The discrepancies between the results from Kaplan-Meier (KM) curves and Cox Proportional Hazards model in your study can probably be attributed to the fundamental differences in how these two methods work. You are comparing a non-parametric model with a semi-parametric one, and therefore it is not surprising at all that the results differ.
The Kaplan-Meier method is non-parametric, which means that no assumptions are made about the underlying distribution of survival times. It estimates survival curves empirically for each group separately. This means that the survival curves for patients with varied levels of Copy Number Variation (CNV) are determined independently in the context of your study. The KM approach will display a drop in the survival curve for a group only when actual events (deaths) happen in that group. The magnitude of these decreases is determined by the number of patients who are still at risk at the time. This technique is especially sensitive to the time and distribution of event occurrences within each group.
The Cox model, on the other hand, is semi-parametric. It does not specify the baseline hazard, but it is assumed that the hazard ratios between groups are proportional over time. This model causes distinct survival curves to have the same general form, with the hazard ratio remaining constant over time. The Cox model estimates the baseline hazard using information from all groups and changes it at each event time depending on the number of events and the hazard ratio-weighted number of cases still at risk.
The differences you observe might be due to several reasons:
Power and Sensitivity: Being non-parametric, the KM method might lack the power to detect differences when the sample size is small or events are few. emphasized textIn contrast, the Cox model, by pooling data and assuming proportional hazards, might be more sensitive to detect differences even with fewer events.
Distribution of Events: If the timing and distribution of events differ significantly between groups, the KM method might fail to capture the overall trend that the Cox model can detect through its assumption of proportional hazards.
Adjustment for Covariates: Cox models allow for the inclusion of other variables, potentially revealing effects not visible in KM curves. Presumably this is not the case in your situation.
Distinctive Characteristics of the Data: Every dataset possesses unique characteristics that can impact the outcomes. For instance, if your data is on the threshold of having a sufficient number of occurrences to establish a relationship with CNV, this could result in variations in significance between the two approaches.
Assumption Violations: If the assumption of proportional hazards in the Cox model is violated, it might give misleading results. It's crucial to test whether this assumption holds with your data.
In deciding which method to use for publication, I would recommend that you report both. If the proportional hazards assumption is not met, then consider a fully parametric model such as Accelerated Failure Time.
