant approach to clinical studies for decades, some limitations associated with the frequentist null hypothesis significance testing have been recognized. Bayesian approaches can provide additional insights into data interpretation and inference by deriving posterior distributions of model parameters reflecting the clinical interest. In this article, we sought to demonstrate how Bayesian approaches can improve the data interpretation by reanalyzing the Rural Engagement in Primary Care for Optimizing Weight Reduction (REPOWER).

Methods

REPOWER is a cluster randomized clinical trial comparing three care delivery models: in-clinic individual visits, in-clinic group visits, and phone-based group visits. The primary endpoint was weight loss at 24 months and the secondary endpoints included the proportions of achieving 5 and 10% weight loss at 24 months. We reanalyzed the data using a three-level Bayesian hierarchical model. The posterior distributions of weight loss at 24 months for each arm were obtained using Hamiltonian Monte Carlo. We then estimated the probability of having a higher weight loss and the probability of having greater proportion achieving 5 and 10% weight loss between groups. Additionally, a four-level hierarchical model was used to assess the partially nested intervention group effect which was not investigated in the original REPOWER analyses.

Results

The Bayesian analyses estimated 99.5% probability that in-clinic group visits, compared with in-clinic individual visits, resulted in a higher percent weight loss (posterior mean difference: 1.8%[95% CrI: 0.5,3.2%]), a greater probability of achieving 5% threshold (posterior mean difference: 9.2% [95% CrI: 2.4, 16.0%]) and 10% threshold (posterior mean difference: 6.6% [95% CrI: 1.7, 11.5%]). The phone-based group visits had similar result. We also concluded that including intervention group did not impact model fit significantly.

Conclusions

We unified the analyses of continuous (the primary endpoint) and categorical measures (the secondary endpoints) of weight loss with one single Bayesian hierarchical model. This approach gained statistical power for the dichotomized endpoints by leveraging the information in the continuous data. Furthermore, the Bayesian analysis enabled additional insights into data interpretation and inference by providing posterior distributions for parameters of interest and posterior probabilities of different hypotheses that were not available with the frequentist approach.

Trial registration

ClinicalTrials.gov Identifier NCT02456636; date of registry: May 28, 2015.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01499-0.

Smoking cessation intentions and attempts one year after the federally mandated smoke-free housing rule

The present study examines public housing residents' smoking cessation intentions, expectancies, and attempts one year after implementation of the Department of Housing and Urban Development's mandatory smoke-free rule in public housing. The sample includes 233 cigarette smokers, ages 18-80, who reside in the District of Columbia Housing Authority. Data collection occurred between March and August 2019. Descriptive statistics, chi-square, and Wilcoxon two-sample test analyses assessed smoking cessation intentions, expectancies, and attempts across resident demographics and characteristics. Findings showed 17.2% of residents reported not thinking about quitting, 39.1% reported thinking about quitting, and 48.6% reported thinking about quitting specifically because of the rule. Residents ages 60-80 were more likely to consider quitting because of the rule, compared to residents ages 18-59. Of those thinking of quitting, 58.6% were sure they could quit if they tried. Those thinking of quitting due to the rule (62.0%) were more likely to have made at least one quit attempt in the past 3 months than those i not attributinging thinking of quitting to the rule. Res Residents trying to quit reported an average of 2.7 attempts in the last 3 months;; most perceived evidence-based cessation supports as not helpful. A A majority reported thinking about quitting and attempting to quit but continuing to smoke, indicating a significant gap between intent to quit and successfully quitting. Results suggest that the rule positively influenced smoking behaviors. However, additional interventions are needed to assist public housing residents with successfully quitting smoking.

COVID-19 attributed mortality and ambient temperature: a global ecological study using a two-stage regression model

A negative correlation between ambient temperature and COVID-19 mortality has been observed. However, the World Meteorological Organization (WMO) has reinforced the importance of government interventions and warned countries against relaxing control measures due to warmer temperatures. Further understanding of this relationship is needed to help plan vaccination campaigns opportunely. Using a two-stage regression model, we conducted cross-sectional and longitudinal analyses to evaluate the association between monthly ambient temperature lagged by one month with the COVID-19 number of deaths and the probability of high-level of COVID-19 mortality in 150 countries during time t = 60, 90, and 120 days since the onset. First, we computed a log-linear regression to predict the pre-COVID-19 respiratory disease mortality to homogenize the baseline disease burden within countries. Second, we employed negative binomial and logistic regressions to analyze the linkage between the ambient temperature and our outcomes, adjusting by pre-COVID-19 respiratory disease mortality rate, among other factors. The increase of one Celsius degree in ambient temperature decreases the incidence of COVID-19 deaths (IRR = 0.93; SE: 0.026, p-value<0.001) and the probability of high-level COVID-19 mortality (OR = 0.96; SE: 0.019; p-value<0.001) over time. High-income countries from the northern hemisphere had lower temperatures and were most affected by pre-COVID respiratory disease mortality and COVID-19 mortality. This study provides a global perspective corroborating the negative association between COVID-19 mortality and ambient temperature. Our longitudinal findings support the statement made by the WMO. Effective, opportune, and sustained reaction from countries can help capitalize on higher temperatures’ protective role including the timely rollout of vaccination campaigns.

Minimal clinically important difference in means in vulnerable populations: challenges and solutions

INTRODUCTION AND MOTIVATION

Many health studies measure a continuous outcome and compare means between groups. Since means for biological data are often difficult to interpret clinically, it is common to dichotomise using a cut-point and present the 'percentage abnormal' alongside or in place of means. Examples include birthweight where 'abnormal' is defined as <2500 g (low birthweight), systolic blood pressure with abnormal defined as >140 mm Hg (high blood pressure) and lung function with varying definitions of the 'limit of normal'. In vulnerable populations with low means, for example, birthweight in a population of preterm babies, a given difference in means between two groups will represent a larger difference in the percentage with low birthweight than in a general population of babies where most will be full term. Thus, in general, the difference in percentage of patients with abnormal values for a given difference in means varies according to the reference population's mean value. This phenomenon leads to challenges in interpreting differences in means in vulnerable populations and in defining an outcome-specific minimal clinically important difference (MCID) in means since the proportion abnormal, which is useful in interpreting means, is not constant-it varies with the population mean. This has relevance for study power calculations and data analyses in vulnerable populations where a small observed difference in means may be difficult to interpret clinically and may be disregarded, even if associated with a relatively large difference in percentage abnormal which is clinically relevant.

