supplementary materials formay 03, 2016 · published 6 may 2016, sci. adv. 2, e1501705 (2016) doi:...

advances.sciencemag.org/cgi/content/full/2/5/e1501705/DC1

Supplementary Materials for

A global quantification of “normal” sleep schedules using smartphone

data

Olivia J. Walch, Amy Cochran, Daniel B. Forger

Published 6 May 2016, Sci. Adv. 2, e1501705 (2016)

DOI: 10.1126/sciadv.1501705

The PDF file includes:

Statistics

table S1. Fixed and random effects on scheduled bedtime and wake time.

table S2. Fixed and random effects on scheduled sleep duration and midsleep.

table S3. Fixed and random effects and their interactions on bedtime and wake

time.

table S4. Fixed and random effects and their interactions on scheduled sleep

duration and midsleep.

table S5. Moderation of wake time and bedtime on the relationship between

regression terms and scheduled sleep duration.

table S6. Effect of scheduled sleep duration and the square of scheduled sleep

duration on midsleep.

table S7. Main effects and interactions between fixed factors and age-squared on

scheduled bedtime and wake time.

table S8. Main effects and interactions between fixed factors and age-squared on

scheduled sleep duration and midsleep.

Supplementary Materials

Statistics

Multiple regression was run in SPSS to predict sleep schedules (wake, bed, sleep duration, and

midsleep) from gender, age, typical light (indoor vs. outdoor), sunrise, sunset, travel frequency

(often vs. not often), and country. The dependent variables (wake, bed, sleep duration, and

midsleep) were checked for approximate normality through visual inspection of Normal Q-Q

plots. Age, sunrise, and sunset were centered on their mean to help improve interpretability of

the regression coefficients.

A multilevel structure, where users are nested in countries, was assumed for the data. As a

consequence, we used a linear mixed effects model for regression where country was considered

a random effect. Specifically, each country contributes to the predicted value a random intercept,

assumed to be independently and identically drawn from a normal distribution with mean zero

and unknown variance. The variance is estimated during regression. There were over 100 distinct

countries, the majority of which had less than 10 samples. By assuming country is a random

rather than fixed effect, we can avoid estimating a large number of regression coefficients

associated with small sample-sizes.

Four different types of regression were performed. First, we ran regressions to predict sleep

schedules from the main effects and the square of the centered age effect (called age-squared).

The latter effect was included to account for nonlinear effects of age. Second, we ran the same

regressions as before, except we included two-way interactions between main effects and

excluded travel frequency due to its limited contribution to the first set of regressions. Third, we

ran regressions to determine how wake times and bed times may moderate the relationship

between sleep and the various dependent variables, along with how sleep duration may moderate

the relationship between midsleep and the various effects. This involved running same

regressions as done for the second set of regressions, except for including moderating variable(s)

(properly centered) as an independent variable. The square of the centered sleep duration (to

explore nonlinearity) was included when determining sleep’s moderating effect on midsleep.

Lastly, we ran regressions as in the first set of regressions, except for including interactions

between age-squared and each of light and gender.

The SPSS procedure GENLINMIXED was used to build the linear mixed models. (The

procedure GENLINMIXED can build linear mixed models, as specific case of a generalized

linear mixed models.) The procedure reports a t-test statistic (and associated p-value) to test

statistical significance for each fixed term and reports a Z-test statistic (and associated p-value)

to test statistical significance for the random term. Significance is considered an alpha level of

0.05.

