Accuracy of adolescent SMS-texting estimation and a model ... · Mary Redmayne a, Euan Smith ,...
Transcript of Accuracy of adolescent SMS-texting estimation and a model ... · Mary Redmayne a, Euan Smith ,...
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