METHODS

To address these issues, we suggest both difference in means and difference in percentage (proportion) abnormal are considered when choosing the MCID, and that both means and percentages abnormal are reported when analysing the data.

CONCLUSIONS

We describe a distributional approach to analyse proportions classified as abnormal that avoids the usual loss of precision and power associated with dichotomisation.

Bayesian EMAX model with a mixture of normal distributions for dose-response in clinical trials

When a dose-response relationship is monotonic, the EMAX model has been shown to provide a good empirical fit for designing and analyzing dose-response data across a wide range of pharmaceutical studies. However, the EMAX model has never been applied to a finite mixture distribution. Motivated by a proposal investigating DHA dose effect on preterm birth (PTB, <37 weeks gestation) rate, we developed a Bayesian EMAX mixture model incorporating the three normal components finite mixture model into the EMAX framework. The proposed Bayesian EMAX mixture model analyzes gestational age as a continuous variable, which allows for statistically efficient estimates of PTB rate using various cut point with the same parsimonious model. For example, we can estimate the rate of early PTB (ePTB, <34 weeks gestation), PTB (<37 weeks gestation), and late-term birth (>41 weeks gestation) using the same model. We compared our proposed EMAX mixture model with an EMAX logistic model and an independent doses logistic model for a dichotomized endpoint using extensive simulations. Across the scenarios under consideration, the EMAX mixture model achieved higher power than the EMAX logistic model and the independent doses logistic model in detecting the effect of DHA supplementation on the PTB rate. The EMAX mixture model also resulted in smaller mean squared errors (MSE) in PTB rate estimates.

Improving analysis practice of continuous adverse event outcomes in randomised controlled trials - a distributional approach

Background

Randomised controlled trials (RCTs) provide valuable information for developing harm profiles but current analysis practices to detect between-group differences are suboptimal. Drug trials routinely screen continuous clinical and biological data to monitor participant harm. These outcomes are regularly dichotomised into abnormal/normal values for analysis. Despite the simplicity gained for clinical interpretation, it is well established that dichotomising outcomes results in a considerable reduction in information and thus statistical power. We propose an automated procedure for the routine implementation of the distributional method for the dichotomisation of continuous outcomes proposed by Peacock and Sauzet, which retains the precision of the comparison of means.

Methods

We explored the use of a distributional approach to compare differences in proportions based on the comparison of means which retains the power of the latter. We applied this approach to the screening of clinical and biological data as a means to detect ‘signals’ for potential adverse drug reactions (ADRs). Signals can then be followed-up in further confirmatory studies. Three distributional methods suitable for different types of distributions are described. We propose the use of an automated approach using the observed data to select the most appropriate distribution as an analysis strategy in a RCT setting for multiple continuous outcomes. We illustrate this approach using data from three RCTs assessing the efficacy of mepolizumab in asthma or COPD. Published reference ranges were used to define the proportions of participants with abnormal values for a subset of 10 blood tests. The between-group distributional and empirical differences in proportions were estimated for each blood test and compared.

Results

Within trials, the distributions varied across the 10 outcomes demonstrating value in a practical approach to selecting the distributional method in the context of multiple adverse event outcomes. Across trials, there were three outcomes where the method chosen by the automated procedure varied for the same outcome. The distributional approach identified three signals (eosinophils, haematocrit, and haemoglobin) compared to only one when using the Fisher’s exact test (eosinophils) and two identified by use of the 95% confidence interval for the difference in proportions (eosinophils and potassium).

Conclusion

When dichotomisation of continuous adverse event outcomes aids clinical interpretation, we advocate use of a distributional approach to retain statistical power. Methods are now easy to implement. Retaining information is especially valuable in the context of the analysis of adverse events in RCTs. The routine implementation of this automated approach requires further evaluation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13063-021-05343-0.

Postnatal dexamethasone exposure and lung function in adolescents born very prematurely

We previously demonstrated corticosteroid administration on the neonatal intensive care unit was associated with reduced lung function at 11 to 14 years of age in children born very prematurely. The objective of this observational study was to assess if lung function remained impaired at 16 to 19 years of age in those who had received postnatal corticosteroids and whether the trajectory of lung function with increasing age differed between those who had and had not received corticosteroids. One hundred and fifty-nine children born prior to 29 weeks of gestational age had comprehensive lung function measurements; 49 had received postnatal dexamethasone. Lung function outcomes were compared between those who had and had not received postnatal dexamethasone after adjustment for neonatal factors. Forced expiratory flow at 75%, 50%, 25% and 25-75% of the expired vital capacity, forced expiratory volume in one second, peak expiratory flow and forced vital capacity and lung volumes (total lung capacity and residual volume) were assessed. The majority of results were significantly lower in those who received dexamethasone (between 0.61 to 0.78 standard deviations). Lung function reduced as the number of courses of dexamethasone increased. Between 11 and 14 years and 16 to 19 years, lung function improved in the unexposed group, but forced expiratory flow at 75% of the expired vital capacity and forced expiratory volume in one second deteriorated in those who had received postnatal corticosteroids (p = 0.0006). These results suggest that prematurely born young people who received postnatal corticosteroids may be at risk of premature onset of chronic obstructive pulmonary disease.

