Analysis of change in patient-reported outcome measures with floor and ceiling effects using the multilevel Tobit model: a simulation study and an example from a National Joint Register using body mass index and the Oxford Hip Score

Adrian Sayers, Michael R Whitehouse, Andrew Judge, Alex J MacGregor, Ashley W Blom, Yoav Ben-Shlomo

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OBJECTIVES: This study has three objectives. (1) Investigate the association between body mass index (BMI) and the efficacy of primary hip replacement using a patient-reported outcome measure (PROMs) with a measurement floor and ceiling, (2) Explore the performance of different estimation methods to estimate change in PROMs score following surgery using a simulation study and real word data where data has measurement floors and ceilings and (3) Lastly, develop guidance for practising researchers on the analysis of PROMs in the presence of floor and ceiling effects.

DESIGN: Simulation study and prospective national medical device register.

SETTING: National Register of Joint Replacement and Medical Devices.

METHODS: Using a Monte Carlo simulation study and data from a national joint replacement register (162 513 patients with pre- and post-surgery PROMs), we investigate simple approaches for the analysis of outcomes with floor and ceiling effects that are measured at two occasions: linear and Tobit regression (baseline adjusted analysis of covariance, change-score analysis, post-score analysis) in addition to linear and multilevel Tobit models.

PRIMARY OUTCOME: The primary outcome of interest is change in PROMs from pre-surgery to 6 months post-surgery.

RESULTS: Analysis of data with floor and ceiling effects with models that fail to account for these features induce substantial bias. Single-level Tobit models only correct for floor or ceiling effects when the exposure of interest is not associated with the baseline score. In observational data scenarios, only multilevel Tobit models are capable of providing unbiased inferences.

CONCLUSIONS: Inferences from pre- post-studies that fail to account for floor and ceiling effects may induce spurious associations with substantial risk of bias. Multilevel Tobit models indicate the efficacy of total hip replacement is independent of BMI. Restricting access to total hip replacement based on a patients BMI can not be supported by the data.

Original languageEnglish
Article numbere033646
JournalBMJ Open
Issue number8
Publication statusPublished - 27 Aug 2020


  • arthroplasty
  • change scores
  • epidemiologic methods
  • longitudinal studies
  • multi-level tobit model
  • patient reported outcome measures

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