Within-subject variability for reference-scaled bioequivalence

be_within_var() estimates the within-subject standard deviations of the log-transformed endpoint separately for the reference (swR) and test (swT) formulations, the quantities that reference-scaling frameworks need. The default model_type = "anova" is an analysis of variance (ANOVA) of the replicate observations within each formulation with subject and period effects; this is the estimator used by both Method A and Method B of the EMA replicateBE reference implementation, and it works for full and partial replicate designs. model_type = "isc" is the estimator of the FDA progesterone and warfarin guidances, used by the FDA frameworks in be_assess(): each subject's difference between its two administrations of a formulation, centered within sequence, so that s2wR = sum((D - mean D within sequence)^2) / (2 * (n - m)) on n - m degrees of freedom for n subjects in m sequences. It equals the "anova" estimate for a two-sequence full replicate (TRTR/RTRT) and differs for a partial replicate (TRR/RTR/RRT), where the period effects of the reference administrations differ by sequence. model_type = "nlme" instead fits a single mixed model with treatment-specific residual variances and requires a fully replicated design; it can differ slightly from "anova".

Usage

be_within_var(
  data,
  value,
  subject,
  period,
  treatment,
  reference_value,
  model_type = c("anova", "nlme", "isc"),
  alpha = 0.1,
  sequence = NULL
)

Arguments

data

A long data.frame with one row per observation for a single endpoint (subject, period, treatment, and the endpoint value).

value

The column name of the (untransformed) endpoint value; it is log-transformed internally.

subject, period, treatment

Column names identifying the subject, period, and treatment.

reference_value

The value of treatment that is the reference.

model_type

"anova" (the default; the EMA estimator), "isc" (the FDA estimator), or "nlme" (mixed model with treatment-specific residual variances; full replicate only).

alpha

The significance level for the swT/swR ratio confidence bound (default 0.10 gives the 90% upper bound used for narrow therapeutic index drugs).

sequence

The column name of the randomization sequence, used by model_type = "isc". When NULL, a subject's sequence is its treatment-by-period pattern.

Value

An object of class be_within_var: a list with swR, swT, s2wR, s2wT, cvwr_percent, cvwt_percent, df_wR, df_wT, sw_ratio (= swT/swR), sw_ratio_ci_upper (the upper 1 - alpha confidence bound of the ratio), model_type, and alpha. swT and the ratio are NA when the test formulation is not replicated (for example a partial replicate design).

See also

be_assess()

Other Bioequivalence: be_assess(), be_compare(), be_dataset(), be_design(), be_expand_limits(), be_extract_param(), be_fit_model_single(), be_fit_models(), be_regulator(), be_table()