The question

In healthy adults, does a warm decoction of fresh D. officinale stem taken before bed increase slow-wave sleep, compared with a placebo matched for temperature and viscosity? And does it warm the hands and feet relative to the trunk, as the thermal route of Chapter 5 would require?

Design

Measurement choices

Three choices in the table refine the original proposal. The thermal measure is the distal–proximal gradient, which Kräuchi and colleagues found to predict sleep onset (Chapter 5); it is recorded with small button loggers taped to the skin, a method validated against conventional skin thermometry (Marken Lichtenbelt et al. 2006). Core temperature is only an exploratory secondary measure. Chapter 5’s model predicts that a drink changes it very little; a rectal probe, the accurate method, is a heavy burden for an outcome expected to be null; and a temperature pill in the stomach would read the warm drink itself, so pills must be swallowed many hours before and are still disturbed by fluid intake (Byrne and Lim 2007). Tympanic readings are taken instead, and their lower accuracy is stated in the report. Slow-wave sleep is measured by polysomnography, not by a consumer ring: rings estimate sleep stages from movement, heart rate and skin temperature, and their agreement with polysomnography for individual stages is moderate (Altini and Kinnunen 2021). Ring data can be collected as a secondary measure.

Sample size

import math
from statistics import NormalDist

N = NormalDist()

def n_crossover(sd_diff, delta, alpha=0.05, power=0.90):
    """Two-period crossover: each person drinks both cups, in random order. One primary outcome,
    two-sided alpha = 0.05."""
    za, zb = N.inv_cdf(1 - alpha / 2), N.inv_cdf(power)
    return math.ceil(((za + zb) * sd_diff / delta) ** 2 + za ** 2 / 2)

def power_at(n, sd_diff, delta, alpha=0.05):
    za = N.inv_cdf(1 - alpha / 2)
    return N.cdf(delta / sd_diff * math.sqrt(n - za ** 2 / 2) - za)

# Primary outcome: minutes of slow-wave sleep (N3) by polysomnography; smallest worthwhile gain 10 min.
for sd in (15, 20, 25):
    print(f"SD of within-person difference {sd} min: {n_crossover(sd, 10, power=0.80)} people for 80 % power, "
          f"{n_crossover(sd, 10)} for 90 %")
print(f"planned 36 completers, SD 20 min: power {100 * power_at(36, 20, 10):.0f} %")
# SD of within-person difference 15 min: 20 people for 80 % power, 26 for 90 %
# SD of within-person difference 20 min: 34 people for 80 % power, 44 for 90 %
# SD of within-person difference 25 min: 51 people for 80 % power, 68 for 90 %
# planned 36 completers, SD 20 min: power 83 %

The protocol plans for 36 completers. If the within-person SD of the difference is 20 minutes, that gives about 83 % power to detect a 10-minute gain; 90 % power would need 44. It recruits 44 to allow for drop-out after the adaptation night. The SD is an assumption to be checked in a pilot of 10 people, and if the pilot shows it to be 25 minutes or more, the sample size will be recalculated before the main trial begins.

Decision rule

SESOI = 10.0     # minutes of N3 sleep: the smallest gain worth acting on

def verdict(diff, lo, hi):
    """diff = decoction night minus placebo night in N3 minutes, with a 95 % confidence
    interval. Fixed before any data are seen."""
    if lo >= SESOI:
        v = "gain of at least 10 minutes"
    elif lo > 0:
        v = "gain; size not shown to reach 10 minutes"
    elif hi < 0:
        v = "less N3 than placebo"
    elif lo >= -SESOI and hi <= SESOI:
        v = "no difference worth acting on"
    else:
        v = "unclear"
    return f"N3 sleep {diff:+.1f} min ({lo:+.1f} to {hi:+.1f}): {v}"

# Invented results, to show how the trial will be reported.
print(verdict(4.0, -3.0, 11.0))
print(verdict(12.5, 10.5, 14.5))
print("Secondary outcomes (distal-proximal gradient, tympanic temperature, sleep latency) are")
print("reported with their intervals but cannot by themselves make the trial positive, and a")
print("positive result is not evidence that the decoction treats insomnia.")
# N3 sleep +4.0 min (-3.0 to +11.0): unclear
# N3 sleep +12.5 min (+10.5 to +14.5): gain of at least 10 minutes
# Secondary outcomes (distal-proximal gradient, tympanic temperature, sleep latency) are
# reported with their intervals but cannot by themselves make the trial positive, and a
# positive result is not evidence that the decoction treats insomnia.

The example results are invented, to show in advance how results will be reported. If N3 rises but the distal–proximal gradient does not change, the result would argue against the thermal route of Chapter 5 and for some other explanation, such as relaxation, routine or an imperfect blind; the report will say so.

What this trial cannot show

The trial compares one preparation with one placebo in healthy adults over single nights. It does not test people with insomnia, regular use over weeks, other doses or other preparations, and a positive result would not show that the decoction treats any sleep disorder. Blinding is difficult, because the decoction has a taste that the placebo can only approximate; the blinding check will show how well it worked, and the result will be reported whatever it is.

Ethics and interests

The trial requires approval from an independent ethics committee, written informed consent and registration of the protocol, with the analysis plan, before the first participant is enrolled (Chan et al. 2013; Nosek et al. 2018). Participants are paid for their time and may withdraw at any point.