index.rst

Survival Analysis

.. todo::

        Insert summary/introduction that explains the purpose of this section, how
        it relates to cause modeling, and what will be covered

• Terms and Definitions
• Survival Function
• Hazard Function
• Implications for Cause Model Transition Rates
  • Impact on YLLs and YLDs
• Open Cohorts
• Event Recurrance

Terms and Definitions

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        Add definitions and descriptions to terms

Term	Definition
Event
Time
Censor
Observation period
Closed cohort
Open cohort

Survival Function

.. todo::

        Include disclaimer that we will first discuss closed cohorts without event
        recurrance until a later section

        Include formula for survival function, interpretation, description, etc.

        Include kaplan-meier plot

Hazard Function

.. todo::

        Include formula for hazard function, interpretation, description, how it
        relates to survival function, etc.

        Include graphic of observed failure rate made up of decreasing early
        infant mortality hazard rate, constant random hazard rate, and increasing
        wear out hazard rate along with corresponding survival curves

        Include an example that contrasts population time (2016) with time
        relative to an event (years since diagnosis).

Implications for Cause Model Transition Rates

.. todo::

        Link to cause model transition rates data source page

        Briefly discuss how incidence is used as transition probability and
        assumption that it is constant over the timeframe it represents

        Discuss how this assumption is valid for constant hazard rates, with
        examples

        Discuss how this assumption is less valid for the following scenarios,
        with examples:

                Increasing hazard rates

                Decreasing hazard rates

                U-shaped and bell shaped hazard rates

                When the hazard rate varies between population timeframe and the
                individual timeframe

Impact on YLLs and YLDs

.. todo::

        Include figures that demonstrate how YLLs and YLDs can be under/
        overestimated with biased hazard rate approximation

        Include examples of how this has been/can be handled (function to increase/
        decrease incidence rate around the mean relative to time since infection?,
        etc.)

Open Cohorts

.. todo::

        Discuss how assumptions/implications will vary with open cohorts (kaplan
        meier plot no longer applies)

Event Recurrance

.. todo::

        Discuss how assumptions/implications vary with event recurrance