Patterns in wireless phone estimation data from a cross-sectional survey: what are the implications for epidemiology?

Abstract

Objective: Self-reported recall data are often used in wireless phone epidemiological studies, which in turn are used to indicate relative risk of health outcomes from extended radiofrequency exposure. We sought to explain features commonly observed in wireless phone recall data and to improve analytical procedures.

Setting: Wellington Region, New Zealand.

Participants: Each of the 16 schools selected a year 7 and/or 8 class to participate, providing a representative regional sample based on socioeconomic school ratings, school type and urban/rural balance. There was an 85% participation rate (N=373).

Main outcome measures: Planned: the distribution of participants' estimated extent of SMS-texting and cordless phone calls, and the extent of rounding to a final zero or five within the full set of recall data and within each order of magnitude. Unplanned: the distribution of the leading digits of these raw data, compared with that of billed data in each order of magnitude.

Results: The nature and extent of number-rounding, and the distribution of data across each order in recall data indicated a logarithmic (ratio-based) mental process for assigning values. Responses became less specific as the leading-digit increased from 1 to 9, and 69% of responses for weekly texts sent were rounded by participants to a single non-zero digit (eg, 2, 20 and 200).

Conclusions: Adolescents' estimation of their cellphone use indicated that it was performed on a mental logarithmic scale. This is the first time this phenomenon has been observed in the estimation of recalled, as opposed to observed, numerical quantities. Our findings provide empirical justification for log-transforming data for analysis. We recommend the use of the geometric rather than arithmetic mean when a recalled numerical range is provided. A point of calibration may improve recall.

Figure 1

(A) Distribution of weekly texting estimation data (second order): 61% of estimates fell in the lower 35% of the order, and there was a strong rounding effect. There were only three unrounded estimates in the upper 65% of all orders (1 in the second order). (B) Distribution of weekly billed texts (second order) shows a homogeneous distribution despite the overall data being log normally distributed; 36% of estimates fell in the lower 35% of the order. All specific (ie, non-range) estimates are shown, with columns representing the number of participants who gave each estimate. Read from the back-left across each row, working forward in rows.

Figure 2

(A) Marks the distribution of ‘tenths’ from 0 to 1 on a log scale (equivalent of 1–10 on a linear scale). (B) Distribution of leading digits of participants’ estimated number of texts sent weekly, n = 181, range 1–1800, and (C) cordless calls made weekly, n = 183, range 1–150. The columns add up to 100% of specific estimates made. All columns are split into participants’ estimates with single non-zero digits (eg, 2, 20 and 200) and the remaining ones for each leading digit (eg, 23, 25 and 270).

Figure 3

Regression of participants’ weekly-to-daily text estimates (log-transformed data). The best-fit line indicates that on average weekly use is underestimated compared to estimates of daily use. For instance, on average, estimates of 10 or 100 daily were allotted 40 or 340 weekly, respectively (blue gridlines).

Figure 4

Bland and Altman plot displaying the difference of the logged estimation and billed weekly texting data against the log-billed. Accurate estimates would all fall on the dotted line. There is a clear and significant trend from overestimation of little use to underestimation of extensive use. All lowest and highest estimates to the left and right of the red lines were too high/too low, respectively.