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# Conflicts: # book/library.bib
# Conflicts: # book/_macros.tex
Signed-off-by: RaphaelS1 <[email protected]>
RaphaelS1
reviewed
Feb 5, 2025
book/P1C5_eha.qmd
Outdated
| $$ {#eq-ms-prodint} | ||
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| Finally, for practical purposes, we express the instantaneous transition probabilities $p_{\ell e}(u)$ in terms of increments of the cumulative hazard using, somewhat informally, the following relationships |
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I got a bit lost here and below
RaphaelS1
reviewed
Feb 6, 2025
| The cumulative transition-specific hazards thereby follow as | ||
| <!-- --> | ||
| $$ | ||
| H_{NA,\ell e}(\tau) = \sum_{k:t_{(k)}\leq \tau} h^d_{\ell e}(t_{(k)}) = \sum_{k:t_{(k)}\leq \tau}\frac{d_{\ell e,t_{(k)}}}{n_{\ell; t_{(k)}}}, |
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Arguably you don't need the far RHS because it's just been stated in the equation above and by now readers will be very used to seeing this format (i.e., H = sum h = sum d/n)
book/P1C5_eha.qmd
Outdated
| The second event (second row) was experienced at 373 days and the subject was then censored for the third event (third row) after 414 days. | ||
| This notation is equivalent to a multi-state representation of the recurrent events process, where each event number represents a different state. | ||
| In @fig-recurrent-events, right panel, this is refered to as "Clock forward" approach. | ||
| For illustration, consider again the `prothr` data set (@tbl-ms-data-prothr), with possible transitions summarized in @fig-multi-state-prothr-states. |
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Slightly more lead-in to the example would be good. Kind of abruptly jumps at the moment
Signed-off-by: RaphaelS1 <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
Co-authored-by: Raphael Sonabend-Friend <[email protected]>
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