# Comparison of Aggregated N-of-1 Trials with Parallel and Crossover Randomized Controlled Trials Using Simulation Studies

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## Abstract

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## 1. Introduction

#### 1.1. Selection Bias, Power, & Sample Size

#### 1.2. Trial Design and Carryover Effects

#### 1.3. Data Analysis in N-of-1 Trials

## 2. Methods

- Scenario 1—Weak heterogeneity and moderate error: ${\sigma}_{\mu}=0.1$ and ${\sigma}_{\u03f5}=0.5$.
- Scenario 2—Homogeneity and moderate error: ${\sigma}_{\mu}=0$ and ${\sigma}_{\u03f5}=0.5$.
- Scenario 3—Strong heterogeneity and moderate error: ${\sigma}_{\mu}=0.5$ and ${\sigma}_{\u03f5}=0.5$.
- Scenario 4—Strong heterogeneity and large error: ${\sigma}_{\mu}=0.5$ and ${\sigma}_{\u03f5}=1$.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Simulation study for representative sample without washout effects. This figure displays the power for detecting $\tau =0.25$ for given sample sizes and the 3 different designs considered.

**Figure 2.**Simulation study for representative sample without washout effects. This figure displays the power for a fixed sample size $n$ with varying true treatment effects $\tau $ for the 3 different designs considered. The power for $\tau =0$ represents the type I error probability.

**Figure 3.**Simulation study for representative sample with a carryover effect size of 0.05 (left), 0.10 (middle) and 0.15 (right). Displays the power for detecting $\tau =0.25$ for given sample sizes and the 3 different designs considered.

**Figure 4.**Simulation study for representative sample with a washout effect size of 0.05 (left), 0.10 (middle), and 0.15 (right). Displays the power for a fixed sample size $n$ with varying true treatment effects $\tau $ for the 3 different designs considered. The power for $\tau =0$ represents the type I error probability.

**Figure 5.**Simulation study for non-representative sample of size 30. This figure displays the probability of making a false discovery (i.e., type I error) for the population as a function of misrepresentation proportions.

**Figure 6.**Simulation study for non-representative sample of size 30. This figure displays the power for the population of interest as a function of the proportion of patients sampled from this population.

**Figure 7.**Average estimated random effect differences between non-representative and representative patients. Densities are shown for scenario 1 with $p=0.5$, $n=100$, and 1000 simulations for N-of-1 and crossover designs.

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**MDPI and ACS Style**

Blackston, J.W.; Chapple, A.G.; McGree, J.M.; McDonald, S.; Nikles, J. Comparison of Aggregated N-of-1 Trials with Parallel and Crossover Randomized Controlled Trials Using Simulation Studies. *Healthcare* **2019**, *7*, 137.
https://doi.org/10.3390/healthcare7040137

**AMA Style**

Blackston JW, Chapple AG, McGree JM, McDonald S, Nikles J. Comparison of Aggregated N-of-1 Trials with Parallel and Crossover Randomized Controlled Trials Using Simulation Studies. *Healthcare*. 2019; 7(4):137.
https://doi.org/10.3390/healthcare7040137

**Chicago/Turabian Style**

Blackston, J. Walker, Andrew G. Chapple, James M. McGree, Suzanne McDonald, and Jane Nikles. 2019. "Comparison of Aggregated N-of-1 Trials with Parallel and Crossover Randomized Controlled Trials Using Simulation Studies" *Healthcare* 7, no. 4: 137.
https://doi.org/10.3390/healthcare7040137