## N-of-1 Trials in Practice

To show you an example of this methodology in practice, I will conduct my own analysis on a selection of data collected from my Whoop strap from April 27th, 2018 to October 5th, 2019. Our research question for this N-of-1 study is:

*Does drinking alcohol lead to poor sleep?*

As an athlete and epidemiologist, I am very aware of how detrimental alcohol can be on your sleep, athletic performance and general wellbeing. I’ve constantly been told how athletes should not drink, however its one thing to be told, but another to see the evidence for yourself. Once I started wearing my Whoop I noticed how my sleep score (a metric calculated by the Whoop app) would suffer after drinking alcohol. Sometimes even a day later, I thought I could still see the effect. These observations made me want to do my own analysis, which I can finally complete now.

## Notes on the Data

The two variables of interest in our analysis is sleep performance score and alcohol consumption. Sleep performance score ranges from 0 to 100 and is a metric calculated by the Whoop app from biometric data like respiratory rate, light sleep duration, slow wave sleep duration, and REM sleep duration.

The alcohol consumption variable is the response to the question “Did you have any alcoholic drinks yesterday?” that is responded to by Whoop users on a daily basis upon waking up. I always answered these questions truthfully and consistently, although we are limited in our data in that the app does not ask questions about how much alcohol was consumed. This means that all levels of alcohol consumption are treated equally, which eliminates the opportunity to analyze the relationship on a deeper level. There was some missing data in our alcohol feature, but this missing information was imputed with ‘No’s as I know from personal experience that if I had drunk the night before I was sure to mark it in the app.

## Exploratory Data Analysis

The first step in any analysis is to do some exploratory data analysis (EDA). This is just to get a general idea of what our data looks like, and to create a visual that will help direct our investigation.

From the above box-plots, we see that average sleep score appears to be higher when no alcohol was consumed, and to have a narrower distribution. Curiously, there seems to be more outliers in sleep performance score when alcohol is not consumed. Perhaps travel days and jet-lag can account for these outliers, as I traveled overseas 5 times during this sample period.

Now that we have gotten a good first look at the data of interest, its time to dig into the statistical analysis.

## Hypothesis Testing

To answer our research question, I will be conducting hypothesis testing. Hypothesis testing is a statistical technique that allows us to make inferences about a population based on some sample data. In this case, we are attempting to infer if me drinking alcohol is associated with having poor sleep that night. We don’t have data on alcohol consumption and sleep for every night I’ve been alive, so we study our sample data as a proxy.

The first step in hypothesis testing is to formulate my hypotheses. A ‘null hypothesis’ is the assumption that nothing interesting is happening or that there is no relationship or effect. In our case the **null hypothesis** is: *There is no difference in mean sleep performance between nights in which alcohol was consumed and was not consumed.*

An ‘alternative hypothesis’ is the hypothesis that contradicts the null, and claims that in fact there is something interesting happening. In our example the **alternative hypothesis** is: *There is a difference in mean sleep performance between nights in which alcohol was consumed and was not consumed.*

## Choosing a Statistical Test

To assess which of these hypotheses is true, we have to chose a statistical test. We are curious if the average sleep score for nights in which I drank alcohol is different from the average sleep score for nights in which I did not drink alcohol, and so will be using a difference in means to test this. Specifically, our **test statistic** is: *Mean sleep performance with no alcohol — Mean sleep performance with alcohol*

Now that we have defined our framework, we can use R to calculate our test statistic and evaluate our hypotheses.

**Conducting our Analysis in R**

From our sample data we can calculate our observed test statistic. The code in R is included below.

`test_stat <- data |> `

specify(formula = sleep_performance ~ alcohol) |>

calculate(

stat = "diff in means",

order = c("No", "Yes")

)

Our test statistic is 8.01. This number means that the average sleep score for nights in which I consumed no alcohol is 8.01 points higher than nights in which I did consume alcohol.

