Quantitative imaging biomarkers (QIBs) are often selected and ranked based on their repeatability performance. In the context of treatment response assessment, however, one must also consider how sensitive a QIB is to measuring changes in the tumour. This work introduces response-to-repeatability ratio (R/R), which weighs the ability of a QIB to detect significant changes with respect to its measurement repeatability and applies it to the case of PET texture features. R/R is evaluated as the proportion of measurable changes from baseline to follow-up for each candidate QIB. We analyse 47 texture features extracted from lesions in bone-metastatic prostate cancer patients who received double baseline and/or baseline to treatment follow-up 18F-NaF PET/CT scans. R/R evaluates the proportion of follow-up changes outside of the 95% limits of agreement (LOA) defined by test-retest values. Intraclass correlation coefficient (ICC) and coefficient of variation (CV) are calculated for each feature. Relationship between ICC and R/R are evaluated with the Spearman's correlation coefficient. R/R varied significantly across texture features: 41/47 (87%) features demonstrated R/R > 5%; 21/47 (45%) features demonstrated R/R > 10%, and 11/47 (23%) features demonstrated R/R > 20%. LOA of features ranged from [0.998, 1.001] to [0.22, 4.86]. Repeatability alone did not qualify a feature for its efficacy at detecting measurable change at follow-up, as shown by weak correlations between R/R and both CV and ICC (ρ = 0.23 and ρ = 0.40, respectively). Three features demonstrated excellent ICC (ICC > 0.75) and R/R greater than that of SUVmax (R/R = 41.8%): skewness (ICC = 0.92, R/R = 75.4%), kurtosis (ICC = 0.88, R/R = 47.0%) and diagonal moment (ICC = 0.88, R/R = 45.5%). R/R characterizes the sensitivity of candidate QIBs to detect measurable changes at follow-up. R/R supplements existing precision performance metrics (e.g. CV, ICC, and LOA) as an index to assess the utility of QIBs for response assessment.