Appendix

Bed Time Wake Time

Estimatea ( SE ) Statisticb p Estimatea ( SE ) Statisticb p

Intercept 10.9770 ( 0.0661 ) 165.956 <0.001 6.9900 ( 0.0622 ) 112.443 <0.001

Sunrise 0.1680 ( 0.0387 ) 4.348 <0.001 0.1960 ( 0.0376 ) 5.209 <0.001

Sunset 0.0590 ( 0.0219 ) 2.672 0.008 0.0810 ( 0.0212 ) 3.805 <0.001

Age -0.0191 ( 0.0012 ) -15.614 <0.001 -0.0231 ( 0.0013 ) -18.271 <0.001

AgeSquared 0.0005 ( 0.0001 ) 5.907 <0.001 0.0009 ( 0.0001 ) 10.792 <0.001

Gender 0.1500 ( 0.0356 ) 4.211 <0.001 -0.1310 ( 0.0369 ) -3.533 <0.001

Light 0.1630 ( 0.0397 ) 4.103 <0.001 0.0340 ( 0.0411 ) 0.833 0.405

Frequency -0.0220 ( 0.0353 ) -0.631 0.528 -0.0410 ( 0.0366 ) -1.124 0.261

Residualc 1.5560 ( 0.0300 ) 51.932 <0.001 1.6770 ( 0.0320 ) 51.928 <0.001

Countryc 0.0850 ( 0.0280) 3.059 0.002 0.0450 ( 0.0210) 2.177 0.029

table S1. Fixed and random effects on scheduled bedtime and wake time.

a Estimates for factors refer to the logical variables Gender=Male, Light=Indoor, and Frequency<Often.

b The t-test statistic was used for fixed effects and the Z-test statistic was used for random effects.

c Country and residual are random effects.

Sleep Duration Midsleep


Intercept 8.0370 ( 0.0475 ) 169.025 <0.001 14.9840 ( 0.0600 ) 249.662 <0.001

Sunrise 0.0430 ( 0.0288 ) 1.503 0.133 0.1840 ( 0.0356 ) 5.155 <0.001

Sunsete 0.0300 ( 0.0162 ) 1.843 0.065 0.0700 ( 0.0201 ) 3.475 0.001

Age -0.0038 ( 0.0010 ) -3.924 <0.001 -0.0211 ( 0.0012 ) -18.407 <0.001

AgeSquared 0.0004 ( 0.0001 ) 6.582 <0.001 0.0007 ( 0.0001 ) 9.122 <0.001

Gender -0.2830 ( 0.0285 ) -9.922 <0.001 0.0090 ( 0.0334 ) 0.283 0.777

Light -0.1300 ( 0.0317 ) -4.118 <0.001 0.0980 ( 0.0371 ) 2.646 0.008

Frequency -0.0170 ( 0.0282 ) -0.608 0.543 -0.0310 ( 0.0331 ) -0.95 0.342

Residualc 0.9970 ( 0.0190 ) 51.975 <0.001 1.3670 ( 0.0260 ) 51.923 <0.001

Countryc 0.0250 ( 0.0110) 2.274 0.023 0.0610 ( 0.0220) 2.749 0.006

table S2. Fixed and random effects on scheduled sleep duration and midsleep.

a Estimates for factors refer to the logical variables Gender=Male, Light=Indoor, and Frequency<Often.



