Technical note
Precision of estimates of mean and peak spinal loads in lifting

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Abstract

A bootstrap procedure was used to determine the statistical precision of estimates of mean and peak spinal loads during lifting as function of the numbers of subjects and measurements per subject included in a biomechanical study. Data were derived from an experiment in which 10 subjects performed 360 lifting trials each. The maximum values per lift of the lumbar flexion angle, L5S1 sagittal plane moment, and L5S1 compression force were determined. From the data set thus compiled, 3000 samples were randomly drawn for each combination of number of subjects and number of measurements considered. The coefficients of variation of mean and peak (defined as mean plus 2 standard deviations) spinal loads across these samples were calculated. The coefficients of variation of the means of the three parameters of spinal load decreased as a linear function of the number of subjects to a power of about −0.48 and number of measurements to a power of about −0.06, while the corresponding powers for peak loads were about −0.44 and −0.11.

Introduction

Lifting is an important risk factor for low back pain (Burdorf and Sorock, 1997; Hoogendoorn et al., 1999; Kuiper et al., 1999). This has motivated many biomechanical studies of low back loads in lifting. Most of these studies are comparative in nature and focus, for instance, on different lifting tasks or techniques in order to decrease the risk of low back pain associated with lifting (for recent reviews see Davis and Marras, 2000; van Dieën et al., 1999a; Poppel et al., 2000).

Even in a standardized lifting task, substantial variance in spinal loading occurs within and between subjects (van Dieën et al., 2001; Granata et al., 1999). Obviously, this variance negatively affects the power to elucidate differences in spinal loading between lifting tasks or techniques. The (statistical) precision of estimates can be enhanced by increasing the number of subjects or the number of measurements per subject. The former strategy is expected to be the most effective, especially given the fact that between-subject variance of spinal loading is larger than within-subject variance (Granata et al., 1999).

To quantify the influence of both strategies on precision of estimates of spinal load during lifting, we used data from a previous experiment on repeated lifting under realistic task constraints. Several parameters of spinal load were taken from this study. First, the maximum lumbar flexion angle was assessed, since hyperflexion and repetitive flexion have been shown to be able to cause ruptures of the anulus fibrosus (Adams and Hutton, 1982; Green et al., 1993) and spinal flexion during lifting is associated with the incidence of HNP (Kelsey et al., 1984). Second, the maximum net moment about the lumbar spine during each lift was assessed. This parameter of spinal load reflects the minimum muscle force required to perform the task and appears to be the most frequently used outcome variable in biomechanical studies of lifting (van Dieën et al., 1999a). Finally, the maximum L5S1 compression force during each lift was considered. Compression forces of the magnitude attained during lifting have been shown to have the potential of causing fractures of the vertebral endplates and can thus contribute to low back pain (e.g. van Dieën et al., 1999b).

When subjects repeatedly lift the same object, the maximum back load in each lift varies considerably between and within subjects (van Dieën et al., 2001; Granata et al., 1999). Therefore, the distribution of maximum back loads imposed by a certain task cannot be characterized by a single value, but it can be described by estimates of its mean and peak value. Therefore, the precision of the estimates of the mean and peak (defined here as the mean plus two standard deviations) loads in samples consisting of varying numbers of subjects and repeated measurements per subject were assessed.

Section snippets

Methods

Experimental data were derived from a previous study (van Dieën et al., 2001), in which a convenience sample of 10 males, repetitively, lifted a 10 kg container for 1 h at a rate of 6 lifts per minute using a stoop technique. This allowed approximately 5 s rest in an upright posture after each lift. Kinematics of the trunk and pelvis were continuously recorded with an automated system with active markers (Optotrak, Northern Digital Inc., Canada). EMG signals of the external oblique and lumbar

Results

The variance components in the data set indicated that between-subject variance was more than twice as large as within-subject variance (Table 1). Precision of estimates of mean and peak values of all parameters increased at a decaying rate with increasing numbers of subjects and measurements per subject (Fig. 1).

The regression coefficients obtained in the statistical analysis clearly indicated that the effect of increasing the number of subjects on precision was most pronounced (Table 2). Note

Discussion

The results confirm that increasing the number of subjects is the most effective strategy to improve precision of estimates of parameters describing low back load. It should be noted though, that beyond 10 subjects, i.e. the number of subjects in the original data set, the effects of number of subjects might be somewhat overestimated. However, fitting the regression lines on a subset of outcomes including only samples of 10 subjects or less, did not substantially affect the results. In

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