The next step in the analysis is to generate a null distribution from our sample data. A null distribution represents all the different values of test statistic we would observe if samples were drawn repeatedly from the population. The distribution is meant to reflect the variation in the test statistic purely due to random sampling. The null distribution is created in R below:

`set.seed(42) #Setting seed for reproducibility`null_distribution <- data |>

specify(formula = sleep_performance ~ alcohol) |>

hypothesize(null = "independence") |>

generate(reps = 1000, type = "permute") |>

calculate(

stat = "diff in means",

order = c("No", "Yes")

)

What we are doing above is taking samples with replacement from our data, and calculating the difference in means from those samples. We do this 1000 times to generate a large enough distribution so that we can determine if our observed test statistic is significant.

After we have our null distribution and test statistic, we can calculate a two-sided p-value for an alpha of 0.05. The p-value can be thought of as the probability of getting a test statistic that is as extreme or more than our observed test statistic if the null hypothesis is true. Put into plain words; it represents how likely it would be to see this result if there was no true association. We calculate a two-sided p-value in R below, as we are interested in the possibility of the test statistic being greater or lesser than expected.

`p_value <- null_distribution|> `

get_p_value(test_stat, direction = "both")

Our p-value is 0.017 which means that our finding is significant at the alpha=0.05 level, which is a commonly accepted level of significance in statistics. It means that the difference in sleep score we found was significant! We have the evidence to reject the null hypothesis and accept the alternative; there *is* a difference in mean sleep performance between nights in which alcohol was consumed and was not consumed.

I’ve included a helpful visualization of the null distribution, test statistic, and 95% quantile range below. The grey bars are the many possible test statistics calculated from our 1000 samples, and the orange line represents the density of these values. The blue dashed lines represent the 97.5th and 2.5th quantiles of this distribution, beyond which our test statistic (in red) is shown to be significant.

**Final Conclusions**

Well, it turns out my coaches were right all along! Our analysis found that my average sleep score when I* did not* consume alcohol was 8.01 points higher than my average sleep score when I *did* consume alcohol. This difference was found to be statistically significant, with a p-value of 0.017, meaning that we reject the null hypothesis in favor of the alternative. This statistical result backs up my personal experience, giving me a quantitative result that I can have confidence in.

## Going Further

Now that I have this initial analysis under my belt, I can explore more associations in my data, and even use more complicated methods like forecasting and machine learning models.

This analysis is a very basic example of an N-of-1 study, and is not without limitations. My study was observational rather than experimental, and we cannot declare causality, as there are many other confounding variables not measured by my Whoop. If I wanted to find a causal relationship, I would have to carefully design a study, record data on all possible confounders, and find a way to blind myself to the treatment. N-of-1 studies are hard to do outside of a clinical setting, however we can still find meaningful associations and relationships by asking simple questions of our data.

I hope that after this tutorial you take the initiative to download your own data from whatever fitness tracker you can get your hands on, and play around with it. I know everyone can come up with a hypothesis about how some variable affects their health, but what most people don’t realize, is that you’re closer to getting a quantifiable answer to that question than you think.

## References and Further Reading

[1] Davidson, K., Cheung, K., Friel, C., & Suls, J. (2022). Introducing Data Sciences to N-of-1 Designs, Statistics, Use-Cases, the Future, and the Moniker ‘N-of-1’ Trial. Harvard Data Science Review, (Special Issue 3). https://doi.org/10.1162/99608f92.116c43fe

[2] Lillie EO, Patay B, Diamant J, Issell B, Topol EJ, Schork NJ. The n-of-1 clinical trial: the ultimate strategy for individualizing medicine? Per Med. 2011 Mar;8(2):161–173. doi: 10.2217/pme.11.7. PMID: 21695041; PMCID: PMC3118090.

[3] Daza EJ. Causal Analysis of Self-tracked Time Series Data Using a Counterfactual Framework for N-of-1 Trials. Methods Inf Med. 2018 Feb;57(1):e10-e21. doi: 10.3414/ME16–02–0044. Epub 2018 Apr 5. PMID: 29621835; PMCID: PMC6087468.

[4] Schork, N. Personalized medicine: Time for one-person trials. *Nature* **520**, 609–611 (2015). https://doi.org/10.1038/520609a

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