Statistical Analysis

Data were analyzed from April 17 to November 3, 2020. Owing to the skewed distribution of back pain–related disability (eFigure 2 in the Supplement), ordinal logistic regression, which holds a proportional odds assumption, was performed.²⁶ Considering that physical activity was measured at a different time point (ie, year 6) compared with other covariates (ie, year 9) and with potential measurement error, we established a stepped modeling framework: step 1, unadjusted analyses; step 2, analyses adjusted for age, BMI, back pain status, bisphosphonate use status, and smoking status (additionally adjusted for year 9 back pain–related disability for the longitudinal analysis); and step 3, analyses further adjusted for physical activity.

Separate analyses were conducted for cross-sectional and longitudinal data. For the longitudinal analyses, data on lumbar spine radiographic changes collected in year 9 were treated as the exposure, and back pain–related disability data collected in year 15 were treated as the outcome. In addition to the confounders mentioned, data on back pain–related disability collected in year 9 were included in the longitudinal analysis as a strong prognostic factor to adjust.²⁷ Based on the recommendation from Modern Epidemiology,²⁸ the exposures were modeled as unordered categorical variables and trend test.²⁶

The proportion of missing data in each covariate is provided in Table 1. Missing data were handled through multiple imputation, which holds a missing-at-random assumption.²⁶ The assumption was graphically tested (eFigure 3 in the Supplement). No additional variables were used; all covariates in the minimal sufficient adjustment sets were used. Flexible additive models with 10 imputed data sets were used.²⁹ We did not impute data for the exposure variables. The relative risk was presented as adjusted proportional odds ratios (ORs) with 95% CIs. Extensive sensitivity analyses were performed (eAppendix 1 in the Supplement). All statistical analyses were performed with rms, Hmisc, and tidyverse packages in R, version 3.6.2 (R Group for Statistical Computing). Details of the statistical methods are provided in eAppendix 2 in the Supplement.

Abbreviations: BMI, body mass index (calculated as weight in kilograms divided by height in meters squared); IQR, interquartile range.