The Fracture Reduction Evaluation (FREE) trial
Detailed methodology for the FREE trial has been presented previously . In brief, the FREE trial was a randomised, non-blinded trial comparing non-surgical care alone with BKP for the treatment of patients with acute painful vertebral fractures. The study included patients from 21 sites in eight countries (Austria, Belgium, France, Germany, Italy, Sweden, the Netherlands and the United Kingdom) and was conducted from February 2003 through December 2005.
All participants had at least one acute thoracic or lumbar (T5-L5) vertebral fracture with bone marrow signal changes on magnetic resonance imaging (MRI), and vertebral height reduction (> 15% of predicted vertebral height) compared with the adjacent vertebrae. Painful vertebral fractures were diagnosed by the local investigator; up to three fractures could be treated if they also had signal changes, rapidly progressive height loss or pseudoarthrosis.
Participants had self-assessed back pain of at least 4 on a scale from 0 (no pain) to 10 (worst pain imaginable) that started within the past 3 months and was not attributable to other causes. Vertebral fractures were included irrespective of aetiology; however, fractures due to primary bone tumours, osteoblastic metastases or high-energy trauma were excluded. Participants gave written informed consent before enrolment, and the protocol and consent forms were approved by local ethics committees. The trial was conducted in accordance with the Declaration of Helsinki, and is registered with ClinicalTrials.gov (number NCT00211211).
Patients were randomly assigned in a 1:1 ratio to receive BKP or non-surgical care using a computer-generated schedule. Study randomisation was stratified for gender, fracture aetiology, use of bisphosphonates at the time of enrolment and use of systemic steroids during the last 12 months before enrolment, but not for number of prevalent fractures per participant. A permuted block randomisation (stratified as indicated) was generated using PROC PLAN prior to the start of the study.
Percutaneous BKP was performed with introducer tools, inflatable bone tamps, and polymethylmethacrylate bone cement and delivery devices (Medtronic Spine LLC, Sunnyvale, CA, USA) using a bilateral, transpedicular or extrapedicular approach. Patients received analgesics, bed rest, bracing, physiotherapy, rehabilitation programmes and walking aids according to the standard practices of participating physicians and hospitals. All patients were referred for treatment with calcium and vitamin D supplements, and antiresorptive or anabolic agents.
The primary endpoint was the change from baseline to 1 month in quality of life (QoL) assessed using the Short-form 36 (SF-36) physical component summary (PCS) scale. Secondary endpoints included: EuroQol 5-Dimension Questionnaire (EQ-5D); SF-36 subscale scores; function measured using the Roland-Morris Disability (RMD) score; back pain assessed with a visual-analogue scale (VAS; scale 0-10); limited days of activity and bed rest because of back pain during the previous 2 weeks; and patient satisfaction assessed on a 20-point Likert scale (extremely dissatisfied to extremely satisfied). Outcomes were assessed at baseline/screening and at 1, 3, 6, 12 and 24 months; back pain was also assessed at 7 days.
Six outcome measures - SF-36 PCS scale, EQ-5D, RMD score, back pain, number of days with restricted activity in last 2 weeks and number of days in bed in last 2 weeks - were analysed using four methods for dealing with missing data: CC analysis, simple imputation with LOCF analysis, MM analysis on all available data and MI analysis.
The CC analysis included only patients with both baseline and all follow-up values for respective outcomes. For the LOCF analysis, only patients with available baseline values were included; missing follow-up values were replaced by the patient's last observed value, based on the assumption that this represented the treatment effect. In contrast with the LOCF method, MI is a stochastic imputation method based on the assumption that missing values can be replaced with values generated by a model incorporating random variation. The generation of such values is performed repeatedly providing a series of complete datasets. These datasets are then analysed using standard methods for complete data, and the results are combined to provide a set of parameter estimates and their standard errors, from which confidence intervals and p-values can be derived. The MI model can be different from the model used for the final data analysis. In this study we imputed data using as-treated models, and analysed them according to ITT .
For the CC, LOCF and MI methods, the analysis was performed using a conventional repeated-measures ANOVA design. The model included treatment group and visit as fixed factors, as well as their interaction, together with covariates representing the randomisation stratification factors (gender, fracture aetiology, use of bisphosphonates at the time of enrolment and use of systemic steroids during the last 12 months before enrolment) and baseline values.
In the MM analysis, all patients with at least one baseline or follow-up value were included. An MM analysis includes both fixed and random factors: in the current analysis, treatment group and visit were included as fixed factors, and patient was included as a random factor. The model included interactions between treatment and visit. Randomisation stratification factors (gender, fracture aetiology, use of bisphosphonates at the time of enrolment and use of systemic steroids during the last 12 months before the time of enrolment) and baseline value were included as covariates. Compound symmetry structure for covariance between measurements was assumed. Maximum restricted likelihood procedure was used to fit the model and denominator degrees of freedom were estimated using Satterthwaite's approximation. This mixed model analysis is, with balanced data, equivalent to the conventional repeated measures ANOVA with sphericity assumption .
The CC approach assumes that data are missing completely at random (MCAR) - i.e. that missing data are a random subsample of all data. The LOCF approach assumes that baseline values are MCAR, and that there is no change in treatment effect during follow-up. It is also assumed that there is no variation in the measurement of treatment effect itself. In both the MM analysis and the MI technique, it is assumed that data are missing at random (MAR), meaning that the probability that an observation is missing may depend on observed data but not on missing data. Thus, the likelihood function for the complete dataset, with respect to inference on the unknown parameters that characterise the complete data distribution, is the same as the likelihood function for the observed data. In the MM approach, the MAR assumption needs to be fulfilled in the analysis model, whereas in the MI approach only the imputation model needs to satisfy the MAR assumption.
In this study, the imputation model included all six outcomes at baseline and follow-up visits, all randomisation stratification factors, age, treatment centre and number of fractures at baseline (≥ 1), in addition to treatment 'as received'. Treatment centres with less than 7% of patients overall were combined. Treatment 'as received', rather than treatment 'as randomised', was used in the imputation model to recover the 'true' outcome values for patients. This was done because the observed outcome values for the patient are influenced by the treatment received not the treatment assigned.
Multiple imputation using fully conditional specification (or 'chained equations')  was used to create 30 imputed datasets, primarily because the distribution of number of days with reduced activity and number of days in bed were substantially non-normal. Therefore, the variables were treated as ordinal in the imputation model. Other outcome variables were treated as continuous. PCS followed a normal distribution and was not transformed. Roland-Morris disability score, VAS and EQ-5D were transformed to normality using Box-Cox transformation and imputed with predictive mean matching method  to ensure that the imputed values did not exceed the natural range of values for those variables. After imputation the values were transformed back to the original scale. Other covariates were included as dummy (0-1) variables. To create the imputation in STATA the imputation by chained equations (ICE) implementation was used .
The MI approach provides the means to estimate the fraction of missing information relative to the complete information for each parameter of interest.(, section 3.3) If the missing data do not provide any additional information about the parameter of interest to that which can be observed from the available data then the fraction will be equal to zero. If the missing data contain a high proportion of information, and this is not also contained within the observed data, then the fraction of missing information will be high.