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Update introduction.ipynb (#28)
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occurence -> occurrence
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eltociear authored Apr 18, 2024
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6 changes: 3 additions & 3 deletions docs/notebooks/introduction.ipynb
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"$$\n",
"\\lambda (t|x_{i}) =\\lambda_{0}(t)\\theta(x_{i})\n",
"$$\n",
"The baseline hazard $\\lambda_{0}(t)$ is identical across subjects (i.e., has no dependency on $i$). The subject-specific risk of event occurence is captured through the relative hazards $\\{\\theta(x_{i})\\}_{i = 1, \\dots, N}$.\n",
"The baseline hazard $\\lambda_{0}(t)$ is identical across subjects (i.e., has no dependency on $i$). The subject-specific risk of event occurrence is captured through the relative hazards $\\{\\theta(x_{i})\\}_{i = 1, \\dots, N}$.\n",
"\n",
"We train a multi-layer perceptron (MLP) to model the subject-specific risk of event occurence, i.e., the log relative hazards $\\log\\theta(x_{i})$. Patients with lower recurrence time are assumed to have higher risk of event. "
"We train a multi-layer perceptron (MLP) to model the subject-specific risk of event occurrence, i.e., the log relative hazards $\\log\\theta(x_{i})$. Patients with lower recurrence time are assumed to have higher risk of event. "
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"\\lambda (t|x_{i}) = \\frac{\\rho(x_{i}) } {\\lambda(x_{i}) } + \\left(\\frac{t}{\\lambda(x_{i})}\\right)^{\\rho(x_{i}) - 1}\n",
"$$\n",
"\n",
"Given the hazard form, it can be shown that the event density follows a Weibull distribution parametrized by scale $\\lambda(x_{i})$ and shape $\\rho(x_{i})$. The subject-specific risk of event occurence at time $t$ is captured through the hazards $\\{\\lambda (t|x_{i})\\}_{i = 1, \\dots, N}$. We train a multi-layer perceptron (MLP) to model the subject-specific log scale, $\\log \\lambda(x_{i})$, and the log shape, $\\log\\rho(x_{i})$. "
"Given the hazard form, it can be shown that the event density follows a Weibull distribution parametrized by scale $\\lambda(x_{i})$ and shape $\\rho(x_{i})$. The subject-specific risk of event occurrence at time $t$ is captured through the hazards $\\{\\lambda (t|x_{i})\\}_{i = 1, \\dots, N}$. We train a multi-layer perceptron (MLP) to model the subject-specific log scale, $\\log \\lambda(x_{i})$, and the log shape, $\\log\\rho(x_{i})$. "
]
},
{
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