The effect of magnesium supplementation on sleep quality: phase II¶
Author: Peter Richens
Date: 17 Jul 2021
Keywords: magnesium, sleep, magnesium supplementation, insomnia, activity trackers, fitbit
Design¶
A randomised trial was conducted on 1 adult male (me). The patient's sleep episodes where randomly allocated into the magnesium group (which recieved 200 mg of magnesium lysinate glycinate chelate) or the control group. Sleep activity was tracked by the patient's Fitbit device.
See related studies.
Source code available at: https://github.com/peterjrichens/personal-rct.
Results¶
- The effect on composite sleep score was not statistically signficant.
- Magnesium had a 0.32 standard deviation decrease on total sleep duration relative to the control treatment (p value=0.011).
- The effect on rem sleep duration was not statistically signficant.
- The effect on deep sleep duration was not statistically signficant.
Sample size¶
| number_of_days | |
|---|---|
| control | 24 |
| magnesium | 21 |
| total | 45 |
Summary statistics during pre-experiment baseline¶
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| total_sleep_duration | 29.0 | 463.517241 | 35.668734 | 403.00 | 448.00 | 462.00 | 484.00 | 555.00 |
| deep_sleep_duration | 29.0 | 72.758621 | 21.423710 | 22.00 | 62.00 | 74.00 | 87.00 | 118.00 |
| rem_sleep_duration | 29.0 | 110.206897 | 26.065000 | 66.00 | 93.00 | 108.00 | 134.00 | 152.00 |
| sleep_start_time | 29.0 | -33.051724 | 52.190986 | -120.50 | -74.50 | -44.00 | -4.00 | 99.50 |
| composite_sleep_score | 30.0 | 81.766667 | 5.069743 | 70.00 | 78.50 | 82.00 | 85.75 | 90.00 |
| steps | 30.0 | 5220.366667 | 2930.243999 | 308.00 | 2698.75 | 5131.00 | 7241.25 | 12205.00 |
| calories | 30.0 | 2317.269333 | 314.401309 | 1671.44 | 2133.45 | 2289.31 | 2474.36 | 3283.53 |
Summary statistics during experiment period¶
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| total_sleep_duration | 42.0 | 448.166667 | 59.371882 | 205.00 | 416.25 | 458.00 | 490.75 | 537.00 |
| deep_sleep_duration | 42.0 | 78.333333 | 17.419735 | 28.00 | 67.00 | 80.00 | 88.25 | 130.00 |
| rem_sleep_duration | 42.0 | 108.595238 | 29.209971 | 11.00 | 93.50 | 109.00 | 128.00 | 172.00 |
| sleep_start_time | 42.0 | -10.500000 | 62.819428 | -92.50 | -47.00 | -16.25 | 6.75 | 289.00 |
| composite_sleep_score | 42.0 | 82.619048 | 6.148378 | 65.00 | 79.50 | 84.00 | 86.00 | 92.00 |
| steps | 45.0 | 5794.777778 | 3127.193230 | 2083.00 | 3277.00 | 4966.00 | 8369.00 | 13028.00 |
| calories | 45.0 | 2395.160667 | 270.646372 | 1969.15 | 2194.60 | 2351.20 | 2524.84 | 3078.27 |
Outcome variables over time¶
Red line shows start of experiment period.
Regression results¶
Results for composite sleep score¶
The effect on composite sleep score was not statistically signficant.
