Multivariable reference centiles for maximum grip strength in childhood to young adults

Grip strength (GS) is a practical proxy for overall muscular strength and predicts important health outcomes across the life course. In youth, higher GS is associated with greater bone mineral density and lower future risk of prediabetes/type 2 diabetes; low GS relates to higher cardiometabolic risk. Because GS development differs by sex and age, reference centiles must account for these factors. GS also depends on height and body mass/BMI. Prior attempts either used multilevel regression including anthropometrics or allometric scaling, but none produced reference centiles ensuring that z-scores are standard normal not only overall but conditional on explanatory variables. Additionally, longitudinal changes in GS (becoming weaker) may predict adverse outcomes better than single low values, yet pediatric reference data to interpret meaningful changes are lacking. Therefore, the study aimed to generate sex-, age-, height-, and BMI-adjusted reference centiles for maximum GS (mGS) and to establish reference centiles for differences in mGS z-scores across repeated measurements in children, adolescents and young adults, and to quantify associations between mGS and anthropometry.

Previous work shows GS is correlated with overall muscle strength and bone health in adolescents and predicts later-life metabolic outcomes. Normative GS data exist across ages and in youth cohorts, but often vary by device, hand, posture, and summary metric. Ploegmakers et al. provided regression-based norms incorporating sex, age, height, and mass. Kocher et al. proposed allometric scaling for GS to remove height and mass dependence, but did not apply LMS smoothing or assess conditional normality of covariates. Dodds et al. compiled life-course GS norms, though temporal resolution was coarse. There remains a need for reference centiles that satisfy conditional standard normality across multiple explanatory variables and for longitudinal centiles describing clinically meaningful changes.

Design and data source: Retrospective analysis of longitudinal data from the Dortmund Nutritional and Anthropometric Longitudinally Designed (DONALD) open cohort study (Germany), with ongoing annual assessments from infancy through adulthood. Data from 2004–2022 were used. Ethical approval was granted by the Medical Faculty of the University of Bonn (Nr. 002/05, 27.04.2005); the study is registered (DRKS00029092). Informed consent was obtained. Participants and sample selection: From 3490 GS measurements, exclusions were applied for visits with fewer than three GS trials (n=160) and missing height (n=5), yielding 3325 eligible measurements from 976 individuals (465 females, 511 males; ages up to 24 years). Median number of repeated measurements per individual was 3 (range 1–8). Measurements: mGS was measured on the non-dominant hand using a Jamar hydraulic dynamometer in a standardized seated posture (shoulder neutral, elbow 90°, forearm neutral, wrist 0–30° extension). At each visit, three maximal efforts were recorded with brief rests; the maximum value (mGS) was used. Height was measured to 0.1 cm (Harpenden stadiometer); mass to 0.1 kg (Seca scale). BMI was calculated as kg/m². Height and BMI z-scores were derived from German reference centiles (Neuhauser et al.). Children from age 6 years were examined biennially; ≥18 years, every 5 years. Statistical approach: The analysis combined multiple linear regression (MLR) to predict GS from age, height, and BMI, and the LMS method to generate smoothed reference centiles such that z-scores are standard normal conditional on explanatory variables. Separate models were fitted by sex. Predicted GS (PGS) equations (from MLR) were:

• Females: PGS = 0.409Age + 0.256Height + 0.391*BMI − 29.46
• Males: PGS = 1.456Age + 0.235Height + 0.490*BMI − 36.82 The measured mGS and PGS were then mapped to multivariable reference centiles using LMS-based centile curves. Model diagnostics included Bland–Altman analysis for unbiased prediction, Q-permutation tests and worm plots to verify conditional standard normality of z-scores across age, height, and BMI. Sex- and age-only centiles were also produced for comparison, and “projections” were visualized at fixed ranges of height and BMI. Longitudinal change: Annualized differences in mGS z-scores were computed to produce age-specific centiles for changes between repeated measurements (presented for ages 8–20 due to limited data beyond 20). Logistic regression assessed misclassification error when using sex- and age-only centiles to detect low mGS, stratified by sums of height and BMI z-scores, to guide when multivariable centiles are warranted.

• Sample: 3325 mGS measurements from 976 participants (465 females, 511 males); median 3 measurements per person (range 1–8). Mean age: females 12.6 ± 3.9 years; males 12.4 ± 4.7 years.
• Anthropometry ranges (z-scores): Height: females −3.2 to 3.6; males −3.4 to 4.2. BMI: females −3.3 to 2.7; males −3.9 to 3.2.
• Sex- and age-adjusted mGS increased through adolescence; boys surpassed girls after puberty; girls plateaued earlier.
• Correlations (age- and sex-adjusted): mGS with height z-score: females r=0.432 (95% CI 0.391–0.471), males r=0.399 (0.359–0.438), p<0.001; mGS with BMI z-score: females r=0.354 (0.310–0.396), males r=0.303 (0.260–0.345), p<0.001.
• Multivariable centiles: MLR provided unbiased PGS (Bland–Altman mean near zero). LMS-derived multivariable centiles produced z-scores conditionally standard normal across age, height, BMI; Q-permutation tests indicated only marginal deviation for BMI in males (Q2 p=0.043); worm plots showed no relevant deviations.
• Residual associations after adjustment: No significant correlation between adjusted mGS z-scores and height (females p=0.893; males p=0.148) or BMI in males (p=0.842). A very small residual correlation with BMI remained in females (r=0.095, p<0.001).
• Longitudinal change: Age-specific centiles for annualized differences in mGS z-scores (8–20 years) showed decreasing variability with age, with puberty-related deviations.
• Clinical decision rule: Using logistic regression, a 10% false negative error rate for detecting low mGS with sex- and age-only centiles occurred when the sum of height and BMI z-scores was below approximately −2.0 SD; similarly, above approximately +4.0 SD. Thus, multivariable centiles are recommended outside these thresholds.
• Practical formulas for PGS were provided by sex, enabling computation of multivariable-adjusted centiles and z-scores.

The study addressed the need for reference centiles of mGS that account for key anthropometric determinants beyond sex and age. By combining MLR with LMS, the authors generated centiles whose z-scores are conditionally standard normal with respect to age, height, and BMI, allowing accurate classification at fixed percentiles (e.g., 3rd centile) across the spectrum of body size. This mitigates false positives in shorter/lower-BMI youth and false negatives in taller/higher-BMI youth when using sex- and age-only centiles. The provision of longitudinal centiles for annualized changes in mGS z-scores fills a gap for interpreting clinically meaningful declines over time, a pattern linked to adverse outcomes in adults and analogous to centile crossing in pediatric growth surveillance. The approach retained familiar centile graphics for clinical usability and provided guidance on when the additional complexity of multivariable centiles is needed, based on the combined height and BMI z-scores.

mGS in children, adolescents, and young adults should be evaluated using reference centiles adjusted for sex, age, height, and BMI, especially when the sum of height and BMI z-scores is < −2.0 or > 4.0. The proposed method generalizes to other pediatric biomarkers influenced by multiple anthropometric factors. For the first time, reference centiles for changes in mGS z-scores across repeated measures are provided, enabling assessment of clinically relevant declines over time.

• Convenience sample from the Dortmund metropolitan area may limit generalizability to all German children or other populations.
• Only the non-dominant hand was tested; results may differ with dominant hand or bilateral measures.
• Potential influential factors such as hand size, forearm girth, sports training, and nutritional status were not assessed.
• Detailed statistical methods are in supplements; no formal mathematical proof is provided for general conditions under which the method guarantees conditional normality, and external validation is needed.