```
library(FormulR)
#> Loading required package: dplyr
#> Warning: package 'dplyr' was built under R version 4.1.3
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
#> Loading required package: ggplot2
#>
#> Attaching package: 'FormulR'
#> The following object is masked from 'package:graphics':
#>
#> boxplot
library(dplyr) # for data manipulation
library(ggplot2) # for data visualization
```

Welcome to the Drug Formulation Analysis vignette! In this tutorial, we’ll explore how to analyze simulated data related to drug formulation using R. We’ll cover various aspects of statistical analysis, data visualization, interpretation of results, comparative analysis, and quality control tools commonly used in pharmaceutical research.

First, let’s generate some simulated data to work with. Our dataset contains information on drug release, particle size, formulation type, viscosity, stability index, storage condition, pH, and drug content over time.

```
<- data.frame(
formulation_data Time = seq(1, 100), # Assuming 100 time points
Excipient_Concentration = runif(100, min = 0, max = 1),
Drug_Release = rnorm(100, mean = 50, sd = 10),
Particle_Size = rnorm(100, mean = 100, sd = 20),
Formulation_Type = sample(c("Type A", "Type B"), 100, replace = TRUE),
Viscosity = rnorm(100, mean = 10, sd = 2),
Stability_Index = rnorm(100, mean = 95, sd = 5),
Storage_Condition = sample(c("Room", "Cold", "Warm"), 100, replace = TRUE),
pH = rnorm(100, mean = 7, sd = 0.5),
Drug_Content = rnorm(100, mean = 95, sd = 2)
)
```

Let’s start by conducting statistical analysis on our data. We’ll perform ANOVA and regression analysis to explore relationships between variables.

```
# Statistical Analysis
<- anova_analysis(formulation_data)
anova_results <- regression_analysis(formulation_data)
regression_results <- hypothesis_testing(formulation_data) hypothesis_test_results
```

Next, we’ll visualize our data using scatterplots, histograms, and boxplots to gain insights into the distribution and relationships between variables.

```
# Data Visualization
scatterplot(formulation_data, x = "Excipient_Concentration", y = "Drug_Release")
```

`histogram(formulation_data, x = "Particle_Size", bins = 20)`

`boxplot(formulation_data, x = "Formulation_Type", y = "Viscosity")`

We’ll interpret the results obtained from our analyses, including summary statistics and confidence intervals.

```
# Interpretation of Results
<- summary_statistics(formulation_data)
summary_stats <- confidence_intervals(formulation_data) confidence_intervals
```

We’ll compare means and distributions across different formulation types and storage conditions to identify any significant differences.

```
# Interpretation of Results
# Comparative Analysis
compare_means(formulation_data, group_var = "Formulation_Type", response_var = "Stability_Index")
#>
#> Welch Two Sample t-test
#>
#> data: formulation_data[[response_var]] by formulation_data[[group_var]]
#> t = 0.72569, df = 96.915, p-value = 0.4698
#> alternative hypothesis: true difference in means between group Type A and group Type B is not equal to 0
#> 95 percent confidence interval:
#> -1.249161 2.689124
#> sample estimates:
#> mean in group Type A mean in group Type B
#> 95.48371 94.76373
compare_distributions(formulation_data, group_var = "Storage_Condition", response_var = "Drug_Content")
```

Finally, we’ll use quality control tools such as control charts and batch variability analysis to monitor and assess the consistency and quality of our formulations.

```
# Quality Control Tools
control_chart(formulation_data, parameter = "pH")
```

```
batch_variability(formulation_data, parameter = "Drug_Content")
#> [1] "Batch-to-batch variability in Drug_Content : 2.08288565837046"
```