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 [2 (link)].
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 [8 ].
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 [2 (link)].
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 [8 ].
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