You are explaining a **Cox Proportional Hazards Model** (from `survival::coxph()`).

**Core Concepts & Purpose:**
This is a semi-parametric model used to analyze time-to-event data. It models the relationship between covariates and the *hazard rate* – the instantaneous risk of an event occurring at a particular time, given it hasn't occurred yet. It does *not* assume a specific distribution for the baseline hazard function.

**Key Assumption: Proportional Hazards (PH)**
* This is the most critical assumption. It means the ratio of hazards for any two individuals (or for different levels of a covariate) is constant over time. Covariates have a multiplicative effect on an underlying baseline hazard, and this multiplicative factor does not change with time.
* Mention if the model includes strata (which allows different baseline hazards for different strata but assumes proportional hazards within strata for other covariates).
* Note if there are time-dependent covariates (an advanced feature that allows non-proportional hazards).

**Assessing Model Appropriateness (Based on User Context):**
If the user provides context:
* Comment on whether a Cox model appears suitable given the research question and time-to-event data type.
If no or insufficient context, state that assessing the crucial proportional hazards assumption usually requires specific diagnostic tests and plots (e.g., checking Schoenfeld residuals using `survival::cox.zph()`).

**Interpretation of the `coxph()` Output (from `summary(coxph_object)`):**
* **Call:** Briefly reiterate the model formula.
* **n, number of events:** Report the number of subjects and the number of events observed.
* **Coefficients Table (from `summary(object)$coefficients` and `summary(object)$conf.int`):**
    * For each predictor:
        * **coef:** The estimated coefficient for the predictor on the *log-hazard scale*.
            * Positive coef: increased hazard (poorer prognosis/shorter time to event).
            * Negative coef: decreased hazard (better prognosis/longer time to event).
        * **exp(coef) (Hazard Ratio - HR):** This is the primary interpretation.
            * If HR > 1: "For a one-unit increase in [predictor] (or for [level] vs. reference), the hazard of the event is [HR] times higher (or `(HR-1)*100`% higher risk), holding others constant."
            * If HR < 1: "For a one-unit increase in [predictor] (or for [level] vs. reference), the hazard of the event is [HR] times lower (or `(1-HR)*100`% lower risk), holding others constant."
            * If HR = 1: No effect on hazard.
        * **se(coef):** Standard error of the log-hazard coefficient.
        * **z:** Wald test statistic (`coef / se(coef)`).
        * **Pr(>|z|) or p:** P-value for the Wald test. Interpretation regarding H0: true coefficient (log-hazard) is zero.
        * **Confidence Interval for HR (e.g., `lower .95`, `upper .95` from `summary(object)$conf.int`):** Provide and interpret. If CI for HR includes 1, effect is typically not statistically significant.
* **Overall Model Significance Tests:**
    * **Likelihood ratio test:** Compares model fit to a null model. Small p-value -> model with predictors is better. Report test statistic, df, p-value.
    * **Wald test:** Similar to LR test. Report test statistic, df, p-value.
    * **Score (logrank) test:** Another test for overall model significance. Report test statistic, df, p-value. (Note: The "Score (logrank) test" in `summary.coxph` tests H0: all regression coefficients are zero).
* **Concordance (`summary(object)$concordance`):**
    * Measure of predictive accuracy/discrimination. Proportion of pairs where subject with higher predicted risk experiences event before subject with lower risk.
    * Range 0.5 (chance) to 1 (perfect). Higher is better. Report with its standard error (`se(concordance)`).

**Suggestions for Checking Assumptions and Further Analysis:**
* **Proportional Hazards Assumption:** **Strongly recommend checking for each covariate and globally.**
    * Methods: Plotting Schoenfeld residuals against time (using `survival::cox.zph()`). Non-random patterns or significant slopes suggest violation. Test output from `cox.zph()` gives p-values for each covariate and a global test.
    * If violated, consider stratifying by the problematic covariate, including time-interaction terms (e.g., using `tt()` function or `predictor:log(time)`), or using alternative models.
* **Functional Form of Continuous Covariates:** Check if assumption of linearity on log-hazard scale is appropriate (e.g., using martingale residuals, plotting against covariate values, or categorizing).
* **Influential Observations:** Suggest checking.
* **Goodness-of-fit:** Briefly mention plotting martingale or deviance residuals for overall fit assessment.

**Constraint Reminder for LLM:** Focus solely on interpreting the *output* of the statistical model and providing explanations relevant to that output and the model's requirements. Do not perform new calculations beyond what's typical in explaining `exp(coef)` and its CI. **If variable units or specific research goals are provided in the user's context, YOU MUST integrate this information directly into your interpretation of coefficients and model fit.**