The differential effect of maternal dietary patterns on quantiles of Birthweight

BACKGROUND

Maternal dietary habits during pregnancy are considered essential for development and growth of the fetus as well as maternal health. It has an effect on the birthweight of infants. However, little is known about the effect of dietary patterns on birthweight in urban South Africa. This study aimed to investigate differential effect of dietary patterns of pregnant women on quantiles of birthweight.

METHODS

Data for the study were obtained from a Mother and Child in the Environment birth cohort study in Durban South Africa. Quantile regression was used to investigate the effect of maternal dietary patterns on quantiles of birthweight. Data collection was conducted during the period of 2013 to 2017 in Durban South Africa. Using factor analysis, eight dietary groups were identified from 687 pregnant women in the cohort. Quantile regression analysis was employed to identify the differential effects of the seven dietary groups and demographic factors on the birthweight.

RESULTS

The quantile regression estimates at the 50^th quantile and the ordinary regression estimates painted the same picture about the conditional mean effect of covariates on the birthweight. But unlike the quantile regression the ordinary regression fails to give insights about the covariates effect disparities at the low and/or upper birthweight quantiles. All the dietary groups show a significant differential effect at different birthweight quantiles. For instance, increased frequency of protein rich foods intake was associated with reduction in birthweight at lower and upper quantiles; increased frequency of junk foods intake has a slight increase in birthweight at the lower quantiles but significantly higher increase at the 95^th quantile (p < 0.001); increase in consuming vegetable rich foods, reduced birthweight at 95^th quantile (p < 0.001). The results further showed that employment (p = 0.006) and family size (p = 0.002) had differential effects across different birthweight quantiles.

CONCLUSIONS

Both maternal undernutrition and overnutrition of protein rich foods, junk foods, snack and energy foods and vegetable rich foods have shown a substantial varying effects on those infants with birthweights in the lower and upper birthweight quantiles.

Small-Area Factors and Their Impact on Low Birth Weight-Results of a Birth Cohort Study in Bielefeld, Germany

Introduction: The location of residence is a factor possibly contributing to social inequalities and emerging evidence indicates that it already affects perinatal development. The underlying pathways remain unknown; theory-based and hypothesis-driven analyses are lacking. To address these challenges, we aim to establish to what extent small-area characteristics contribute to low birth weight (LBW), independently of individual characteristics. First, we select small-area characteristics based on a conceptual model and measure them. Then, we empirically analyse the impact of these characteristics on LBW. Material and methods: Individual data were provided by the birth cohort study "Health of infants and children in Bielefeld/Germany." The sample consists of 892 eligible women and their infants distributed over 80 statistical districts in Bielefeld. Small-area data were obtained from local noise maps, emission inventory, Google Street View and civil registries. A linear multilevel analysis with a two-level structure (individuals nested within statistical districts) was conducted. Results: The effects of the selected small-area characteristics on LBW are small to non-existent, no significant effects are detected. The differences in proportion of LBW based on marginal effects are small, ranging from zero to 1.1%. Newborns from less aesthetic and subjectively perceived unsafe neighbourhoods tend to have higher proportions of LBW. Discussion: We could not find evidence for negative effects of small-area factors on LBW, but our study confirms that obtaining adequate sample size, reliable measure of exposure and using available data for operationalisation of the small-area context represent the core challenges in this field of research.

Lung function and respiratory outcomes in teenage boys and girls born very prematurely

OBJECTIVES

Male sex in prematurely born infants has been associated with worse respiratory outcomes in early childhood.

WORKING HYPOTHESIS

Respiratory outcomes at 11 to 14 years of age in children born very prematurely and routinely exposed to antenatal corticosteroids and postnatal surfactant would differ according to sex.

STUDY DESIGN

Analysis of follow-up data.

PATIENT-SUBJECT SELECTION

Three hundred and nineteen children born before 29 weeks of gestational age from the United Kingdom Oscillation Study.

METHODOLOGY

Spirometry was used to assess forced expiratory flow at 75%, 50%, and 25% of expired vital capacity (FEF₇₅ , FEF₅₀ , and FEF₂₅ ), forced expiratory volume in 1 second (FEV₁ ), peak expiratory flow (PEF), and forced vital capacity (FVC). Lung volumes were measured using a helium dilution technique (FRC_He ) and by plethysmography (FRC_pleth ). Total lung capacity (TLC) and residual volume (RV) were calculated. Mean lung function measurements were compared using linear mixed models and reported as unadjusted and adjusted for neonatal and age 11 to 14 years factors. The participants also completed health questionnaires and provided a urine sample for assessment of passive or active smoking.

RESULTS

Three (FEF₂₅ , FEF_25-75 , FEV₁ ) lung function measures showed significant differences in favor of females after adjustment. The percentage of children with abnormal lung function (below 5th centile for normal) had adjusted differences between 10 and 30 percentage points, for example, for FEF₂₅ 15% females compared with 26% males.

CONCLUSIONS

Among extremely prematurely born school children airway function was significantly worse in males.

Predictive Validity, Diagnostic Accuracy and Test-Retest Reliability of the Strength of Urges to Drink (SUTD) Scale

This study compared the 1-item Strength of Urges to Drink (SUTD) scale with the 10-item Alcohol Use Disorders Identification Test (AUDIT) on (i) test-retest reliability, (ii) predictive validity, and (iii) diagnostic accuracy. Data come from 2960 participants taking part in the Alcohol Toolkit Study (ATS), a monthly population survey of adults in England. The long-term test-retest reliability of the SUTD was 'fair', but lower than that for the AUDIT (Kappaweighted 0.24 versus 0.49). Individuals with "slight/moderate" urges to drink had higher odds of reporting an attempt to cut down relative to those not experiencing urges (adjusted odds ratios (AdjORs) 1.78 95% confidence interval (CI) 1.43-2.22 and 1.54 95% CI 1.20-1.96). Drinkers reporting "moderate/slight/strong" urges to drink had mean change in consumption scores which were 0.16 (95% CI -0.31 to -0.02), 0.40 (95% CI -0.56 to -0.24) and 0.37 (95% CI -0.69 to -0.05) units lower than those reporting no urges. For all outcomes, strong associations were found with AUDIT scores. The accuracy of the SUTD for discriminating between drinkers who did and did not reduce their consumption was 'acceptable', and similar to that for the AUDIT (ROCAUC 0.6). The AUDIT had better diagnostic accuracy in predicting change in alcohol consumption. The SUTD may be an efficient dynamic measure of urges to drink for population surveys and studies assessing the impact of alcohol-reduction interventions.

Using marginal standardisation to estimate relative risk without dichotomising continuous outcomes

Background

Although criticisms regarding the dichotomisation of continuous variables are well known, applying logit model to dichotomised outcomes is the convention because the odds ratios are easily obtained and they approximate the relative risks (RRs) for rare events.

Methods

To avoid dichotomisation when estimating RR, the marginal standardisation method that transforms estimates from logit or probit model to RR estimate is extended to include estimates from linear model in the transformation. We conducted a simulation study to compare the statistical properties of the estimates from: (i) marginal standardisation method between models for continuous (i.e., linear model) and dichotomised outcomes (i.e., logit or probit model), and (ii) marginal standardisation method and distributional approach (i.e., marginal mean method) applied to linear model. We also compared the diagnostic test for probit, logit and linear models. For the real dataset analysis, we applied these analytical approaches to assess the management of inpatient hyperglycaemia in a pilot intervention study.

Results

Although the RR estimates from the marginal standardisation method were generally unbiased for all models in the simulation study, the marginal standardisation method for linear model provided estimates with higher precision and power than logit or probit model, especially when the baseline risks were at the extremes. When comparing approaches that avoid dichotomisation, RR estimates from these approaches had comparable performance. Assessing the assumption of error distribution was less powerful for logit or probit model via link test when compared with diagnostic test for linear model. After accounting for multiple thresholds representing varying levels of severity in hyperglycaemia, marginal standardisation method for linear model provided stronger evidence of reduced hyperglycaemia risk after intervention in the real dataset analysis although the RR estimates were similar across various approaches.

Conclusions

When compared with approaches that do not avoid dichotomisation, the RR estimated from linear model is more precise and powerful, and the diagnostic test from linear model is more powerful in detecting mis-specified error distributional assumption than the diagnostic test from logit or probit model. Our work describes and assesses the methods available to analyse data involving studies of continuous outcomes with binary representations.

Electronic supplementary material

The online version of this article (10.1186/s12874-019-0778-9) contains supplementary material, which is available to authorized users.

Two-Part Models and Quantile Regression for the Analysis of Survey Data With a Spike. The Example of Satisfaction With Health Care

Background: Results of patient satisfaction questionnaires can contain a spike at the value corresponding to a complete satisfaction. A possible interpretation is that there are two types of respondents, those who are willing to provide a negative evaluation to one or more items proposed in the questionnaire and those who will always provide a completely positive evaluation irrespective of the item. The aim of the present study is to compare various statistical approaches to the analysis of such data using data from a rehabilitation patient survey of the German Statutory Pension Insurance Scheme as an example.

Method: We used data from 272,806 respondents who participated in the survey from 2008 to 2011. We illustrate four models: linear regression, logistic regression, a two-part model based on the assumption of two underlying populations and quantile regression, which does not require any distributional assumptions. For each model we consider the relationship of the satisfaction score with two covariates.

Results: While providing correct estimates of the mean values (marginal effects), the assumptions of the linear model are violated which can lead to false interpretations. A two-part regression which consists of a logistic regression followed by a linear regression conditional on not being fully satisfied is a useful alternative. For research questions focusing on specific parts of the distribution, logistic regression as well as quantile regression are to be considered.

Discussion: Data with a spike represents a statistical challenge but a range of modeling approaches is available to provide sound interpretations and correct answers to research questions.

Odds ratios from logistic, geometric, Poisson, and negative binomial regression models

Background

The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.

Methods

We propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.

Results

In simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.

Conclusions

More precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0568-9) contains supplementary material, which is available to authorized users.

Effect of dexamethasone exposure on the neonatal unit on the school age lung function of children born very prematurely

The objective of this study was to determine the impact of postnatal dexamethasone treatment on the neonatal unit on the school age lung function of very prematurely born children. Children born prior to 29 weeks of gestational age had been entered into a randomised trial of two methods of neonatal ventilation (United Kingdom Oscillation Study). They had comprehensive lung function measurements at 11 to 14 years of age. One hundred and seventy-nine children born at a mean gestational age of 26.9 (range 23–28) weeks were assessed at 11 to 14 years; 50 had received postnatal dexamethasone. Forced expiratory flow at 75% (FEF₇₅), 50%, 25% and 25–75% of the expired vital capacity, forced expiratory volume in one second, peak expiratory flow and forced vital capacity and lung volumes including total lung capacity and residual volume were assessed. Lung function outcomes were compared between children who had and had not been exposed to dexamethasone after adjustment for neonatal factors using linear mixed effects regression. After adjustment for confounders all the mean spirometry results were between 0.38 and 0.87 standard deviations lower in those exposed to dexamethasone compared to the unexposed. For example, the mean FEF₇₅ z-score was 0.53 lower (95% CI 0.21 to 0.85). The mean lung function was lower as the number of courses of dexamethasone increased. In conclusion, postnatal dexamethasone exposure was associated with lower mean lung function at school age in children born extremely prematurely. Our results suggest the larger the cumulative dose the greater the adverse effect on lung function at follow-up.

Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants

Background

The analysis of perinatal outcomes often involves datasets with some multiple births. These are datasets mostly formed of independent observations and a limited number of clusters of size two (twins) and maybe of size three or more. This non-independence needs to be accounted for in the statistical analysis. Using simulated data based on a dataset of preterm infants we have previously investigated the performance of several approaches to the analysis of continuous outcomes in the presence of some clusters of size two. Mixed models have been developed for binomial outcomes but very little is known about their reliability when only a limited number of small clusters are present.

Methods

Using simulated data based on a dataset of preterm infants we investigated the performance of several approaches to the analysis of binomial outcomes in the presence of some clusters of size two. Logistic models, several methods of estimation for the logistic random intercept models and generalised estimating equations were compared.

Results

The presence of even a small percentage of twins means that a logistic regression model will underestimate all parameters but a logistic random intercept model fails to estimate the correlation between siblings if the percentage of twins is too small and will provide similar estimates to logistic regression. The method which seems to provide the best balance between estimation of the standard error and the parameter for any percentage of twins is the generalised estimating equations.

Conclusions

This study has shown that the number of covariates or the level two variance do not necessarily affect the performance of the various methods used to analyse datasets containing twins but when the percentage of small clusters is too small, mixed models cannot capture the dependence between siblings.

A socioecological model of posttraumatic stress among Australian midwives

OBJECTIVE

to develop a comprehensive model of personal, trauma event-related and workplace-related risk factors for posttraumatic stress subsequent to witnessing birth trauma among Australian midwives.

DESIGN

a descriptive, cross-sectional design was used.

PARTICIPANTS

members of the Australian College of Midwives were invited to complete an online survey.

MEASUREMENTS

the survey included items about witnessing a traumatic birth event and previous experiences of life trauma. Trauma symptoms were assessed with the Posttraumatic Stress Disorder Symptom Scale Self-Report measure. Empathy was assessed with the Interpersonal Reactivity Index. Decision authority and psychological demand in the workplace were measured with the Job Content Questionnaire. Variables that showed a significant univariate association with probable posttraumatic stress disorder were entered into a multivariate logistic regression model.

FINDINGS

601 completed survey responses were analysed. The multivariable model was statistically significant and explained 27.7% (Nagelkerke R square) of the variance in posttraumatic stress symptoms and correctly classified 84.1% of cases. Odds ratios indicated that intention to leave the profession, a peritraumatic reaction of horror, peritraumatic feelings of guilt, and a personal traumatic birth experience were strongly associated with probable Posttraumatic Stress Disorder.

CONCLUSIONS

risk factors for posttraumatic stress following professional exposure to traumatic birth events among midwives are complex and multi-factorial. Posttraumatic stress may contribute to attrition in midwifery. Trauma-informed care and practice may reduce the incidence of traumatic births and subsequent posttraumatic stress reactions in women and midwives providing care.

Comparison of Dichotomized and Distributional Approaches in Rare Event Clinical Trial Design: a Fixed Bayesian Design

This research was motivated by our goal to design an efficient clinical trial to compare two doses of docosahexaenoic acid supplementation for reducing the rate of earliest preterm births and/or preterm births. Dichotomizing continuous gestational age data using a classic binomial distribution will result in a loss of information and reduced power. A distributional approach is an improved strategy to retain statistical power from the continuous distribution. However, appropriate distributions that fit the data properly, particularly in the tails, must be chosen, especially when the data are skewed. A recent study proposed a skew-normal method. We propose a three-component normal mixture model and introduce separate treatment effects at different components of gestational age. We evaluate operating characteristics of mixture model, beta-binomial model, and skew-normal model through simulation. We also apply these three methods to data from two completed clinical trials from the USA and Australia. Finite mixture models are shown to have favorable properties in preterm births analysis but minimal benefit for earliest preterm births analysis. Normal models on log transformed data have the largest bias. Therefore we recommend finite mixture model for preterm births study. Either finite mixture model or beta-binomial model is acceptable for earliest preterm births study.

Logistic regression for dichotomized counts

Sometimes there is interest in a dichotomized outcome indicating whether a count variable is positive or zero. Under this scenario, the application of ordinary logistic regression may result in efficiency loss, which is quantifiable under an assumed model for the counts. In such situations, a shared-parameter hurdle model is investigated for more efficient estimation of regression parameters relating to overall effects of covariates on the dichotomous outcome, while handling count data with many zeroes. One model part provides a logistic regression containing marginal log odds ratio effects of primary interest, while an ancillary model part describes the mean count of a Poisson or negative binomial process in terms of nuisance regression parameters. Asymptotic efficiency of the logistic model parameter estimators of the two-part models is evaluated with respect to ordinary logistic regression. Simulations are used to assess the properties of the models with respect to power and Type I error, the latter investigated under both misspecified and correctly specified models. The methods are applied to data from a randomized clinical trial of three toothpaste formulations to prevent incident dental caries in a large population of Scottish schoolchildren.

A distributional approach to obtain adjusted comparisons of proportions of a population at risk

BACKGROUND

Dichotomisation of continuous data has statistical drawbacks such as loss of power but may be useful in epidemiological research to define high risk individuals.

METHODS

We extend a methodology for the presentation of comparison of proportions derived from a comparison of means for a continuous outcome to reflect the relationship between a continuous outcome and covariates in a linear (mixed) model without losing statistical power. The so called "distributional method" is described and using perinatal data for illustration, results from the distributional method are compared to those of logistic regression and to quantile regression for three different outcomes.

RESULTS

Estimates obtained using the distributional method for the comparison of proportions are consistently more precise than those obtained using logistic regression. For one of the three outcomes the estimates obtained from the distributional method and from logistic regression disagreed highlighting that the relationships between outcome and covariate differ conceptually between the two models.

CONCLUSION

When an outcome follows the required condition of distribution shift between exposure groups, the results of a linear regression model can be followed by the corresponding comparison of proportions at risk. This dual approach provides more precise estimates than logistic regression thus avoiding the drawback of the usual dichotomisation of continuous outcomes.

Commensurate Priors on a Finite Mixture Model for Incorporating Repository Data in Clinical Trials

Docosahexaenoic acid (DHA) is a good source of fat that can be taken up through food, such as fish, or taken as a supplement. Evidence is building that DHA provides a high yield, low risk strategy to reduce preterm birth and/or low birth weight. These births are great costs to society. A recently completed phase III trial revealed that higher birth weight and gestational age were associated with DHA dosed at 600 mg/day. In this paper we take a posterior predictive approach to assess impacts of these findings on public health. Simple statistical models are not adequate for accurate posterior predictive distribution estimation. Of particular interest is a paper by Schwartz et al. (2010) who discovered that the joint distribution of birth weight and gestational age is well modeled by a finite mixture of three normal distributions. Data from our own clinical trial exhibit similar features. Using the mean and variance-covariance matrices from Schwartz et al. (2010) and flexible commensurate priors (Hobbs et al., 2012) for the mixing parameters, we estimate the effect of DHA supplementation on the over 20,000 infants born in hospitals demographically similar to the hospital where the clinical trial was conducted.

Sample size determination for fold-increase endpoints defined by paired interval-censored data

Medical studies often define binary end-points by comparing the ratio of a pair of measurements at baseline and end-of-study to a clinically meaningful cut-off. For example, vaccine trials may define a response as at least a four-fold increase in antibody titers from baseline to end-of-study. Accordingly, sample size is determined based on comparisons of proportions. Since the pair of measurements is quantitative, modeling the bivariate cumulative distribution function to estimate the proportion gives more precise results than using dichotomization of data. This is known as the distributional approach to the analysis of proportions. However, this can be complicated by interval-censoring. For example, due to the nature of some laboratory measurement methods, antibody titers are interval-censored. We derive a sample size formula based on the distributional approach for paired interval-censored data. We compare the sample size requirement in detecting an intervention effect using the distributional approach to a conventional approach of dichotomization. Some practical guidance on applying the sample size formula is given.

Promotion of rapid testing for HIV in primary care (RHIVA2): a cluster-randomised controlled trial

BACKGROUND

Many people with HIV are undiagnosed. Early diagnosis saves lives and reduces onward transmission. We assessed whether an education programme promoting rapid HIV testing in general practice would lead to increased and earlier HIV diagnosis.

METHODS

In this cluster randomised controlled trial in Hackney (London, UK), general practices were randomly assigned (1:1) to offer either opt-out rapid HIV testing to newly registering adults or continue usual care. All practices were invited to take part. Practices were randomised by an independent clinical trials unit statistician with a minimisation program, maintaining allocation concealment. Neither patients nor investigators were masked to treatment allocation. The primary outcome was CD4 count at diagnosis. Secondary outcomes were rate of diagnosis, proportion with CD4 count less than 350 cells per μL, and proportion with CD4 count less than 200 cells per μL. This study is registered with ClinicalTrials.gov, number ISRCTN63473710.

FINDINGS

40 of 45 (89%) general practices agreed to participate: 20 were assigned to the intervention group (44 971 newly registered adult patients) and 20 to the control group (38 464 newly registered adult patients), between April 19, 2010, and Aug 31, 2012. Intervention practices diagnosed 32 people with HIV versus 14 in control practices. Mean CD4 count at diagnosis was 356 cells per μL (SD 254) intervention practices versus 270 (SD 257) in control practices (adjusted difference of square root CD4 count 3·1, 95% CI -1·2 to 7·4; p=0·16);); in a pre-planned sensitivity analysis excluding patients diagnosed via antenatal care, the difference was 6·4 (95% CI, 1·2 to 11·6; p=0·017). Rate of HIV diagnosis was 0·30 (95% CI 0·11 to 0·85) per 10 000 patients per year in intervention practices versus 0·07 (0·02 to 0·20) in control practices (adjusted ratio of geometric means 4·51, 95% CI 1·27 to 16·05; p=0·021). 55% of patients in intervention practices versus 73% in control practices had CD4 count less than 350 cells per μL (risk ratio 0·75, 95% CI 0·53 to 1·07). 28% versus 46% had CD4 count less than 200 cells per μL (0·60, 0·32 to 1·13). All patients diagnosed by rapid testing were successfully transferred into specialist care. No adverse events occurred.

INTERPRETATION

Promotion of opt-out rapid testing in general practice led to increased rate of diagnosis, and might increase early detection, of HIV. We therefore recommend implementation of HIV screening in general practices in areas with high HIV prevalence.

FUNDING

UK Department of Health, NHS City and Hackney.

Dichotomisation using a distributional approach when the outcome is skewed

BACKGROUND

Dichotomisation of continuous outcomes has been rightly criticised by statisticians because of the loss of information incurred. However to communicate a comparison of risks, dichotomised outcomes may be necessary. Peacock et al. developed a distributional approach to the dichotomisation of normally distributed outcomes allowing the presentation of a comparison of proportions with a measure of precision which reflects the comparison of means. Many common health outcomes are skewed so that the distributional method for the dichotomisation of continuous outcomes may not apply.

METHODS

We present a methodology to obtain dichotomised outcomes for skewed variables illustrated with data from several observational studies. We also report the results of a simulation study which tests the robustness of the method to deviation from normality and assess the validity of the newly developed method.

RESULTS

The review showed that the pattern of dichotomisation was varying between outcomes. Birthweight, Blood pressure and BMI can either be transformed to normal so that normal distributional estimates for a comparison of proportions can be obtained or better, the skew-normal method can be used. For gestational age, no satisfactory transformation is available and only the skew-normal method is reliable. The normal distributional method is reliable also when there are small deviations from normality.

CONCLUSIONS

The distributional method with its applicability for common skewed data allows researchers to provide both continuous and dichotomised estimates without losing information or precision. This will have the effect of providing a practical understanding of the difference in means in terms of proportions.

Janus kinase-1 and Janus kinase-2 inhibitors for treating myelofibrosis

BACKGROUND

Myelofibrosis is a bone marrow disorder characterized by excessive production of reticulin and collagen fiber deposition caused by hematological and non-hematological disorders. The prognosis of myelofibrosis is poor and treatment is mainly palliative. Janus kinase inhibitors are a novel strategy to treat people with myelofibrosis.

OBJECTIVES

To determine the clinical benefits and harms of Janus kinase-1 and Janus kinase-2 inhibitors for treating myelofibrosis secondary to hematological or non-hematological conditions.

SEARCH METHODS

We searched the Cochrane Central Register of Controlled Trials (CENTRAL, the Cochrane Library 2014, Issue 11), Ovid MEDLINE (from 1946 to 13 November 2014), EMBASE (from 1980 to 12 January 2013), and LILACS (from 1982 to 20 November 2014). We searched WHO International Clinical Trials Registry Platform and The metaRegister of Controlled Trials. We also searched for conference proceedings of the American Society of Hematology (from 2009 to October 2013), European Hematology Association (from 2009 to October 2013), American Society of Clinical Oncology (from 2009 to October 2013), and European Society of Medical Oncology (from 2009 to October 2013). We included searches in FDA, European Medicines Agency, and Epistemonikos. We handsearched the references of all identified included trials, and relevant review articles. We did not apply any language restrictions. Two review authors independently screened search results.

SELECTION CRITERIA

We included randomized clinical trials comparing Janus kinase-1 and Janus kinase-2 inhibitors with placebo or other treatments. Both previously treated and treatment naive patients were included.

DATA COLLECTION AND ANALYSIS

We used the hazard ratio (HR) and 95% confidence interval (95% CI) for overall survival, progression-free survival and leukemia-free survival, risk ratio (RR) and 95% CI for reduction in spleen size and adverse events binary data, and standardized mean differences (SMD) and 95% CI for continuous data (health-related quality of life). Two review authors independently extracted data and assessed the risk of bias of included trials. Primary outcomes were overall survival, progression-free survival and adverse events.

MAIN RESULTS

We included two trials involving 528 participants, comparing ruxolitinib with placebo or best available therapy (BAT). As the two included trials had different comparators we did not pool the data. The confidence in the results estimates of these trials was low due to the bias in their design, and their limited sample sizes that resulted in imprecise results.There is low quality evidence for the effect of ruxolitinib on survival when compared with placebo at 51 weeks of follow-up (HR 0.51, 95% CI 0.27 to 0.98) and compared with BAT at 48 weeks of follow-up (HR 0.70, 95% CI 0.20 to 2.47). Similarly there was very low quality evidence for the effect of ruxolitinib on progression free survival compared with BAT (HR 0.81, 95% CI 0.47 to 1.39).There is low quality evidence for the effect of ruxolitinib in terms of quality of life. Compared with placebo, the drug achieved a greater proportion of patients with a significant reduction of symptom scores (RR 8.82, 95% CI 4.40 to 17.69), and treated patients with ruxolitinib obtained greater MFSAF scores at the end of follow-up (MD -87.90, 95% CI -139.58 to -36.22). An additional trial showed significant differences in EORTC QLQ-C30 scores when compared ruxolitinib with best available therapy (MD 7.60, 95% CI 0.35 to 14.85).The effect of ruxolitinib on reduction in the spleen size of participants compared with placebo or BAT was uncertain (versus placebo: RR 64.58, 95% CI 9.08 to 459.56, low quality evidence; versus BAT: RR 41.78, 95% CI 2.61 to 669.75, low quality evidence).There is low quality evidence for the effect of the drug compared with placebo on anemia (RR 2.35, 95% CI 1.62 to 3.41), neutropenia (RR 3.57, 95% CI 1.02 to 12.55) and thrombocytopenia (RR 9.74, 95% CI 2.32 to 40.96). Ruxolitinib did not result in differences versus BAT in the risk of anemia (RR 1.35, 95% CI 0.91 to 1.99, low quality evidence) or thrombocytopenia (RR 1.20; 95% CI 0.44 to 3.28, low quality evidence). The risk of non-hematologic grade 3 or 4 adverse events (including fatigue, arthralgia, nausea, diarrhea, extremity pain and pyrexia) was similar when ruxolitinib was compared with placebo or BAT. The rate of neutropenia comparing ruxolitinib with standard medical treatment was not reported by the trial.

AUTHORS' CONCLUSIONS

Currently, there is insufficient evidence to allow any conclusions regarding the efficacy and safety of ruxolitinib for treating myelofibrosis. The findings of this Cochrane review should be interpreted with caution as they are based on trials sponsored by industry, and include a small number of patients. Unless powered randomized clinical trials provide strong evidence of a treatment effect, and the trade-off between potential benefits and harms is established, clinicians should be cautious when administering ruxolitinib for treating patients with myelofibrosis.

Estimation of intervention effect using paired interval-censored data with clumping below lower detection limit

Outcome variables that are semicontinuous with clumping at zero are commonly seen in biomedical research. In addition, the outcome measurement is sometimes subject to interval censoring and a lower detection limit (LDL). This gives rise to interval-censored observations with clumping below the LDL. Level of antibody against influenza virus measured by the hemagglutination inhibition assay is an example. The interval censoring is due to the assay's technical procedure. The clumping below LDL is likely a result of the lack of prior exposure in some individuals such that they either have zero level of antibodies or do not have detectable level of antibodies. Given a pair of such measurements from the same subject at two time points, a binary 'fold-increase' endpoint can be defined according to the ratio of these two measurements, as it often is in vaccine clinical trials. The intervention effect or vaccine immunogenicity can be assessed by comparing the binary endpoint between groups of subjects given different vaccines or placebos. We introduce a two-part random effects model for modeling the paired interval-censored data with clumping below the LDL. Based on the estimated model parameters, we propose to use Monte Carlo approximation for estimation of the 'fold-increase' endpoint and the intervention effect. Bootstrapping is used for variance estimation. The performance of the proposed method is demonstrated by simulation. We analyze antibody data from an influenza vaccine trial for illustration.

On responder analyses in the framework of within subject comparisons - considerations and two case studies

A responder analysis is a common tool when clinical data are reported. In this paper, we extend the definition of responders to within subject comparisons and present a rigorous definition of the corresponding statistical functional. Via simulation studies, we get further insights under which conditions these analyses can even result in a higher power compared with an analysis based on the arithmetic mean. We report two case studies where these analyses contributed to a better understanding of the clinical data especially as some large observations were present that had a notable impact on the observed standard deviation.

The interaction between anxiety and depressive symptoms on brachial artery reactivity in cardiac patients

The association between anxiety, depression, and endothelial function (EF) was assessed in a sample of 295 cardiac outpatients (n=222 men; mean age=59). Patients were administered the Beck Depression Inventory-II and the State-Trait Anxiety Inventory, trait scale. EF was assessed through forearm hyperemic reactivity, a nuclear medicine variation of the flow-mediated dilatation technique, which calculates the rate of uptake ratio (RUR) between hyperaemic and non-hyperaemic arms. Neither effect of anxiety (F=1.40, p=.24) nor depression (F=2.66, p=.10) was found in a model predicting EF, however there was an interaction (F=4.11, p=.04). Higher anxiety and lower depressive symptoms were associated with superior RUR compared to lower anxiety and lower depressive symptoms. Anxiety had no influence on RUR in those patients with higher depressive symptoms, who generally displayed the lowest levels of RUR, i.e., poor function. It is speculative whether this potential protective role of anxiety may be guided by behavioral or physiological mechanisms.

Estimating dichotomised outcomes in two groups with unequal variances: a distributional approach

Dichotomisation in medical research is sometimes necessary for decision-making or communication purposes. This practice has been criticised in the case of continuous data, and it has been said that means should be compared instead. However when the two groups have unequal variances, comparing means might not show the whole picture as a particular group with a risk defined by a threshold in an outcome may have been affected differently by an intervention than when there is a simple shift of distribution. A statistically sound method using a distributional approach for the dichotomisation of normally distributed outcomes has been described under the assumption of equal variances. This assumption is not sustainable in some situations, and in this work, we develop the method further to cover the case of unequal variances. Through examples from the literature and our own data, we illustrate the effect of unequal variance on dichotomised estimates and present a validation of the method through simulations.

Dichotomisation of a continuous outcome and effect on meta-analyses: illustration of the distributional approach using the outcome birthweight

BACKGROUND

Power and precision are greater in meta-analyses than individual study analyses. However, dichotomisation of continuous outcomes in certain studies poses a problem as estimates from primary studies can only be pooled if they have a common outcome. Meta-analyses may include pooled summaries of either or both the continuous and dichotomous forms, and potentially have a different combination of studies for each depending on whether the outcome was dichotomised in the primary studies or not. This dual-outcome issue can lead to loss of power and/or selection bias. In this study we aimed to illustrate how dichotomisation of a continuous outcome in primary studies may result in biased estimates of pooled risk and odds ratios in meta-analysis using secondary analyses of published meta-analyses with the outcome, birthweight, which is commonly analysed both as continuous, and dichotomous (low birthweight: birthweight < 2,500 g).

METHODS

Meta-analyses published in January 2010 - December 2011 were obtained using searches in PubMed, Embase, Web of Science, and Cochrane Database of Systematic Reviews with the outcome birthweight. We used a distributional method to estimate the pooled odds/risk ratio of low birthweight and its standard error as a function of the data reported in the primary studies of the included meta-analyses where accessible.

RESULTS

Seventy-six meta-analyses were identified. Thirty-seven percent (28/76) of the meta-analyses reported only the dichotomous form of the outcome while 26% (20/76) reported only the continuous form. In one meta-analysis (1/76), birthweight was analysed as continuous for one intervention and as binary for another and 36% (27/76) presented both dichotomous and continuous birthweight summaries. In meta-analyses with a continuous outcome, primary studies data were accessible in 39/48 and secondary analyses using the distributional approach provided consistent inferences for both the continuous and distributional estimates in 38/39.

CONCLUSION

The distributional method applied in primary studies allows both a continuous and dichotomous outcome to be estimated providing consistent inferences. The use of this method in primary studies may restrict selective outcome bias in meta-analyses.

Late outcomes of a randomized trial of high-frequency oscillation in neonates

BACKGROUND

Results from an observational study involving neonates suggested that high-frequency oscillatory ventilation (HFOV), as compared with conventional ventilation, was associated with superior small-airway function at follow-up. Data from randomized trials are needed to confirm this finding.

METHODS

We studied 319 adolescents who had been born before 29 weeks of gestation and had been enrolled in a multicenter, randomized trial that compared HFOV with conventional ventilation immediately after birth. The trial involved 797 neonates, of whom 592 survived to hospital discharge. We compared follow-up data from adolescents who had been randomly assigned to HFOV with follow-up data from those who had been randomly assigned to conventional ventilation, with respect to lung function and respiratory health, health-related quality of life, and functional status, as assessed with the use of questionnaires completed when the participants were 11 to 14 years of age. The primary outcome was forced expiratory flow at 75% of the expired vital capacity (FEF75).

RESULTS

The HFOV group had superior results on a test of small-airway function (z score for FEF75, -0.97 with HFOV vs. -1.19 with conventional therapy; adjusted difference, 0.23 [95% confidence interval, 0.02 to 0.45]). There were significant differences in favor of HFOV in several other measures of respiratory function, including forced expiratory volume in 1 second, forced vital capacity, peak expiratory flow, diffusing capacity, and impulse-oscillometric findings. As compared with the conventional-therapy group, the HFOV group had significantly higher ratings from teachers in three of eight school subjects assessed, but there were no other significant differences in functional outcomes.

CONCLUSIONS

In a randomized trial involving children who had been born extremely prematurely, those who had undergone HFOV, as compared with those who had received conventional ventilation, had superior lung function at 11 to 14 years of age, with no evidence of poorer functional outcomes. (Funded by the National Institute for Health Research Health Technology Assessment Programme and others.).