Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Average bioequivalence and generic price function

b(d,SE,t_crit) = (GMR_L,GMR_U)

For an ANDA, bioequivalence to the reference listed drug is shown when the 90% confidence interval for the ratio of geometric means of a pharmacokinetic measure, such as AUC or Cmax, lies within 80.00% to 125.00% after rounding. The interval is computed on the log scale and exponentiated. For economic models, the approval of generic competitors is then translated into a post-entry price.

  • 90 per cent confidence interval for the geometric mean ratio

    GMR = exp(d); GMR_L = exp(d - t_crit * SE); GMR_U = exp(d + t_crit * SE)

    The mean difference d between test and reference in natural logs of AUC or Cmax is exponentiated to give the geometric mean ratio, and the limits of the 90% interval are d plus or minus the one-sided 95% t quantile times the standard error, exponentiated. This interval corresponds to the two one-sided tests procedure at the 5% level. Average bioequivalence is concluded when the interval, expressed in per cent and rounded to two decimal places, is at least 80.00 and no more than 125.00.

  • Standard error of the log difference in a balanced two-period crossover

    SE = sqrt(2 * MSE / n)

    In a two-treatment, two-period, two-sequence crossover with n subjects split equally between sequences, the variance of the estimated mean log difference is twice the within-subject variance divided by n, where the within-subject variance is the residual mean square from the analysis of the log data. The within-subject coefficient of variation on the original scale is the square root of exp(MSE) minus 1.

  • Post-entry generic price and annual drug cost

    P_g = P_b * (1 - k); C_ann = P_b * (1 - k) * N_d

    Applies a proportional price reduction associated with a given number of generic competitors to the brand price before entry, then multiplies by the doses used in a year. This is the simplest way to reflect generic entry in a cost-effectiveness model, and it assumes immediate and complete switching at a single reduction.