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Redmayne

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Redmayne

  1. 1. Accuracy of adolescent SMS-textingestimation and a model to forecastactual 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. 2. Non-Ionizing Radiation& Children‟s Health International 100 kmsJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  3. 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-estimationNon-Ionizing Radiation& Children‟s Health International of relative riskJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia for high-users
  4. 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, 237-243Non-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  5. 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 theNon-Ionizing Radiation& Children‟s Health International gold standard forJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia billed/actual use
  6. 6. Increasing scatter with increased Linear after log numerosity transformationNon-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  7. 7. 0-99 recalled 100-999 recalled weekly texts sent weekly texts sent 1510 8 10 6 5 4 2 0 0 NAVY number <35 RED rounded recalls>35 BLUE mean of range >35
  8. 8. Mean over- estimation of weekly use 2.7 %Non-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  9. 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 10Non-Ionizing Radiation& Children‟s Health International ActualJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  10. 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 toNon-Ionizing Radiation under-estimation of relative risk for& Children‟s Health InternationalJoint Workshop, 18-20 May 2011, high-usersLjubljana, Slovenia
  11. 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-endNon-Ionizing Radiation& Children‟s Health International exaggeration in theJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia model
  12. 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 sampleNon-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  13. 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 ActualNon-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  14. 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 forecastNon-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia
  15. 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.gifNon-Ionizing Radiation& Children‟s Health InternationalJoint Workshop, 18-20 May 2011,Ljubljana, Slovenia

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