Bed Time Wake Time


Intercept 10.9970 ( 0.0762 ) 144.237 <0.001 6.9700 ( 0.0730 ) 95.438 <0.001

Sunrise 0.2640 ( 0.0738 ) 3.58 <0.001 0.3050 ( 0.0754 ) 4.045 <0.001

Sunset 0.0830 ( 0.0399 ) 2.087 0.037 0.1700 ( 0.0405 ) 4.195 <0.001

Age -0.0176 ( 0.0027 ) -6.511 <0.001 -0.0208 ( 0.0028 ) -7.44 <0.001

AgeSquared 0.0004 ( 0.0001 ) 5.907 <0.001 0.0009 ( 0.0001 ) 10.688 <0.001

Gender 0.0920 ( 0.0706 ) 1.296 0.195 -0.1400 ( 0.0732 ) -1.911 0.056

Light 0.1100 ( 0.0654 ) 1.685 0.092 0.0220 ( 0.0678 ) 0.318 0.751

Age*Gender -0.0017 ( 0.0024 ) -0.688 0.491 -0.0037 ( 0.0025 ) -1.47 0.142

Age*Light -0.0006 ( 0.0026 ) -0.216 0.829 0.0001 ( 0.0027 ) 0.02 0.984

Age*Sunrise 0.0026 ( 0.0021 ) 1.244 0.214 0.0037 ( 0.0022 ) 1.715 0.086

Age*Sunset 0.0025 ( 0.0011 ) 2.263 0.024 0.0008 ( 0.0011 ) 0.722 0.47

Gender*Light 0.0860 ( 0.0819 ) 1.049 0.294 0.0210 ( 0.0849 ) 0.249 0.803

Sunrise*Gender -0.0780 ( 0.0605 ) -1.293 0.196 -0.0930 ( 0.0626 ) -1.479 0.139

Sunset*Gender 0.0220 ( 0.0322 ) 0.698 0.485 -0.0060 ( 0.0333 ) -0.172 0.863

Sunrise*Light -0.0680 ( 0.0685 ) -0.997 0.319 -0.0770 ( 0.0709 ) -1.081 0.28

Sunset*Light -0.0170 ( 0.0357 ) -0.48 0.631 -0.0800 ( 0.0369 ) -2.176 0.03

Sunrise*Sunset -0.0580 ( 0.0194 ) -2.979 0.003 -0.0650 ( 0.0195 ) -3.342 0.001

Residualc 1.5520 ( 0.0300 ) 51.881 <0.001 1.6710 ( 0.0320 ) 51.903 <0.001

Countryc 0.0960 ( 0.0300) 3.168 0.002 0.0510 ( 0.0210) 2.374 0.018

table S3. Fixed and random effects and their interactions on bedtime and wake time.

a Estimates for factors refer to the logical variables Gender=Male and Light=Indoor.





Intercept 8.0000 ( 0.0548 ) 145.872 <0.001 14.9840 ( 0.0696 ) 215.212 <0.001

Sunrise 0.0530 ( 0.0579 ) 0.91 0.363 0.2860 ( 0.0688 ) 4.158 <0.001

Sunset 0.0970 ( 0.0310 ) 3.143 0.002 0.1270 ( 0.0371 ) 3.423 0.001

Age -0.0030 ( 0.0022 ) -1.408 0.159 -0.0192 ( 0.0025 ) -7.581 <0.001

AgeSquared 0.0004 ( 0.0001 ) 6.42 <0.001 0.0006 ( 0.0001 ) 9.065 <0.001

Gender -0.2310 ( 0.0565 ) -4.094 <0.001 -0.0250 ( 0.0661 ) -0.376 0.707

Light -0.0890 ( 0.0523 ) -1.701 0.089 0.0650 ( 0.0612 ) 1.068 0.285

Age*Gender -0.0020 ( 0.0019 ) -1.032 0.302 -0.0027 ( 0.0023 ) -1.178 0.239

Age*Light 0.0006 ( 0.0021 ) 0.297 0.766 -0.0003 ( 0.0024 ) -0.104 0.917

Age*Sunrise 0.0010 ( 0.0017 ) 0.602 0.547 0.0031 ( 0.0020 ) 1.593 0.111

Age*Sunset -0.0018 ( 0.0009 ) -2.035 0.042 0.0016 ( 0.0010 ) 1.596 0.11

Gender*Light -0.0670 ( 0.0655 ) -1.027 0.304 0.0540 ( 0.0767 ) 0.704 0.482

Sunrise*Gender -0.0080 ( 0.0483 ) -0.163 0.87 -0.0850 ( 0.0566 ) -1.502 0.133

Sunset*Gender -0.0250 ( 0.0257 ) -0.974 0.33 0.0090 ( 0.0301 ) 0.285 0.775

Sunrise*Light -0.0080 ( 0.0547 ) -0.155 0.877 -0.0730 ( 0.0641 ) -1.137 0.256

Sunset*Light -0.0620 ( 0.0285 ) -2.189 0.029 -0.0480 ( 0.0334 ) -1.448 0.148

Sunrise*Sunset -0.0180 ( 0.0149 ) -1.188 0.235 -0.0620 ( 0.0180 ) -3.451 0.001

Residualc 0.9970 ( 0.0190 ) 51.941 <0.001 1.3620 ( 0.0260 ) 51.883 <0.001

Countryc 0.0220 ( 0.0100) 2.157 0.031 0.0690 ( 0.0240) 2.915 0.004

table S4. Fixed and random effects and their interactions on scheduled sleep duration and midsleep.




