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

Accuracy of adolescent SMS-texting estimation and a model to forecast actual use from self-reported data

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

100 kms

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

The regression method leads to under-estimation

of relative risk for high-users

100

101

102

103

104

100

101

102

103

104

Recalled

Actu

al

Weekly2000 Actual v. Recalled

Data

ML forecast actual

Regression forecast actual

Actual v. Recalled use: Data (+)

Forecast data from regression (+)

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

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

Vrijheid, M. et al. (2006) Validations of short term recall of mobile

phone use for the Interphone study. Occup Environ Med 63, 237-243

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

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 gold standard for billed/actual use

METHOD

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

Linear after log transformation

Increasing scatter with increased

numerosity

0

2

4

6

8

10

0

5

10

15

0-99 recalled weekly texts sent

100-999 recalled weekly texts sent

NAVY number <35 RED rounded recalls>35 BLUE mean of range >35

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

Mean over-estimation of weekly use

2.7 %

10-1

100

101

102

103

104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Actual

Cum

ula

tive p

robabili

ty

Distribution of Actual

Exponential model 500

Data 500

Exponential model 2000

Data 2000

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

Because of the big scatter in recall, the regression method leads to

under-estimation of relative risk for high-users

100

101

102

103

104

100

101

102

103

104

Recalled

Actu

al

Weekly2000 Actual v. Recalled

Data

ML forecast actual

Regression forecast actual

Actual v. Recalled use:

Data (+)

Inverse linear regression model (-)

log(a) = (1/β1) (log(r) – β0) Where „a‟ is „actual‟ and „r‟ is „recalled‟

Forecast data from regression (+)

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

This approach overcomes high-end exaggeration in the

model

100

101

102

103

104

100

101

102

103

104

Recalled

Actu

al

Weekly2000 Actual v. Recalled

Data

ML forecast actual

Regression forecast actual

Actual v. Recalled use: Data (+)

Inverse linear regression model (-)

Forecast data from regression (+)

Bayesian model with ML:

(log(r) – β0 – β1log(a)) = (σ2/β1μ) a

Where σ2 is the variance of the recall data, and μ is the mean of the actual data

Forecast data from Bayesian model (+)

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

0 10 20 30 40 50 6010

-1

100

101

102

103

104

Forecasts (Bayesian blue with error bars, regression red) and actual

Ordered sample

Actu

al

Billed data (○) Black; Forecast from regression (○) Red; Forecast from Bayesian model (○) Blue; 95% confidence interval for Bayesian forecast based on Gaussian statistics (+).

These outliers were from users with recalls much lower than actual use

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

100

101

102

103

104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Actual

Cum

ula

tive p

robabili

ty

Weekly 2000 No. = 58 Distribution of actual

Data

Regression forecast from recalled

ML forecast from recalled

Cumulative distribution of actual usage: data (-) BLACK; forecast from regression model (-) RED; forecast from Bayesian model (-) BLUE.

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

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia

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

Non-Ionizing Radiation & Children‟s Health International Joint Workshop, 18-20 May 2011, Ljubljana, Slovenia