Research letter.

In our recently published paper by Landgrebe et al. (2008), earlier investigations (Frick et al. 2005) describing reduced ability in subjective electromagnetic hypersensitive patients (EHS) to discriminate real from sham transcranial magnetic pulses were confirmed. Transcranial magnetic stimulation (TMS) was performed with Magstim (Frick et al. 2005) and Medtronic (Landgrebe et al. 2008) equipment. However, the description of the sham condition was not clear-cut in either of the papers. For example, in Landgrebe et al. (2008), we stated that probands knew ‘that each pulse had a 50% probability of representing a real magnetic stimulus or to be only an acoustic click without an accompanying magnetic pulse ’. Regarding both papers, it should be clarified that both Magstim and Medtronic sham coils produce a magnetic field ; however, this is very low compared to the verum coils. This has given rise to doubts concerning our statistical analysis, although the statistical tool (ANCOVA) does not require a null-exposure as the control condition to investigate differences in the perceptive ability. Nevertheless, we wish to present an alternative analysis of the pooled data of both studies, without distinguishing ‘sham’ and ‘real ’ exposure conditions which includes magnetic field strength, administered at each stimulation, as a predictor into the statistical model. We measured induced electric voltage directly on the surface at the centre of the coils using a dipole probe similar to Rossi et al. (2007) resulting in an indirect measure of the magnetic flux density. Thus, a dose–response relationship between emission and perception can be estimated and tested. Subjects were tested using Medtronic (n=194) and Magstim (n=84) equipment. Each subject received four series of single transcranial magnetic pulses at the dorsolateral prefrontal cortex and after each pulse answered whether he/she had experienced any sensory perception. We pooled both datasets of 13 691 single perception experiments performed on 278 subjects (average age 48.1 years, S.D.=12.0, 58.3% females, 42.4% EHS). The outcome variable (perceiving a sensation) is dichotomous and its log odds were modelled as a linear function of increasing exposure level and of individual learning throughout the experiment. Subjects’ characteristics (age, sex, claimed hypersensitivity) were introduced into the model as level-2 variables within a hierarchical approach (see Raudenbush & Bryk, 2002, ch. 10) impacting both the intercept parameter and the slope for exposure. The individually randomized sequence of the experiment (starting with either sham or verum coil) was also modelled as a level-2 predictor variable. Estimation was performed using HLM5. Results are given for the population-average model with robust standard errors (Zeger et al. 1988). Fig. 1 gives the electric voltage measured at the surface of the coils used. The Magstim equipment provides a larger difference between the sham and the verum condition than the Medtronic equipment. The truth table underlying Fig. 1 was used to transform the presets (% of maximum stimulation power) of the magnetic coils into emission parameters (voltage measured). Variance components associated with both random intercept b0 and random slope for b2 had significant p values (p<0.0001). We therefore included the respective level-2 equations into the final statistical model. Differences of the equipment (Magstim v. Medtronic) could not be shown to have an impact either on the intercept parameter b0 (t ratio=1.74, p=0.08) or on the slope parameter b2 (t ratio=0.03, p=0.078). Table 1 summarizes the numerical results. From Table 1 can be concluded that a sensory perception is a function of three significant determinants :