| Dep. Variable: | standardize(composite_sleep_score) | R-squared: | 0.384 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.185 |
| Method: | Least Squares | F-statistic: | 9.277 |
| Date: | Sat, 17 Jul 2021 | Prob (F-statistic): | 7.13e-07 |
| Time: | 15:45:22 | Log-Likelihood: | -49.423 |
| No. Observations: | 42 | AIC: | 120.8 |
| Df Residuals: | 31 | BIC: | 140.0 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.0065 | 0.273 | 0.024 | 0.981 | -0.528 | 0.541 |
| C(treatment, Treatment(reference='control'))[T.magnesium] | -0.3713 | 0.236 | -1.575 | 0.115 | -0.833 | 0.091 |
| C(day_of_week)[T.Monday] | 0.1473 | 0.387 | 0.380 | 0.704 | -0.612 | 0.907 |
| C(day_of_week)[T.Saturday] | 1.1475 | 0.267 | 4.294 | 0.000 | 0.624 | 1.671 |
| C(day_of_week)[T.Sunday] | 0.2899 | 0.394 | 0.735 | 0.462 | -0.483 | 1.063 |
| C(day_of_week)[T.Thursday] | -0.4599 | 0.484 | -0.949 | 0.342 | -1.409 | 0.490 |
| C(day_of_week)[T.Tuesday] | -0.4473 | 0.561 | -0.797 | 0.425 | -1.547 | 0.652 |
| C(day_of_week)[T.Wednesday] | 0.2826 | 0.444 | 0.636 | 0.525 | -0.588 | 1.153 |
| standardize(sleep_start_time) | -0.6537 | 0.117 | -5.601 | 0.000 | -0.882 | -0.425 |
| standardize(steps) | -0.2749 | 0.292 | -0.940 | 0.347 | -0.848 | 0.298 |
| standardize(calories) | 0.1000 | 0.324 | 0.308 | 0.758 | -0.535 | 0.735 |
| Omnibus: | 8.057 | Durbin-Watson: | 1.843 |
|---|---|---|---|
| Prob(Omnibus): | 0.018 | Jarque-Bera (JB): | 6.895 |
| Skew: | -0.867 | Prob(JB): | 0.0318 |
| Kurtosis: | 3.965 | Cond. No. | 11.9 |
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction
Results for total sleep duration¶
Magnesium had a 0.32 standard deviation decrease on total sleep duration relative to the control treatment (p value=0.011).
| Dep. Variable: | standardize(total_sleep_duration) | R-squared: | 0.774 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.701 |
| Method: | Least Squares | F-statistic: | 38.73 |
| Date: | Sat, 17 Jul 2021 | Prob (F-statistic): | 9.89e-15 |
| Time: | 15:45:22 | Log-Likelihood: | -28.354 |
| No. Observations: | 42 | AIC: | 78.71 |
| Df Residuals: | 31 | BIC: | 97.82 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | -0.0183 | 0.316 | -0.058 | 0.954 | -0.638 | 0.602 |
| C(treatment, Treatment(reference='control'))[T.magnesium] | -0.3151 | 0.124 | -2.545 | 0.011 | -0.558 | -0.072 |
| C(day_of_week)[T.Monday] | 0.1638 | 0.356 | 0.460 | 0.645 | -0.534 | 0.861 |
| C(day_of_week)[T.Saturday] | 1.1831 | 0.295 | 4.017 | 0.000 | 0.606 | 1.760 |
| C(day_of_week)[T.Sunday] | 0.2131 | 0.326 | 0.653 | 0.514 | -0.427 | 0.853 |
| C(day_of_week)[T.Thursday] | -0.2582 | 0.391 | -0.661 | 0.509 | -1.024 | 0.508 |
| C(day_of_week)[T.Tuesday] | -0.4781 | 0.368 | -1.300 | 0.194 | -1.199 | 0.243 |
| C(day_of_week)[T.Wednesday] | 0.1598 | 0.321 | 0.497 | 0.619 | -0.470 | 0.789 |
| standardize(sleep_start_time) | -0.9517 | 0.073 | -13.086 | 0.000 | -1.094 | -0.809 |
| standardize(steps) | -0.3344 | 0.180 | -1.854 | 0.064 | -0.688 | 0.019 |
| standardize(calories) | 0.2325 | 0.177 | 1.310 | 0.190 | -0.115 | 0.580 |
| Omnibus: | 3.905 | Durbin-Watson: | 1.907 |
|---|---|---|---|
| Prob(Omnibus): | 0.142 | Jarque-Bera (JB): | 2.796 |
| Skew: | 0.599 | Prob(JB): | 0.247 |
| Kurtosis: | 3.405 | Cond. No. | 11.9 |
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction
Results for rem sleep duration¶
The effect on rem sleep duration was not statistically signficant.
