The effect of magnesium supplementation on sleep quality: evidence from my fitbit¶
Author: Peter Richens
Date: 25 May 2021
Keywords: magnesium, sleep, magnesium supplementation, insomnia, activity trackers, fitbit
Design¶
A blinded randomised trial was conducted on 1 adult male (me). The patient's sleep episodes where randomly allocated into the magnesium or the control group and received 400 mg magnesium citrate or an over-the-counter multivitamin supplement. Sleep activity was tracked by the patient's Fitbit device.
See related studies.
Source code available at: https://github.com/peterjrichens/personal-rct.
Results¶
- Magnesium had a 0.61 standard deviation decrease on composite sleep score relative to the multivitamin treatment (p value=0.022).
- Magnesium had a 0.47 standard deviation decrease on total sleep duration relative to the multivitamin treatment (p value=0.036).
- 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 | |
|---|---|
| multivitamin | 21 |
| magnesium | 18 |
| total | 39 |
Summary statistics during pre-experiment baseline¶
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| total_sleep_duration | 31.0 | 455.096774 | 46.125448 | 351.00 | 432.50 | 461.0 | 483.50 | 538.00 |
| deep_sleep_duration | 31.0 | 74.064516 | 14.897283 | 42.00 | 62.00 | 76.0 | 82.00 | 101.00 |
| rem_sleep_duration | 31.0 | 88.645161 | 27.983982 | 36.00 | 73.50 | 88.0 | 107.00 | 140.00 |
| sleep_start_time | 31.0 | -10.241935 | 57.244777 | -150.00 | -43.25 | -16.0 | 14.50 | 132.00 |
| composite_sleep_score | 31.0 | 79.322581 | 6.640216 | 63.00 | 77.00 | 81.0 | 83.00 | 89.00 |
| steps | 31.0 | 4580.032258 | 2423.843277 | 1201.00 | 2426.00 | 3850.0 | 6294.00 | 12022.00 |
| calories | 31.0 | 2259.266129 | 192.678554 | 1835.01 | 2139.78 | 2233.0 | 2384.74 | 2739.58 |
Summary statistics during experiment period¶
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| total_sleep_duration | 39.0 | 469.333333 | 34.868424 | 403.00 | 449.500 | 462.00 | 487.5 | 555.00 |
| deep_sleep_duration | 39.0 | 74.230769 | 20.303567 | 22.00 | 62.000 | 73.00 | 87.5 | 118.00 |
| rem_sleep_duration | 39.0 | 110.666667 | 29.720924 | 45.00 | 89.000 | 112.00 | 132.5 | 178.00 |
| sleep_start_time | 39.0 | -42.435897 | 45.255732 | -120.50 | -75.000 | -47.50 | -19.5 | 99.50 |
| composite_sleep_score | 39.0 | 81.230769 | 5.193425 | 68.00 | 78.000 | 82.00 | 85.0 | 90.00 |
| steps | 39.0 | 5077.358974 | 2714.442935 | 1450.00 | 2532.500 | 5056.00 | 7160.5 | 12205.00 |
| calories | 39.0 | 2316.572308 | 254.479274 | 1884.07 | 2123.755 | 2302.92 | 2474.2 | 3283.53 |
Outcome variables over time¶
Red line shows start of experiment period.
Regression results¶
Results for composite sleep score¶
Magnesium had a 0.61 standard deviation decrease on composite sleep score relative to the multivitamin treatment (p value=0.022).
