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How do treatments for chronic fatigue syndrome work? Exploration of instrumental variable methods for mediation analysis in PACE – a randomised controlled trial of adaptive pacing therapy, cognitive behaviour therapy, graded exercise therapy, and specialist medical care

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Chronic fatigue syndrome (CFS) is characterised by chronic disabling fatigue. The PACE trial compared four treatments for CFS and found that for therapies added to specialist medical care (SMC), cognitive behaviour therapy (CBT) and graded exercise therapy (GET) were more effective than adaptive pacing therapy (APT) and SMC alone in improving physical function and fatigue. What are the mechanisms of these treatments? CBT and GET may affect outcomes through thought processes and behaviours (mediators). Traditional Baron, Judd and Kenny (BJK) methods for estimating mediation effects can be subject to bias; instrumental variable methods (IV) can address this problem. The aims were:

To explore potential IVs for causal analysis of mediation in PACE.

To compare IV estimates to those obtained using BJK methods, which are unbiased only under restrictive assumptions such as no unmeasured confounding.


Two treatment arms were compared at a time. BJK methods were applied using three ordinary least squares (OLS) regression models. IV methods were applied by compiling a list of baseline variables that could act as IVs in interaction terms with treatment arm and then assessing these using OLS with the mid-treatment measurement of the putative mediator as the outcome. Instrument strength was assessed using the R2 change between models with main effects only and with the interaction term. Two-stages least squares regression (2SLS) was used to estimate effects in the presence of IVs. Collective instrument strength was assessed using an F test and partial R2.


The IVs were weak, with a maximum R2 change of 0.03. The five strongest IVs were therefore used in the 2SLS in each case. There was modest mediation of CBT and GET effects (approximately 20% of the total effect). The IV-derived estimators were somewhat different in magnitude than the BJK estimators and were less precise. There is scope for modelling a common effect of mediators on outcomes across trial arms.


There was evidence for modest mediation of CBT and GET effects. Potential IVs for the study of PACE treatment mechanisms can be found, however, these were weak. Combining trial arms may allow for more efficient analysis using IVs.

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Correspondence to Kimberley Goldsmith.

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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About this article


  • Ordinary Little Square
  • Chronic Fatigue Syndrome
  • Instrumental Variable
  • Mediation Analysis
  • Ordinary Little Square


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