= Solution
These are separate data, so results from the randomized trial must not be carried over. First inspect the construction of the survival response: a command creating a <survival time> object must pair follow-up in months with an event indicator, whose death/censoring coding should be checked explicitly. A censoring time is not an observed death time. Stratified product-limit fits would then summarize <Kaplan–Meier estimators> for the dose groups before adjusted regression.
If the fitted command is a <Cox proportional-hazards model> with dose, sex and age, its specification is
$$
h(t\mid G,F,A)=h_0(t)\exp(\beta_GG+\beta_FF+\beta_AA).
$$
There is no separate intercept estimate because an intercept is absorbed into the unspecified baseline hazard $h_0$. With the stated coding, $e^{\beta_G}$ compares high-dose with low-dose death hazards at equal sex and age; $e^{\beta_F}$ compares female with male hazards at equal dose and age; $e^{\beta_A}$ is the hazard multiplier for a one-year age increase. A negative treatment coefficient would correspond to a lower fitted hazard under high dose. A <hazard ratio> is not a ratio of survival probabilities, nor directly a ratio of survival times. Under this model the survivor function is $S(t\mid x)=S_0(t)^{\exp(x^T\beta)}$.
The coefficient <standard errors>, Wald ratios and exponentiated <confidence intervals> should be read together. The common large-sample interval for a coefficient's <hazard ratio> is
$$
\exp\{\widehat\beta\pm1.96\operatorname{se}(\widehat\beta)\}.
$$
Global likelihood-ratio, score and Wald tests assess the included slopes jointly; for exactly these three one-coefficient terms their reference degrees of freedom are three. They need not coincide in a small sample. The <Cox partial likelihood> uses the event risk sets; the fitted log-likelihood is not a full likelihood for an estimated baseline survival curve. The method for tied event times should be recorded.
Check the <proportional hazards> assumption using <scaled Schoenfeld residuals> and time trends; check the functional form of age, influential subjects and <independent censoring>. Dose-by-age or dose-by-sex <interaction terms> are scientifically possible but require enough information and a stated model comparison. Adjustment can alter a crude dose association, and the allocation mechanism here is not specified as randomized. \b[No coefficients, confidence limits, significance results, exact fitted calls or diagnostics for this dataset are recoverable without the output sheet.] The displayed model is an interpretation template, not a claim that it was the exact missing command.
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