Appendix 1: Multiple Imputation to Account for Missing Data

Appendix 1: Multiple imputation to account for missing data

At the 10-year clinic assessments, 489 (47%) participants were lost to follow-up. Compared to participants retained at the 10-year follow-up assessment, participants lost to follow-up were older (P < 0.001), had more morbidity (P < 0.001), and higher baseline falls risk score (P < 0.001). Multiple imputations by chained equation was used in the estimation of missing data. Using the known participants’ characteristics multiple imputations replaces missing values with plausible values in a way that minimises bias, and helps preserve the sample size (1). The ability to perform analysis on multiple imputed datasets helps to minimise bias in the parameter estimates. Both the outcomes (excluding mortality) and exposure variables used for analyses in this paper were included in the multiple imputation models. Other variables such as co-morbidity, physical activity, knee pain and dysfunction which were not used in the substantive analysis were also included in the multiple imputation models. Although 3 to 5 imputations are considered adequate to obtain excellent results (2), higher numbers of imputations have been proposed by Graham et. al in order to prevent loss of statistical power (3). As suggested by Horton and Lipsitz (4), we performed a number of imputations (5, 10, 20 and 50 imputations) and we explored the results using different numbers of imputations. We found consistency in the parameter estimates and results using 50 imputations, as is presented in this paper.

Supplementary Table 1: Associations between low muscle mass and function at baseline and falls risk at 10-year, incident fractures and mortality over 10 years (imputed data).
Cut-point for low muscle mass and function* / Falls risk z-score / Fracture
Low muscle mass/ function / (n=1041) / (n=1041)
Male / Female / β (95% CI) / RR (95% CI)
Performance-based definitions
LMQLOW / 3.85 / 1.85 / 0.44 (0.23, 0.65) / 0.90 (0.54, 1.48)
UMQLOW / 1.08 / 1.15 / 0.33 (0.13, 0.53) / 1.16 (0.73, 1.86)
LMSLOW / 69.18 / 26.40 / 0.64 (0.44, 0.83) / 0.82 (0.50, 1.38)
HGSLOW / 10.68 / 7.54 / 0.44 (0.23, 0.66) / 1.72 (1.08, 2.71)
Anthropometric definitions
ALMHHLOW / 8.32 / 6.64 / 0.02 (-0.19, 0.23) / 0.91 (0.53, 1.55)
ALMBMILOW / 0.88 / 0.60 / 0.19 (-0.03, 0.41) / 1.12 (0.68, 1.84)
ALMWLOW / 29.96 / 24.36 / 0.08 (-0.15, 0.32) / 1.28 (0.80, 2.05)
ALMRLOW / – 0.87 / – 1.82 / 0.07 (-0.14, 0.28) / 1.08 (0.67, 1.75)
*Lowest 20%, Data in bold indicate statistical significance at p < 0.05, All analyses are adjusted for age.
UMQ: upper-limb muscle quality (kg/kg) LMQ: leg muscle quality; (kg/kg) LMS: leg muscle strength (kg) HGS: handgrip strength (psi) ALMHH: appendicular lean mass (ALM)/height2 (kg/m2),) ALMBMI: low ALM/body mass index(kg/ kg/m2) ALMW: ALM / weight * 100 (kg/kg) ALMR: residual of ALM on height and total body fats (kg)

References:

1. van der Heijden GJ, Donders ART, Stijnen T, Moons KG. Imputation of missing values is superior to complete case analysis and the missing-indicator method in multivariable diagnostic research: a clinical example. Journal of Clinical Epidemiology. 2006;59:1102-1109.

2. Rubin DB. Inference and missing data. Biometrika. 1976;63:581-592.

3. Graham JW, Olchowski AE, Gilreath TD. How many imputations are really needed? Some practical clarifications of multiple imputation theory. Prevention Science. 2007;8:206-213.

4. Horton NJ, Lipsitz SR. Multiple imputation in practice: comparison of software packages for regression models with missing variables. The American Statistician. 2001;55:244-254.