| Dep. Variable: | standardize(composite_sleep_score) | R-squared: | 0.481 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.296 |
| Method: | Least Squares | F-statistic: | 6.673 |
| Date: | Tue, 25 May 2021 | Prob (F-statistic): | 3.28e-05 |
| Time: | 10:37:19 | Log-Likelihood: | -42.544 |
| No. Observations: | 39 | AIC: | 107.1 |
| Df Residuals: | 28 | BIC: | 125.4 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.1803 | 0.556 | 0.324 | 0.746 | -0.909 | 1.270 |
| C(treatment, Treatment(reference='multivitamin'))[T.magnesium] | -0.6064 | 0.266 | -2.283 | 0.022 | -1.127 | -0.086 |
| C(day_of_week)[T.Monday] | -0.5101 | 0.557 | -0.916 | 0.360 | -1.602 | 0.582 |
| C(day_of_week)[T.Saturday] | 0.6945 | 0.875 | 0.794 | 0.427 | -1.020 | 2.409 |
| C(day_of_week)[T.Sunday] | 0.3510 | 0.711 | 0.494 | 0.621 | -1.042 | 1.744 |
| C(day_of_week)[T.Thursday] | -0.8519 | 0.655 | -1.301 | 0.193 | -2.135 | 0.431 |
| C(day_of_week)[T.Tuesday] | 1.1999 | 0.501 | 2.394 | 0.017 | 0.218 | 2.182 |
| C(day_of_week)[T.Wednesday] | -0.1440 | 0.696 | -0.207 | 0.836 | -1.508 | 1.220 |
| standardize(sleep_start_time) | -0.0616 | 0.265 | -0.232 | 0.816 | -0.582 | 0.458 |
| standardize(steps) | 0.2548 | 0.206 | 1.234 | 0.217 | -0.150 | 0.659 |
| standardize(calories) | -0.2180 | 0.223 | -0.976 | 0.329 | -0.656 | 0.220 |
| Omnibus: | 1.416 | Durbin-Watson: | 1.808 |
|---|---|---|---|
| Prob(Omnibus): | 0.493 | Jarque-Bera (JB): | 1.223 |
| Skew: | -0.259 | Prob(JB): | 0.543 |
| Kurtosis: | 2.304 | Cond. No. | 13.8 |
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 0.47 standard deviation decrease on total sleep duration relative to the multivitamin treatment (p value=0.036).
| Dep. Variable: | standardize(total_sleep_duration) | R-squared: | 0.240 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | -0.032 |
| Method: | Least Squares | F-statistic: | 3.403 |
| Date: | Tue, 25 May 2021 | Prob (F-statistic): | 0.00508 |
| Time: | 10:37:19 | Log-Likelihood: | -49.997 |
| No. Observations: | 39 | AIC: | 122.0 |
| Df Residuals: | 28 | BIC: | 140.3 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.3586 | 0.255 | 1.406 | 0.160 | -0.141 | 0.859 |
| C(treatment, Treatment(reference='multivitamin'))[T.magnesium] | -0.4653 | 0.222 | -2.093 | 0.036 | -0.901 | -0.030 |
| C(day_of_week)[T.Monday] | -0.3340 | 0.504 | -0.662 | 0.508 | -1.322 | 0.654 |
| C(day_of_week)[T.Saturday] | -0.0439 | 0.577 | -0.076 | 0.939 | -1.175 | 1.087 |
| C(day_of_week)[T.Sunday] | -0.0802 | 0.428 | -0.187 | 0.852 | -0.920 | 0.760 |
| C(day_of_week)[T.Thursday] | -0.5838 | 0.638 | -0.916 | 0.360 | -1.833 | 0.666 |
| C(day_of_week)[T.Tuesday] | 0.3578 | 0.498 | 0.719 | 0.472 | -0.618 | 1.334 |
| C(day_of_week)[T.Wednesday] | -0.3098 | 0.385 | -0.804 | 0.421 | -1.065 | 0.445 |
| standardize(sleep_start_time) | -0.4793 | 0.185 | -2.586 | 0.010 | -0.843 | -0.116 |
| standardize(steps) | -0.0132 | 0.209 | -0.063 | 0.949 | -0.422 | 0.396 |
| standardize(calories) | 0.1083 | 0.223 | 0.487 | 0.626 | -0.328 | 0.544 |
| Omnibus: | 3.535 | Durbin-Watson: | 1.336 |
|---|---|---|---|
| Prob(Omnibus): | 0.171 | Jarque-Bera (JB): | 2.364 |
| Skew: | 0.558 | Prob(JB): | 0.307 |
