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.

Quantifying the impact of different approaches for handling continuous predictors on the performance of a prognostic model.

Continuous predictors are routinely encountered when developing a prognostic model. Investigators, who are often non-statisticians, must decide how to handle continuous predictors in their models. Categorising continuous measurements into two or more categories has been widely discredited, yet is still frequently done because of its simplicity, investigator ignorance of the potential impact and of suitable alternatives, or to facilitate model uptake. We examine three broad approaches for handling continuous predictors on the performance of a prognostic model, including various methods of categorising predictors, modelling a linear relationship between the predictor and outcome and modelling a nonlinear relationship using fractional polynomials or restricted cubic splines. We compare the performance (measured by the c-index, calibration and net benefit) of prognostic models built using each approach, evaluating them using separate data from that used to build them. We show that categorising continuous predictors produces models with poor predictive performance and poor clinical usefulness. Categorising continuous predictors is unnecessary, biologically implausible and inefficient and should not be used in prognostic model development. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

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.

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.

On discretising continuous data for subgroup analysis in baseball pitching and alternative analytical methodologies.

There is a plethora of research attempting to contrast high- and low-velocity pitchers to identify traits to target for increasing velocity. However, pitch velocity exists on a continuum. Therefore, our purpose is to display the analytical discrepancies between creating velocity subgroups and leaving velocity as a continuous variable by examining the influence of ball velocity on elbow valgus torque. Motion capture data for 1315 actively competing pitchers were retrospectively extracted from a private database. We compared three analytic methods: (1) linear regression of valgus torque on ball velocity, (2) t-test between low- and high-velocity groups formed by a median split, and (3) t-test between very low- and very high-velocity groups formed by upper and lower velocity quartiles. Linear regression indicates ball velocity influenced valgus torque (p < 0.001, R2 = 0.280). Median splitting reduced the predictability of ball velocity on valgus torque (p < 0.001, R2 = 0.180). Conversely, extreme group splitting artificially inflated the effect size (p < 0.001, R2 = 0.347). We recommend sports biomechanics researchers not discretise a continuous variable to form subgroups for analysis because (1) it distorts the relationship between the variables of interest and (2) a regression equation can be used to estimate the dependent variable at any value of the independent variable, not just the group means.

Predicting dichotomised outcomes from high-dimensional data in biomedicine.

In many biomedical applications, we are more interested in the predicted probability that a numerical outcome is above a threshold than in the predicted value of the outcome. For example, it might be known that antibody levels above a certain threshold provide immunity against a disease, or a threshold for a disease severity score might reflect conversion from the presymptomatic to the symptomatic disease stage. Accordingly, biomedical researchers often convert numerical to binary outcomes (loss of information) to conduct logistic regression (probabilistic interpretation). We address this bad statistical practice by modelling the binary outcome with logistic regression, modelling the numerical outcome with linear regression, transforming the predicted values from linear regression to predicted probabilities, and combining the predicted probabilities from logistic and linear regression. Analysing high-dimensional simulated and experimental data, namely clinical data for predicting cognitive impairment, we obtain significantly improved predictions of dichotomised outcomes. Thus, the proposed approach effectively combines binary with numerical outcomes to improve binary classification in high-dimensional settings. An implementation is available in the R package cornet on GitHub (https://github.com/rauschenberger/cornet) and CRAN (https://CRAN.R-project.org/package=cornet).

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.

Dichotomising poor self-reported health status: Using secondary cross-sectional survey data for Jamaica.

BACKGROUND: Caribbean scholars continue to dichotomise self-reported health status without empirical justification for inclusion or exclusion of moderate health status in the dichotomisation of poor health. AIMS: This study will 1) evaluate which cut-off point should be used for self-reported health status; 2) assess whether dichotomisation of self-reported data should be practiced; 3) ascertain any disparity in dichotomisation by some covariates (i.e., marital status, age cohort, social class); and 4) examine the odds of reporting poor or moderate-to-very poor self-reported health status if one has an illness. MATERIALS AND METHODS: The current study used cross-sectional survey data for 2007. The survey used stratified probability sampling techniques to collect the data from Jamaicans. The sample consisted of 6,783 respondents, with a focus on participants aged 46+ years (n=1,583 respondents). Self-reported health status was a 5-item Likert scale question. The dichotomisation was poor health status or otherwise and poor (including moderate) self-reported health. Odds ratios were calculated in order to estimate the effect of the covariates. RESULT: When moderate self-reported health status was used in poor health status, the cut-off revealed moderate effect on specified covariates across the age cohorts for women. However, for men, exponential effects were used on social class, but not on area of residence or marital status across the different age cohorts. CONCLUSIONS: The cut-off point in the dichotomisation of self-reported health status does not make a difference for women and must be taken into consideration in the use of self-reported health data for Jamaica.