typos

book/eha.qmd

@@ -105,15 +105,15 @@ Once all hazards are estimated, the all-cause survival probability and CIFs can
 Multi-state models can be considered the most general type of survival data, as other types (single-event, competing risks, recurrent events) can be viewed as special cases.
 
 A common multi-state model, the illness-death model, is illustrated in @fig-multi-state, left panel.
-Here healthy subjects can either transition to the terminal evant death (state 2) either directly (transition $0\rightarrow 1$) or after previous illness (transitions $0\rightarrow 1 \rightarrow 2$), without the possibility of back-transitions.
-This is for example appropriate for chronic diseases or terminal illnesses.
+The states are 'healthy' (State 0), with illness (State 1), or death (State 2).
+Healthy subjects can transition directly to death ($0\rightarrow 1$) or after previous illness ($0\rightarrow 1 \rightarrow 2$), without the possibility of back-transitions.
 Similar to competing risks, individual transitions are characterised by transition-specific hazards, denoted by $h_{\ell\rightarrow e}(\tau)$ or short $h_{\ell e}(\tau)$, where $\ell$ is the starting state and $e$ the end state  for a transition, $\ell, e \in \{0,\ldots,k\}$.
 Remaining in the same state (transition into the same sate $h_{\ell\ell}(\tau)$) is equivalent to being censored for any transition possible from that state.
 
-![Left: The illness-death model where subjects can transition from state healthy (0) to state diseased (1) and terminal state death (2) without back-transitions. Right: Illustration of a general multi-state model with back-transitions. Here subjects can transition from state healthy (0) to different disease progressions with (partial) recovery and terminal state death.](Figures/survival/multi-state-examples-w-transitions.png){#fig-multi-state fig-alt="Schematic illustration of different multi-state models."}
+![Left: The illness-death model where subjects can transition from states: healthy (0), with illness (1), and terminal state death (2) without back-transitions. Right: Illustration of a general multi-state model with back-transitions. Here subjects can transition from state healthy (0) to different disease progressions (1, 2) with (partial) recovery (0, 1) and terminal state death (3).](Figures/survival/multi-state-examples-w-transitions.png){#fig-multi-state fig-alt="Schematic illustration of different multi-state models."}
 
 The right panel of @fig-multi-state depicts a more general multi-state setting with back-transitions.
-One can think of transitions between a healthy state (0) to different disease progressions (1, 2) with possibilty of improvement and recovery, with possible transition to a terminal state (3).
+One can think of transitions between a healthy state (0) to different disease progressions (1, 2) with possibilty of improvement and recovery, and possible transition to a terminal state (3).
 
 When modeling such data, interest often lies in estimation of the transition hazards, but also in transition probabilities $P_{\ell e}(\zeta, \tau)$, that is the probability to transition from state $\ell$ to $e$ between time points $\zeta$ and $\tau$ or state occupation probabilities $P_e(\tau)$, the probability to occupy state $e$ at time $\tau$.
 Transition probabilities are often summarized in a matrix of transtion probabilities $\mathbf{P}(\zeta, \tau)$, where rows indicate starting states and columns indicate end states.