# Putting two well-controlled trials in proportion.
# (1) Hall et al. (2016): 17 men in metabolic chambers, a high-carbohydrate baseline diet, then an
#     isocaloric ketogenic diet. Daily energy expenditure rose by about 57 kcal/day in the
#     respiratory chamber (doubly labelled water gave a larger, less certain estimate, ~151 kcal/day).
#     What would a sustained 57 kcal/day mean for body fat? Two ways to compute it:
#     static: 7,700 kcal per kg of fat, no adaptation (overstates long-run change);
#     dynamic: Hall et al. (2011): eventual weight change ~ 1 kg per ~22-24 kcal/day (100 kJ/day per kg,
#     or 10 kcal/day per lb) of sustained
#     imbalance, approached with a time constant of roughly a year (half after ~1 year).
import math
for dE, label in ((57, "chamber estimate"), (151, "doubly labelled water estimate")):
    static_1y = dE * 365 / 7700
    final = dE / 22
    tau_years = 1 / math.log(2)                     # half the eventual change after one year
    dyn_1y = final * (1 - math.exp(-1 / tau_years))
    print(f"{dE:3d} kcal/day ({label}): static rule {static_1y:.1f} kg in a year;"
          f" dynamic {dyn_1y:.1f} kg in a year, {final:.1f} kg eventually")
# (2) Liu et al. (2022, NEJM): 139 adults with obesity, 12 months, calorie restriction with
#     time-restricted eating (08:00-16:00) versus the same calorie restriction alone.
#     Reported difference in weight change: -1.8 kg (95% CI -4.0 to 0.4).
d, lo, hi = -1.8, -4.0, 0.4
se = (hi - lo) / (2 * 1.96)
z = d / se
p = 2 * (1 - 0.5 * (1 + math.erf(abs(z) / math.sqrt(2))))
print(f"Liu 2022: difference {d} kg, SE {se:.2f}, z = {z:.2f}, two-sided p ~ {p:.2f}:"
      " no clear added effect of the eating window once calories are matched")
#  57 kcal/day (chamber estimate): static rule 2.7 kg in a year; dynamic 1.3 kg in a year, 2.6 kg eventually
# 151 kcal/day (doubly labelled water estimate): static rule 7.2 kg in a year; dynamic 3.4 kg in a year, 6.9 kg eventually
# Liu 2022: difference -1.8 kg, SE 1.12, z = -1.60, two-sided p ~ 0.11: no clear added effect of the eating window once calories are matched