# A simple model of why the choice of standard matters in the DMAC assay.
# Assumption (a simplification): each chain gives about the same colour per
# molecule, so colour per milligram falls as the chain gets longer.
# Procyanidin A2, the BL-DMAC standard, is a dimer (DP 2).

def apparent_share(mix):
    """mix: {degree of polymerisation: share of PAC mass}. Returns the
    measured PAC mass, as a share of the true mass, read against A2."""
    return sum(share * 2 / dp for dp, share in mix.items())

mixes = {
    "mostly dimers":              {2: 0.6, 3: 0.2, 4: 0.2},
    "tetramers and pentamers":    {2: 0.1, 3: 0.1, 4: 0.4, 5: 0.4},
    "longer chains (DP 4 to 10)": {4: 0.2, 5: 0.2, 6: 0.2, 8: 0.2, 10: 0.2},
}
for name, mix in mixes.items():
    a = apparent_share(mix)
    print(f"{name:27s} reads {100 * a:3.0f} % of true mass "
          f"(true/measured = {1 / a:.1f})")
print("Feliciano et al. (2012): cranberry-PAC standard gave values 2.2 × those with A2")
# mostly dimers               reads  83 % of true mass (true/measured = 1.2)
# tetramers and pentamers     reads  53 % of true mass (true/measured = 1.9)
# longer chains (DP 4 to 10)  reads  34 % of true mass (true/measured = 3.0)
# Feliciano et al. (2012): cranberry-PAC standard gave values 2.2 × those with A2

# Relative risks from the Cochrane review (Williams et al. 2023), cranberry
# products against placebo or no treatment, symptomatic culture-verified UTI.
reviews = {
    "women with recurrent UTI": (0.74, 0.55, 0.99),
    "children":                 (0.46, 0.32, 0.68),
    "pregnant women":           (1.06, 0.75, 1.50),
}

def per_100(rr, baseline):
    """Infections per 100 people over the study period, and the number who
    would need to take cranberry for one fewer infection (if any)."""
    treated = 100 * baseline * rr
    fewer = 100 * baseline - treated
    nnt = 100 / fewer if fewer > 0 else float("inf")
    return treated, fewer, nnt

baseline = 0.30   # an assumed risk without cranberry, for illustration only
print(f"assumed risk without cranberry: {100 * baseline:.0f} in 100")
print("group                     RR (95% CI)        change per 100     NNT")
for group, (rr, lo, hi) in reviews.items():
    t, f, n = per_100(rr, baseline)
    _, f_lo, _ = per_100(hi, baseline)
    _, f_hi, _ = per_100(lo, baseline)
    nnt = f"{n:.0f}" if n != float("inf") else "none"
    print(f"{group:25s} {rr:.2f} ({lo:.2f}–{hi:.2f})  "
          f"{-f:+5.1f} ({-f_hi:+.1f} to {-f_lo:+.1f})  {nnt:>4s}")
# assumed risk without cranberry: 30 in 100
# group                     RR (95% CI)        change per 100     NNT
# women with recurrent UTI  0.74 (0.55–0.99)   -7.8 (-13.5 to -0.3)    13
# children                  0.46 (0.32–0.68)  -16.2 (-20.4 to -9.6)     6
# pregnant women            1.06 (0.75–1.50)   +1.8 (-7.5 to +15.0)  none