1. Accuracy of adolescent SMS-texting
estimation and a model to forecast
actual use from self-reported data
Mary Redmaynea, Euan Smitha, Michael Abramsonb
a Victoria University of Wellington, New Zealand
b Monash University, Melbourne, Australia
Non-Ionizing Radiation & Children‟s
Health International Joint Workshop
18-20 May 2011, Ljubljana, Slovenia

2. Non-Ionizing Radiation
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100 kms
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3. 4
Weekly2000 Actual v. Recalled
10
Data Actual v. Recalled use:
ML forecast actual
Regression forecast actual Data (+)
3
Forecast data from regression (+)
10
Actual
2
10
1
10
0
10
0 1 2 3 4
10 10 10 10 10
Recalled The regression method
leads to under-estimation
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of relative risk
Joint Workshop, 18-20 May 2011,
Ljubljana, Slovenia for high-users

4.  Assess the accuracy of adolescent SMS (texting)
recall
 Explore the occurrence of logarithmic thinking
 Produce a model to forecast „actual‟ texting rates,
with uncertainties, from recalled data
Vrijheid, M. et al. (2006) Validations of short term recall of mobile
phone use for the Interphone study. Occup Environ Med 63, 237-243
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5. METHOD
Survey start:
What is the average number of text messages you send?
____Per day OR ____Per week OR ____Per month
Survey end:
Students accessed their phone record.
“As of _________you have texts remaining on…(plan type)”
Or
“Your text balance is … and recurs on …”
The provider‟s record
of use in the current
month formed the
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gold standard for
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billed/actual use

6. Increasing
scatter with
increased Linear after log
numerosity transformation
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7. 0-99 recalled 100-999 recalled
weekly texts sent weekly texts sent
15
10
8 10
6
5
4
2 0
0
NAVY number <35
RED rounded recalls>35
BLUE mean of range >35

8. Mean over-
estimation of
weekly use
2.7 %
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9. Distribution of Actual
1
Exponential model 500
0.9 Data 500
Exponential model 2000
0.8
Data 2000
0.7
Cumulative probability
0.6
0.5
0.4
0.3
0.2
0.1
0
-1 0 1 2 3 4
10 10 10 10 10 10
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Joint Workshop, 18-20 May 2011,
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10. 4
Weekly2000 Actual v. Recalled
10
Data Actual v. Recalled use:
ML forecast actual
Regression forecast actual Data (+)
3
-)
10
Inverse linear regression model (
log(a) = (1/β1) (log(r) – β0)
Actual
10
2
Where „a‟ is „actual‟ and „r‟ is „recalled‟
Forecast data from regression ( +)
1
10
0
10
0 1 2 3 4
10 10 10 10 10
Recalled
Because of the big scatter in recall,
the regression method leads to
Non-Ionizing Radiation under-estimation of relative risk for
& Children‟s Health International
Joint Workshop, 18-20 May 2011, high-users
Ljubljana, Slovenia

11. 4
Weekly2000 Actual v. Recalled
10
Data Actual v. Recalled use:
ML forecast actual
Regression forecast actual Data (+)
3 Inverse linear regression model (-)
10
Forecast data from regression (+)
Bayesian model with ML:
(log(r) – β0 – β1log(a)) = (σ2/β1μ) a
Actual
2
10 Where σ2 is the variance of the recall
data, and μ is the mean of the actual
data
Forecast data from Bayesian model (+)
1
10
0
10
0 1 2 3 4
10 10 10 10 10
Recalled This approach
overcomes high-end
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exaggeration in the
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12. 4
Forecasts (Bayesian blue with error bars, regression red) and actual
10
Billed data (○) Black;
3
10 Forecast from regression
(○) Red;
2
10
Forecast from Bayesian model
(○) Blue;
Actual
1 95% confidence interval for
Bayesian forecast based on
10
These outliers were from Gaussian statistics (+).
0
users with recalls much
10
lower than actual use
-1
10
0 10 20 30 40 50 60
Ordered sample
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13. Weekly 2000 No. = 58 Distribution of actual
1
Cumulative distribution of
0.9 Data actual usage:
Regression forecast from recalled
0.8
ML forecast from recalled
data (-) BLACK;
0.7
Cumulative probability
0.6 forecast from regression
0.5
model (-) RED;
0.4
forecast from Bayesian
0.3 model (-) BLUE.
0.2
0.1
0
0 1 2 3 4
10 10 10 10 10
Actual
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14.  Our data conform to well-described psychological
tendencies of how numerosity is estimated
 The wide variance in recalled numerosity data leads to
exaggeration of inferred upper-end use when using a
regression model for forecasting
 If using this to calculate brain tumour-risk from
cellphone use, it will lead to under-estimation of
relative risk for high users
 A Bayesian approach using maximum likelihood
function provides a good mid to upper-end
forecast
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15.  Dehaene S, Izard V, Spelke E. Pica P. (2008). Log or linear? Distinct intuitions of the number scale in
Western and Amazonian indigene culture. Science 320(5880):1217-20.
 Inyang I, Benke G, Morrissey JJ, McKenzie RJ, Abramson M. (2009). How well do adolescents recall use of
mobile telephones? Results of a validation study. BMC Medical Research methodology 9(1):36-45.
 Vrijheid M, Cardis, E, Armstrong BK, et al. (2006). Validation of short term recall of mobile phone use for
the Interphone study. Occupational Environmental Medicine 63(4);237-43
 Vrijheid M, Armstrong G, Bedard D, et al. (2009). Recall bias in the assessment of exposure to mobile
phones. Journal of Exposure Science and Environmental Epidemiology 19(4):369-81.
 Whalen J, Gallistel CR, Gelman R. (1999). Non-verbal counting in humans: The psychophysics of number
representation. Psychological Science 10(2),130-7.
Acknowledgments:
 We thank Dr Richard Arnold, Senior Lecturer, School of Mathematics, Statistics and
Operations Research, Victoria University of Wellington for his advice during development of
the forecast method
 Map of Wellington region www.stats.govt.nz/census/images/maps/1000009-lo.gif&imgrefurl
 Images of child thinking and hands texting http://www.dreamstime.com/free-
results.php?searchby=cordless+&changecontentfiltered=0&searchtype=free
 Statistics New Zealand boundary map of Wellington region
http://statistics.govt.nz/census/images/maps/1000009-lo.gif
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Joint Workshop, 18-20 May 2011,
Ljubljana, Slovenia