| Dep. Variable: | standardize(rem_sleep_duration) | R-squared: | 0.527 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.374 |
| Method: | Least Squares | F-statistic: | 9.587 |
| Date: | Sat, 17 Jul 2021 | Prob (F-statistic): | 5.00e-07 |
| Time: | 15:45:22 | Log-Likelihood: | -43.895 |
| No. Observations: | 42 | AIC: | 109.8 |
| Df Residuals: | 31 | BIC: | 128.9 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.8529 | 0.372 | 2.294 | 0.022 | 0.124 | 1.582 |
| C(treatment, Treatment(reference='control'))[T.magnesium] | -0.2428 | 0.212 | -1.144 | 0.253 | -0.659 | 0.173 |
| C(day_of_week)[T.Monday] | -1.0019 | 0.507 | -1.978 | 0.048 | -1.995 | -0.009 |
| C(day_of_week)[T.Saturday] | 0.0652 | 0.458 | 0.142 | 0.887 | -0.833 | 0.963 |
| C(day_of_week)[T.Sunday] | -0.6404 | 0.501 | -1.279 | 0.201 | -1.622 | 0.341 |
| C(day_of_week)[T.Thursday] | -1.0826 | 0.407 | -2.662 | 0.008 | -1.880 | -0.286 |
| C(day_of_week)[T.Tuesday] | -1.3899 | 0.441 | -3.150 | 0.002 | -2.255 | -0.525 |
| C(day_of_week)[T.Wednesday] | -1.0941 | 0.461 | -2.374 | 0.018 | -1.997 | -0.191 |
| standardize(sleep_start_time) | -0.8058 | 0.104 | -7.721 | 0.000 | -1.010 | -0.601 |
| standardize(steps) | 0.2030 | 0.330 | 0.616 | 0.538 | -0.443 | 0.849 |
| standardize(calories) | -0.2598 | 0.282 | -0.922 | 0.357 | -0.812 | 0.293 |
| Omnibus: | 2.536 | Durbin-Watson: | 1.712 |
|---|---|---|---|
| Prob(Omnibus): | 0.281 | Jarque-Bera (JB): | 1.381 |
| Skew: | 0.032 | Prob(JB): | 0.501 |
| Kurtosis: | 2.114 | Cond. No. | 11.9 |
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction
Results for deep sleep duration¶
The effect on deep sleep duration was not statistically signficant.
| Dep. Variable: | standardize(deep_sleep_duration) | R-squared: | 0.427 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.243 |
| Method: | Least Squares | F-statistic: | 5.566 |
| Date: | Sat, 17 Jul 2021 | Prob (F-statistic): | 0.000102 |
| Time: | 15:45:22 | Log-Likelihood: | -47.888 |
| No. Observations: | 42 | AIC: | 117.8 |
| Df Residuals: | 31 | BIC: | 136.9 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.1395 | 0.150 | 0.927 | 0.354 | -0.155 | 0.434 |
| C(treatment, Treatment(reference='control'))[T.magnesium] | 0.2052 | 0.244 | 0.841 | 0.401 | -0.273 | 0.684 |
| C(day_of_week)[T.Monday] | -0.3509 | 0.311 | -1.128 | 0.259 | -0.961 | 0.259 |
| C(day_of_week)[T.Saturday] | 0.4595 | 0.396 | 1.161 | 0.245 | -0.316 | 1.235 |
| C(day_of_week)[T.Sunday] | -0.6768 | 0.273 | -2.477 | 0.013 | -1.212 | -0.141 |
| C(day_of_week)[T.Thursday] | -0.8250 | 0.416 | -1.983 | 0.047 | -1.641 | -0.010 |
| C(day_of_week)[T.Tuesday] | -0.3442 | 0.493 | -0.698 | 0.485 | -1.310 | 0.622 |
| C(day_of_week)[T.Wednesday] | 0.1425 | 0.271 | 0.527 | 0.598 | -0.388 | 0.673 |
| standardize(sleep_start_time) | -0.6352 | 0.130 | -4.889 | 0.000 | -0.890 | -0.381 |
| standardize(steps) | -0.0316 | 0.225 | -0.140 | 0.889 | -0.473 | 0.410 |
| standardize(calories) | 0.2189 | 0.229 | 0.957 | 0.339 | -0.230 | 0.668 |
| Omnibus: | 1.000 | Durbin-Watson: | 1.655 |
|---|---|---|---|
| Prob(Omnibus): | 0.606 | Jarque-Bera (JB): | 0.840 |
| Skew: | 0.335 | Prob(JB): | 0.657 |
| Kurtosis: | 2.824 | Cond. No. | 11.9 |
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction