Hazard function h t chance of event at time t for the

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Unformatted text preview: Hazard function h (t ) = chance of event at time t for the subset of people at risk. 5 Proportional Hazards Regression Proportional hazards regression (D.R Cox, 1972) assumes that different groups have proportional hazard functions: for two groups A and B, there is a constant proportion r such that h A (t ) = r · h B (t ). Since hazards are chances, this means that the ratio of the hazard functions r= h A (t ) h B (t ) can be interpreted as a relative risk or relative rate. Proportional hazards regression assumes that the two groups have constant relative risk over time. 6 Proportional hazards regression makes several assumptions: 1. There is a baseline hazard function h 0(t ) common to all individuals in all the study groups. 2. Study group j has a hazard function h j (t ) that is a positive multiple of the baseline hazard: h j (t ) = r j h 0(t ). Each group has its own hazard ratio r j . For reference group, r = 1. 3. Explanatory variables act only on the hazard ratios (relative risks) r j . They d...
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