Constructing Conditional Reference Charts for Grip Strength Measured with Error

Muscular strength, usually quantified through the grip strength, can be used in humans and animals as an indicator of neuromuscular function or to assess hand function in patients with trauma or congenital problems. Because grip strength cannot be accurately measured, several contaminated measurements are often taken on the same subject. A research interest in grip strength studies is estimating the conditional quantiles of the latent grip strength, which can be used to construct conditional grip strength charts. Current work in the literature often applies conventional quantile regression method using the subject-specific average of the repeated measurements as the response variable. We show that this approach suffers from model misspecification and often leads to biased estimates of the conditional quantiles of the latent grip strength. We propose a new semi-nonparametric estimation approach, which is able to account for measurement errors and allows the subject-specific random effects to follow a flexible distribution. We demonstrate through simulation studies that the proposed method leads to consistent and efficient estimates of the conditional quantiles of the latent response variable. The value of the proposed method is assessed by analyzing a grip strength data set on laboratory mice.