Sleep Duration Sleep Duration


Intercept 7.9800 ( 0.0527 ) 151.495 <0.001 7.9750 ( 0.0492 ) 162.047 <0.001

Wake 0.3320 ( 0.0094 ) 35.132 <0.001 - - -

Bed - - - -0.2840 ( 0.0101 ) -28.077 <0.001

Sunrise -0.0520 ( 0.0530 ) -0.981 0.327 0.1230 ( 0.0536 ) 2.29 0.022

Sunset 0.0370 ( 0.0285 ) 1.287 0.198 0.1180 ( 0.0286 ) 4.126 <0.001

Age 0.0038 ( 0.0020 ) 1.938 0.053 -0.0081 ( 0.0020 ) -4.008 <0.001

AgeSquared 0.0001 ( 0.0001 ) 2.019 0.043 0.0005 ( 0.0001 ) 9.093 <0.001

Gender -0.1860 ( 0.0510 ) -3.644 <0.001 -0.2040 ( 0.0529 ) -3.853 <0.001

Light -0.0970 ( 0.0472 ) -2.046 0.041 -0.0570 ( 0.0490 ) -1.167 0.243

Age*Gender -0.0008 ( 0.0017 ) -0.445 0.657 -0.0025 ( 0.0018 ) -1.365 0.172

Age*Light 0.0006 ( 0.0019 ) 0.318 0.751 0.0005 ( 0.0019 ) 0.236 0.813

Age*Sunrise -0.0002 ( 0.0015 ) -0.154 0.878 0.0019 ( 0.0016 ) 1.183 0.237

Age*Sunset -0.0020 ( 0.0008 ) -2.538 0.011 -0.0010 ( 0.0008 ) -1.27 0.204

Gender*Light -0.0720 ( 0.0591 ) -1.222 0.222 -0.0440 ( 0.0613 ) -0.717 0.473

Sunrise*Gender 0.0200 ( 0.0437 ) 0.461 0.645 -0.0320 ( 0.0452 ) -0.7 0.484

Sunset*Gender -0.0240 ( 0.0232 ) -1.047 0.295 -0.0200 ( 0.0240 ) -0.818 0.413

Sunrise*Light 0.0170 ( 0.0494 ) 0.335 0.737 -0.0270 ( 0.0511 ) -0.522 0.602

Sunset*Light -0.0360 ( 0.0258 ) -1.381 0.167 -0.0680 ( 0.0266 ) -2.558 0.011

Sunrise*Sunset 0.0080 ( 0.0138 ) 0.589 0.556 -0.0310 ( 0.0136 ) -2.265 0.024

Residualc 0.8110 ( 0.0160 ) 51.906 <0.001 0.8730 ( 0.0170 ) 51.952 <0.001

Countryc 0.0350 ( 0.0120) 2.828 0.005 0.0100 ( 0.0060) 1.556 0.12

table S5. Moderation of wake time and bedtime on the relationship between regression terms and scheduled

sleep duration.




