Table 1 Interpretation of probabilities estimated from each multi-state structure

Single-event survival analysis of time to antidepressant medication initiation (Fig. 1A)

What is the probability of ever been prescribed medication in the hypothetical situation that the individual cannot die due to any causes?

Competing risks for time to medication initiation with death as a competing event (Fig. 1B)

What is the probability of ever been prescribed medication up to time \(t\) after the start of the follow-up, accounting for the fact that individuals may die?

3-state Illness-Death model adding a transition from medication initiation to death (Fig. 1C)

What is the probability of ever been prescribed medication and still be alive up to time \(t\) after the start of the follow-up?

4-state unidirectional multi-state model with a medication discontinuation state (Fig. 1D)

What is the probability of being in the 1^st medication cycle since start of follow up/ since entering the 1^st medication cycle?

4-state Bidirectional multi-state structure with medication discontinuation state (Fig. 1E)

What is the probability of being in a medication cycle (or in a medication discontinuation period) since the start of follow-up or given entering one?

Recurrent events multi-state structure (with or w/o restrictions)

(Fig. 1F and G)

• What is the total probability of being in a medication cycle since the start of follow-up or given entering the 1^st, 2^nd, 3^rd one?

• What is probability of being in the current medication cycle given entering the 1^st, 2^nd, 3^rd medication cycle or the 1^st, 2^nd, 3^rd discontinuation period?