In shirewoman2/Consultancy: Standardized tools for using R within the Simcyp Consultancy Team

A note on calculations: The geometric means and confidence intervals for each PK parameter were calculated for an unpaired study design, meaning that the subjects in the numerator simulation were not matched to the subjects in the denominator simulation. The calculations used the following steps:

1. Calculate the log-transformed geometric mean ratio as the difference of the log-transformed means. $$\text{log-transformed geometric mean ratio} = \mu_{ln(\text{numerator values})} - \mu_{ln(\text{denominator values})}$$

2. Calculate the variance of the ratio. $$\text{variance of the log-transformed ratio} = \frac{Var(ln(\text{numerator values}))}{N_{\text{numerator values}}} +$$ $$\frac{Var(ln(\text{denominator values}))}{N_{\text{denominator values}}} $$ where N is the number of observations in that simulation and variance (Var) is calculated as $$Var(X) = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2 $$

3. Calculate the standard deviation of the difference. $$\text{standard deviation of the difference} = \sqrt{\text{variance of the log-transformed ratio from step 2}}$$

CriticalVal <- ifelse(distribution_type == "Z", 
                      round(qnorm(1-(1-conf_int)/2), 3), 
                      round(qt(p = 1-(1-conf_int)/2, 
                         df = (99)), 3))

1. Calculate the critical value for a significance level of r conf_int * 100% (α = r 1 - conf_int). For a r distribution_type distribution where there are 100 observations in both simulations (e.g., 10 trials of 10 subjects), this is $$t_{1 - \frac{\alpha}{2}} = r CriticalVal$$ NB: The Simcyp Simulator uses a t distribution when calculating geometric confidence intervals.

2. Calculate the log-transformed confidence level. $$\text{log-transformed r conf_int * 100% CI} = (\mu_\text{numerator} - \mu_\text{denominator}) \pm$$ $$t_{1 - \frac{\sigma}{2}} \times \text{standard deviation of the difference}$$

3. Return the values to normal (not log-transformed) space by taking the exponential. $$ \text{r conf_int * 100% CI} = e^{\text{log-transformed r conf_int * 100% CI}}$$

Note that this order changes if the subjects are paired. In that scenario, the order of operations is to first calculate the ratios and then calculate any statistics on that set of ratios.

To summarize: For paired data, calculate the mean of ratios. For unpaired data, calculate the ratio of means.

shirewoman2/Consultancy documentation built on Feb. 18, 2025, 10 p.m.