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Cosinor analysis of accident risk using SPSS’s regression procedures

Cosinor analysis of accident risk using SPSS’s regression procedures. Peter Watson 31st October 1997 MRC Cognition & Brain Sciences Unit. Aims & Objectives. To help understand accident risk we investigate 3 alertness measures over time

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Cosinor analysis of accident risk using SPSS’s regression procedures

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  1. Cosinor analysis of accident risk using SPSS’s regression procedures Peter Watson 31st October 1997 MRC Cognition & Brain Sciences Unit

  2. Aims & Objectives • To help understand accident risk we investigate 3 alertness measures over time • Two self-reported measures of sleep: Stanford Sleepiness Score (SSS) and Visual Analogue Score (VAS) • Attention measure: Sustained Attention to Response Task (SART)

  3. Study • 10 healthy Peterhouse college undergrads (5 male) • Studied at 1am, 7am, 1pm and 7pm for four consecutive days • How do vigilance (SART) and perceived vigilance (SSS, VAS) behave over time?

  4. Characteristics of Sleepiness • Most subjects “most sleepy” early in morning or late at night • Theoretical evidence of cyclic behaviour (ie repeated behaviour over a period of 24 hours)

  5. SSS variation over four days

  6. VAS variation over four days

  7. Aspects of cyclic behaviour • Features considered: • Length of a cycle (period) • Overall value of response (mesor) • Location of peak and nadir (acrophase) • Half the difference between peak and nadir scores (amplitude)

  8. Cosinor Model - cyclic behaviour • f(t) = M + AMP.Cos(2t + ) + t T Parameters of Interest: f(t) = sleepiness score; M = intercept (Mesor); AMP = amplitude; =phase; T=trial period (in hours) under study = 24; t = Residual

  9. Period, T • May be estimated • Previous experience (as in our example) • Constrained so that Peak and Nadir are T/2 hours apart (12 hours in our sleep example)

  10. Periodicity • 24 hour Periodicity upheld via absence of Time by Day interactions • SSS : F(9,81)=0.57, p>0.8 • VAS : F(9,81)=0.63, p>0.7

  11. Fitting using SPSS “linear” regression For g(t)=2t/24 and since Cos(g(t)+) = Cos()Cos(g(t))-Sin()Sin(g(t)) it follows the linear regression: f(t) = M + A.Cos(2t/24) + B.Sin(2t/24) is equivalent to the above single cosine function - now fittable in SPSS “linear” regression combining Cos and Sine function

  12. SPSS:Regression: “Linear” • Look at the combined sine and cosine • Evidence of curviture about the mean? • SSS F(2,157)=73.41, p<0.001; R2=48% • VAS F(2,13)=86.67, p<0.001; R2 =53% • Yes!

  13. Fitting via SPSS NLR • Estimates f, AMP and M • SSS: Peak at 5-11am • VAS Peak at 5-05am • M not generally of interest • Can also obtain CIs for AMP and Peak sleepiness time

  14. Amplitude: A = AMP Cos(f) B = -AMP Sin(f) Hence AMP = Acrophase: A = AMP Cos(f) B = -AMP Sin(f) Hence f = ArcTan(-B/A) Equivalence of NLR and “Linear” regression models

  15. Amplitude = 1/2(peak-nadir) Mesor = M = Mean Response (Acro)Phase =  = time of peak in 24 hour cycle In hours: peak = - 24 2 In degrees: peak = - 360 2 Model terms

  16. Fitted Cosinor Functions (VAS in black; SSS in red)

  17. % Amplitude • % Amplitude = 100 x (Peak-Nadir) overall mean = 100 x 2 AMP MESOR

  18. 95% Confidence interval for peak • Use SPSS NLR - estimates acrophase directly • acrophase ± t13,0.025 x standard error • multiply endpoints by -3.82 (=-24/2) • Ie standard error(C.) = |Cx standard error()

  19. Levels of Sleepiness • CIs for peak sleepiness and % amplitude • Stanford Sleepiness Score: 95% CI = (4-33,5-48), amplitude=97% Visual Analogue Score: 95% CI = (4-31,5-40), amplitude=129%

  20. 95% confidence intervals for predictions • Using Multiple “Linear” Regression: • Individual predictions in “statistics” option window • This corresponds to prediction pred ± t 13, 0.025 standard error of prediction

  21. SSS - 95% Confidence Intervals

  22. VAS 95% Confidence Intervals

  23. Rules of Thumb for Fit • De Prins J, Waldura J (1993) • Acceptable Fit 95% CI phase range < 30 degrees SSS 19 degrees (from NLR) VAS 17 degrees (from NLR)

  24. Conclusions • Perceived alertness has a 24 hour cycle • No Time by Day interaction - alertness consistent each day • We feel most sleepy around early morning

  25. Unperceived Vigilance • Vigilance task (same 10 students as sleep indices) • Proportion of correct responses to an attention task at 1am, 7am, 1pm and 7pm over 4 days

  26. Vigilance over the four days

  27. Linear regression F(2,13)=1.02, p>0.35, R2 = 1% No evidence of curviture NLR Peak : 3-05am 95% CI of peak (9-58pm , 8-03am) Phase Range 151 degrees Amplitude 18% Results of vigilance analysis

  28. Vigilance - linear over time • Plot suggests no obvious periodicity • Acrophase of 151 degrees > 30 degrees (badly inaccurate fit) • Cyclic terms statistically nonsignificant, low R2 • Flat profile suggested by low % amplitude • Vigilance, itself, may be linear with time

  29. Polynomial Regression • An alternative strategy is the fitting of cubic polynomials • Similar results to cosinor functions • two turning points for perceived sleepiness • no turning points (linear) for attention measure

  30. Conclusions • Cosinor analysis is a natural way of modelling cyclic behaviour • Can be fitted in SPSS using either “linear” or nonlinear regression procedures

  31. Thanks to helpful colleagues….. • Avijit Datta • Geraint Lewis • Tom Manly • Ian Robertson

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