| Kurtosis: | 3.459 | Cond. No. | 13.8 |
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: | 0.402 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.189 |
| Method: | Least Squares | F-statistic: | 7.091 |
| Date: | Tue, 25 May 2021 | Prob (F-statistic): | 1.91e-05 |
| Time: | 10:37:19 | Log-Likelihood: | -45.301 |
| No. Observations: | 39 | AIC: | 112.6 |
| Df Residuals: | 28 | BIC: | 130.9 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 0.1771 | 0.236 | 0.751 | 0.452 | -0.285 | 0.639 |
| C(treatment, Treatment(reference='multivitamin'))[T.magnesium] | -0.1963 | 0.330 | -0.595 | 0.552 | -0.843 | 0.450 |
| C(day_of_week)[T.Monday] | -1.0741 | 0.397 | -2.708 | 0.007 | -1.852 | -0.297 |
| C(day_of_week)[T.Saturday] | 0.7146 | 0.563 | 1.269 | 0.204 | -0.389 | 1.818 |
| C(day_of_week)[T.Sunday] | -0.2669 | 0.554 | -0.481 | 0.630 | -1.353 | 0.820 |
| C(day_of_week)[T.Thursday] | -0.7682 | 0.394 | -1.950 | 0.051 | -1.541 | 0.004 |
| C(day_of_week)[T.Tuesday] | 0.3933 | 0.304 | 1.293 | 0.196 | -0.203 | 0.989 |
| C(day_of_week)[T.Wednesday] | 0.6695 | 0.504 | 1.329 | 0.184 | -0.318 | 1.657 |
| standardize(sleep_start_time) | -0.3539 | 0.222 | -1.597 | 0.110 | -0.788 | 0.080 |
| standardize(steps) | -0.2730 | 0.148 | -1.841 | 0.066 | -0.564 | 0.018 |
| standardize(calories) | 0.3231 | 0.267 | 1.212 | 0.225 | -0.199 | 0.845 |
| Omnibus: | 3.822 | Durbin-Watson: | 2.050 |
|---|---|---|---|
| Prob(Omnibus): | 0.148 | Jarque-Bera (JB): | 3.373 |
| Skew: | -0.118 | Prob(JB): | 0.185 |
| Kurtosis: | 4.421 | Cond. No. | 13.8 |
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: | 0.256 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | -0.009 |
| Method: | Least Squares | F-statistic: | 3.182 |
| Date: | Tue, 25 May 2021 | Prob (F-statistic): | 0.00758 |
| Time: | 10:37:19 | Log-Likelihood: | -49.561 |
| No. Observations: | 39 | AIC: | 121.1 |
| Df Residuals: | 28 | BIC: | 139.4 |
| Df Model: | 10 | ||
| Covariance Type: | HAC |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | -0.3950 | 0.539 | -0.733 | 0.463 | -1.451 | 0.661 |
| C(treatment, Treatment(reference='multivitamin'))[T.magnesium] | 0.0187 | 0.272 | 0.069 | 0.945 | -0.514 | 0.552 |
| C(day_of_week)[T.Monday] | -0.0551 | 0.613 | -0.090 | 0.928 | -1.257 | 1.147 |
| C(day_of_week)[T.Saturday] | 0.4400 | 0.913 | 0.482 | 0.630 | -1.349 | 2.229 |
| C(day_of_week)[T.Sunday] | -0.0659 | 0.638 | -0.103 | 0.918 | -1.317 | 1.185 |
| C(day_of_week)[T.Thursday] | 0.4252 | 0.652 | 0.653 | 0.514 | -0.852 | 1.702 |
| C(day_of_week)[T.Tuesday] | 1.1436 | 0.589 | 1.942 | 0.052 | -0.011 | 2.298 |
| C(day_of_week)[T.Wednesday] | 0.8362 | 0.623 | 1.343 | 0.179 | -0.384 | 2.057 |
| standardize(sleep_start_time) | 0.1290 | 0.278 | 0.464 | 0.642 | -0.416 | 0.674 |
| standardize(steps) | -0.0071 | 0.215 | -0.033 | 0.974 | -0.428 | 0.414 |
| standardize(calories) | 0.1472 | 0.252 | 0.584 | 0.559 | -0.347 | 0.641 |
| Omnibus: | 2.128 | Durbin-Watson: | 1.521 |
|---|---|---|---|
| Prob(Omnibus): | 0.345 | Jarque-Bera (JB): | 1.171 |
| Skew: | 0.372 | Prob(JB): | 0.557 |
| Kurtosis: | 3.408 | Cond. No. | 13.8 |
Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction