Measurement error in continuous endpoints in randomised trials: Problems and solutions

Abstract

In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error and proposes methods to improve statistical inference in the presence of measurement error. Three main types of measurement error in continuous endpoints are considered: classical, systematic, and differential. For each measurement error type, a corrected effect estimator is proposed. The corrected estimators and several methods for confidence interval estimation are tested in a simulation study. These methods combine information about error‐prone and error‐free measurements of the endpoint in individuals not included in the trial (external calibration sample). We show that, if measurement error in continuous endpoints is ignored, the treatment effect estimator is unbiased when measurement error is classical, while Type‐II error is increased at a given sample size. Conversely, the estimator can be substantially biased when measurement error is systematic or differential. In those cases, bias can largely be prevented and inferences improved upon using information from an external calibration sample, of which the required sample size increases as the strength of the association between the error‐prone and error‐free endpoint decreases. Measurement error correction using already a small (external) calibration sample is shown to improve inferences and should be considered in trials with error‐prone endpoints. Implementation of the proposed correction methods is accommodated by a new software package for R.

Importance of incorporating quantitative imaging biomarker technical performance characteristics when estimating treatment effects

“…The technical performance characteristics of a QIB, that is, its precision and bias, are essential in understanding individual patient’s QIB measurements and planning and interpreting clinical trial results. Nab et al 2 and Obuchowski et al 4 have shown that imprecision in QIBs increases the type II errors in clinical trials. Furthermore, in this article, we have illustrated that estimates of treatment effects are biased when the slope of the regression of measured versus true biomarker values differs from one.…”

“…Good technical performance validation studies are essential when developing and testing a QIB for its potential use in a clinical trial. 2,4 Test–retest studies, in which subjects are imaged two or more times over a short period, provide estimates of a QIB’s precision. 5 Phantom studies, where synthetic objects with known properties are imaged, provide estimates of a QIB’s bias.…”

“…failure to reject the null hypothesis when a true benefit to treatment exists). 2,4 Methods to correct the sample size of studies using QIBs have been described previously. 4…”

“…When measuring the change between two time points, an estimate of the true change will be underestimated when linearity exists but the regression slope <1; similarly, the true change will be overestimated when the slope >1. In a clinical trial comparing two treatment arms where the QIB displays the third measurement error pattern, the type I error rate is maintained at the alpha level, 2 the type II error may increase because of the random error component, but most importantly the estimate of the treatment effect will be biased. Next, we discuss how to estimate the treatment effect in the presence of non-constant bias.…”

“…There has been a tendency to ignore the biomarker measurement error when estimating treatment effect. 2,3 However, the measurement error of a QIB cannot be ignored if one wants to correctly estimate change over time, estimate treatment effect in a randomized clinical trial, or appropriately power a clinical trial. Previously, Obuchowski et al 4 described how to determine sample size for clinical trials using QIBs.…”