A data scientist is conducting a survival analysis to model customer churn for a subscription-based service. The dataset includes the tenure of each customer and a status indicator for whether they have churned or are still active (censored data). The initial analysis with a non-parametric Kaplan-Meier estimator was used to visualize the survival probability.
The next objective is to understand how covariates, such as the customer's subscription plan and monthly spending, influence the risk of churn over time. The data scientist wants to quantify the effect of these covariates but is hesitant to make a strong assumption about the specific shape of the underlying baseline hazard function.
Given these requirements, which of the following models is the most appropriate choice?
The correct answer is the Cox Proportional Hazards model. This model is a semi-parametric regression model and is ideal for this scenario because it allows for the estimation of the effects of covariates (like subscription plan and spending) on the hazard rate without making any assumptions about the shape of the baseline hazard function. This directly addresses the requirement to quantify covariate effects while avoiding strong distributional assumptions.
The Kaplan-Meier estimator is a non-parametric method used to estimate and visualize the survival function. While useful for initial analysis, it cannot incorporate multiple or continuous covariates into a regression framework to quantify their individual effects on the hazard rate.
The Weibull AFT (Accelerated Failure Time) model is a fully parametric model. It requires the assumption that survival times follow a specific distribution (the Weibull distribution). This contradicts the data scientist's goal of avoiding strong assumptions about the underlying distribution.
An ARIMA model is used for time series forecasting, which analyzes data points collected over time to predict future values (e.g., monthly sales). It is not designed for time-to-event analysis, which involves understanding the duration until an event occurs and must account for censored data and individual-level covariates.
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What makes the Cox Proportional Hazards model semi-parametric?
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How is the Kaplan-Meier estimator different from the Cox model?
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Why isn’t the Weibull AFT model suitable for this scenario?