Midsleep

Estimatea ( SE ) Statisticb p

Intercept 14.9400 ( 0.0706 ) 211.709 <0.001

Sleep 0.0560 ( 0.0158 ) 3.557 <0.001

SleepSquared 0.0300 ( 0.0089 ) 3.321 0.001

Sunrise 0.2840 ( 0.0687 ) 4.14 <0.001

Sunset 0.1200 ( 0.0371 ) 3.233 0.001

Age -0.0184 ( 0.0025 ) -7.266 <0.001

AgeSquared 0.0006 ( 0.0001 ) 8.533 <0.001

Gender=0 -0.0030 ( 0.0661 ) -0.045 0.964

Light=0 0.0760 ( 0.0612 ) 1.24 0.215

Age*Gender -0.0027 ( 0.0023 ) -1.183 0.237

Age*Light -0.0005 ( 0.0024 ) -0.196 0.844

Age*Sunrise 0.0030 ( 0.0020 ) 1.53 0.126

Age*Sunset 0.0017 ( 0.0010 ) 1.638 0.101

Gender*Light 0.0510 ( 0.0766 ) 0.668 0.504

Sunrise*Gender -0.0840 ( 0.0565 ) -1.493 0.135

Sunset*Gender 0.0090 ( 0.0301 ) 0.315 0.753

Sunrise*Light -0.0710 ( 0.0640 ) -1.115 0.265

Sunset*Light -0.0420 ( 0.0334 ) -1.247 0.212

Sunrise*Sunset -0.0620 ( 0.0180 ) -3.427 0.001

Residual 1.3560 ( 0.0260 ) 51.873 <0.001

Country 0.0690 ( 0.0240) 2.926 0.003

table S6. Effect of scheduled sleep duration and the square of scheduled sleep duration on midsleep.




Bed Wake


Intercept 10.9440 ( 0.0740 ) 147.969 <0.001 7.0470 ( 0.0712 ) 99.046 <0.001

Sunrise 0.1690 ( 0.0387 ) 4.359 <0.001 0.1960 ( 0.0377 ) 5.191 <0.001

Sunset 0.0590 ( 0.0219 ) 2.682 0.007 0.0820 ( 0.0213 ) 3.835 <0.001

Age -0.0189 ( 0.0012 ) -15.437 <0.001 -0.0228 ( 0.0013 ) -17.992 <0.001

AgeSquared 0.0006 ( 0.0002 ) 3.278 0.001 0.0005 ( 0.0002 ) 3.024 0.003

Gender 0.2260 ( 0.0495 ) 4.561 <0.001 -0.1300 ( 0.0513 ) -2.527 0.012

Light 0.1260 ( 0.0543 ) 2.321 0.02 -0.0640 ( 0.0562 ) -1.143 0.253

AgeSquared * Gender -0.0003 ( 0.0002 ) -2.08 0.038 0.0000 ( 0.0002 ) 0.201 0.841

AgeSquared * Light 0.0001 ( 0.0002 ) 0.878 0.38 0.0004 ( 0.0002 ) 2.524 0.012

Residualc 1.5550 ( 0.0300 ) 51.928 <0.001 1.6750 ( 0.0320 ) 51.922 <0.001

Countryc 0.0850 ( 0.0280) 3.066 0.002 0.0460 ( 0.0210) 2.206 0.027

table S7. Main effects and interactions between fixed factors and age-squared on scheduled bedtime and wake

time.






Intercept 8.1280 ( 0.0543 ) 149.662 <0.001 14.9960 ( 0.0676 ) 221.734 <0.001

Sunrise 0.0420 ( 0.0287 ) 1.468 0.142 0.1840 ( 0.0356 ) 5.15 <0.001

Sunset 0.0300 ( 0.0162 ) 1.871 0.061 0.0700 ( 0.0201 ) 3.496 <0.001

Age -0.0037 ( 0.0010 ) -3.798 <0.001 -0.0208 ( 0.0012 ) -18.158 <0.001

AgeSquared -0.0000 ( 0.0001 ) -0.21 0.833 0.0006 ( 0.0002 ) 3.418 0.001

Gender -0.3580 ( 0.0395 ) -9.054 <0.001 0.0480 ( 0.0464 ) 1.027 0.305

Light -0.1930 ( 0.0433 ) -4.452 <0.001 0.0300 ( 0.0508 ) 0.599 0.549

AgeSquared * Gender 0.0004 ( 0.0001 ) 2.882 0.004 -0.0001 ( 0.0001 ) -0.996 0.319

AgeSquared * Light 0.0003 ( 0.0001 ) 2.202 0.028 0.0003 ( 0.0001 ) 1.871 0.061

Residualc 0.9950 ( 0.0190 ) 51.968 <0.001 1.3660 ( 0.0260 ) 51.919 <0.001

Countryc 0.0250 ( 0.0110) 2.259 0.024 0.0610 ( 0.0220) 2.768 0.006

table S8. Main effects and interactions between fixed factors and age-squared on scheduled sleep duration

and midsleep.




supplementary materials formay 03, 2016 · published 6 may 2016, sci. adv. 2, e1501705 (2016) doi:...

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