Hazard ratio of 0.45 seems implausibly high, especially when it's just the exact same treatment dichotomized to before/after 3pm. My money is on something other than a real circadian effect: either the result of a 'fishing expedition' in the data, or some other variable that incidentally varies by time of day. Maybe breaking randomization, leaving the drugs out for too long at room temp, etc. If you really believe this is an important and biologically plausible effect it should be a top candidate for a replication attempt.
>some other variable that incidentally varies by time of day.
glucose level? low in the morning, and cancer likes glucose (among other effects of low glucose a cancer site would probably have lower local acidity, and the high local acidity is one of the tools used by cancer to protect and spread itself) .
AM/PM glucose differences are probably going to be swamped by mundane stuff like who has a snack before treatment vs. who doesn't. Are you not supposed to eat before immunotherapy? If so, maybe (non)compliance with that requirement is what's underneath.
i'd think the local acidity (build up of lactic acid resulting from glucose over-consumption by the cancer cells) would take a bit to build back up once glucose ups after the night.