################################################################################
# TABLE     : t_dose_proportionality_ss  (MAD - Multiple Ascending Dose)
# TITLE     : Assessment of Dose Proportionality of Steady-State PK Exposure
#             (Power Model): Slope (beta) and 90% Confidence Interval
# POPULATION: PK Parameter Population (PKFL == "Y")
# INPUT     : ADPP (PARAMCD = CMAXSS, AUCTAU, CAVGSS at Day N / steady state) +
#             numeric assigned dose (TRT01AN, matching the SAS twin)
# NOTE      : PSEUDOCODE. THIS is a file that differs by design (MAD). Dose
#             proportionality assessed AT STEADY STATE (Day N), so the parameters
#             are the steady-state exposures Cmax,ss (CMAXSS) and AUC over tau
#             (AUCTAU) -- NOT the Day 1 single-dose AUClast/AUCinf.
#
#             Power model on the LOG scale: log(parameter) ~ log(dose), so
#             parameter = a * dose^beta. beta = slope. Dose proportionality is
#             concluded when the 90% CI for beta lies entirely inside the
#             critical region [betaL, betaH], with
#                 r      = max(dose) / min(dose)               (dose range ratio)
#                 betaL  = 1 + log(0.80) / log(r)
#                 betaH  = 1 + log(1.25) / log(r)
#             MAD = parallel cohorts, repeated dosing: each participant contributes
#             ONE steady-state exposure at ONE maintenance dose level. Placebo
#             (dose 0) excluded from the log-log model. Active drug only;
#             geometric scale throughout. Accumulation / steady-state attainment
#             are in t_accumulation.R.
################################################################################
source("../00_setup_helpers.R")
env <- setup(study = "CP-101", adam = "/data/adam", out = "/data/tfl")
dv  <- design_vars("MAD")                       # cohorts = ascending dose levels (TRT01A)

## --- assigned maintenance dose per participant, active arms only ---------------
## Use the numeric assigned dose TRT01AN (same source as the SAS twin) so the
## dose-range ratio r = max/min dose is identical across languages. MAD repeats
## the same daily maintenance dose. Exclude placebo (dose 0) from the model.
dose_lk <- adam$adpp %>%
  filter(PKFL == "Y", !is.na(TRT01AN), TRT01AN > 0) %>%
  distinct(USUBJID, dose = TRT01AN) %>%                    # numeric assigned dose (mg)
  filter(is.finite(dose), dose > 0)

## --- STEADY-STATE exposures at Day N: Cmax,ss, AUCtau and Cavg,ss ----------
pp <- adam$adpp %>%
  filter(PKFL == "Y", PARAMCD %in% c("CMAXSS","AUCTAU","CAVGSS"), AVAL > 0) %>%
  inner_join(dose_lk, by = "USUBJID") %>%                  # active-arm participants w/ dose > 0
  mutate(lnval  = log(AVAL),
         lndose = log(dose))

## --- critical region for beta from the dose-range ratio r = max/min dose ----
r     <- max(dose_lk$dose) / min(dose_lk$dose)
betaL <- 1 + log(0.80) / log(r)
betaH <- 1 + log(1.25) / log(r)

## --- power-model fit per parameter: log(param) ~ log(dose), 90% CI on slope -
dp_one <- function(param) {
  d <- pp %>% filter(PARAMCD == param)
  ## ordinary least squares on the log-log scale; slope = beta (the power exponent)
  m  <- lm(lnval ~ lndose, data = d)
  ci <- confint(m, "lndose", level = 0.90)                # 90% CI for beta
  est <- coef(m)[["lndose"]]
  lo  <- ci[1, 1]; hi <- ci[1, 2]
  tibble(
    param     = param,
    n         = nrow(d),
    n_dose    = dplyr::n_distinct(d$dose),
    beta      = sprintf("%.3f", est),
    ci        = sprintf("%.3f - %.3f", lo, hi),
    ## proportional when the WHOLE 90% CI sits inside [betaL, betaH]
    conclude  = if_else(lo >= betaL & hi <= betaH,
                        "Dose proportional", "Not concluded"),
    ## also report the exposure ratio implied by the slope across the dose range
    exp_ratio = sprintf("%.2f", r^est))
}

dp <- map_dfr(c("CMAXSS","AUCTAU","CAVGSS"), dp_one)

ttl <- tfl_titles(num = "14.4.5.2", type = "Table",
   text = "Assessment of Steady-State Dose Proportionality (Power Model): Slope and 90% CI",
   pop  = "Pharmacokinetic Parameter Population",
   foot = paste(
     "Steady-state exposures at Day N: Cmax,ss (CMAXSS), AUCtau (AUCTAU) and Cavg,ss (CAVGSS).",
     sprintf("Power model ln(parameter) ~ ln(dose); slope = beta. Dose range ratio r = %.2f.", r),
     sprintf("Critical region for beta = [%.3f, %.3f]  (betaL = 1+ln(0.80)/ln(r), betaH = 1+ln(1.25)/ln(r)).",
             betaL, betaH),
     "Dose proportionality concluded when the entire 90% CI for beta lies within the critical region.",
     "Active arms only; placebo (dose 0) excluded. One steady-state value per participant;",
     "accumulation / steady-state attainment in t_accumulation.R."))

## --- assemble: parameters as rows ------------------------------------------
tab <- dp %>% transmute(
  `Steady-State Parameter`        = recode(param, CMAXSS = "Cmax,ss", AUCTAU = "AUCtau,ss", CAVGSS = "Cavg,ss"),
  `n`                             = as.character(n),
  `# Dose Levels`                 = as.character(n_dose),
  `Slope (beta)`                  = beta,
  `90% CI (beta)`                 = ci,
  `Critical Region`               = sprintf("%.3f - %.3f", betaL, betaH),
  `Conclusion`                    = conclude,
  `Exposure Ratio (max/min dose)` = exp_ratio)

print(tab)