What is the form of the Cox proportional hazards model?

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Multiple Choice

What is the form of the Cox proportional hazards model?

The form of the Cox proportional hazards model is semi-parametric: the baseline hazard h0(t) is left unspecified, while covariates enter through a multiplicative exp(beta'X) term. In other words, the hazard at time t for an individual with covariates X is h(t|X) = h0(t) exp(beta'X). This means the log hazard is a linear function of the predictors, so the hazard ratio between two individuals with different covariates is exp(beta'(X1 − X2)), a quantity that does not depend on time under the proportional hazards assumption. That combination—unknown baseline hazard plus a parametric, linear effect of covariates on the log-hazard—defines the Cox model. This matches the description of a semi-parametric model with an unspecified baseline hazard and covariate effects that produce hazard ratios via a linear predictor. It’s not fully parametric because it doesn’t specify h0(t), it’s not non-parametric because it models covariate effects, and it’s not logistic regression, which models odds rather than hazards.

The form of the Cox proportional hazards model is semi-parametric: the baseline hazard h0(t) is left unspecified, while covariates enter through a multiplicative exp(beta'X) term. In other words, the hazard at time t for an individual with covariates X is h(t|X) = h0(t) exp(beta'X). This means the log hazard is a linear function of the predictors, so the hazard ratio between two individuals with different covariates is exp(beta'(X1 − X2)), a quantity that does not depend on time under the proportional hazards assumption. That combination—unknown baseline hazard plus a parametric, linear effect of covariates on the log-hazard—defines the Cox model.

This matches the description of a semi-parametric model with an unspecified baseline hazard and covariate effects that produce hazard ratios via a linear predictor. It’s not fully parametric because it doesn’t specify h0(t), it’s not non-parametric because it models covariate effects, and it’s not logistic regression, which models odds rather than hazards.

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