key: cord-0688009-fn30b453
authors: Kipourou, Dimitra-Kleio; Leyrat, Clémence; Alsheridah, Nourah; Almazeedi, Sulaiman; Al-Youha, Sarah; Jamal, Mohammad H.; Al-Haddad, Mohannad; Al-Sabah, Salman; Rachet, Bernard; Belot, Aurélien
title: Correction to: Probabilities of ICU admission and hospital discharge according to patient characteristics in the designated COVID-19 hospital of Kuwait
date: 2021-06-22
journal: BMC Public Health
DOI: 10.1186/s12889-021-11146-4
sha: 1aed6fd90edd7d5ab4a9880bbba8381edf06c1d3
doc_id: 688009
cord_uid: fn30b453

nan

S1.1 Event-specific cumulative probabilities 1 The cumulative progression over time to the event of interest is known as the causespecific cumulative probability F j (t) and it is defined as the probability of progressing to event j in the presence of other events between time 0 and t as a function of time since diagnosis

This quantity is determined by all event -specific hazards hence, the probability of 2 event j is defined as 3 F j (t) = P(T ≤ t, event = j) t 0 λ j (u)S (u)du (1) where S (t) is the overall survival, S (t) = exp − t 0 J j=1 λ j (u)du [1, 2] . 4 Non-Parametric estimation of probabilities 5 We can use the Aalen -Johansen estimator for the non -parametric estimation of the 6 event -specific cumulative probabilities as follows With this estimator we are able to compute the cumulative probability of a specific 10 event for a population or a subgroup but not for individuals.

Estimation with Flexible Regression Models (FRM) 1 Conversely, using a modelling approach we are able to predict for specific covariate combinations allowing for individual (and population) predictions. Here, we employ an FRM for the (logarithm of) the (event j)-specific hazard expressed as

where β j is a vector of regression parameters used which includes the parameters for 2 (i) the baseline hazard and (ii) the time-dependent (cause j)-specific hazard ratios, i.e. where Ω = exp ±z α s.e. log − log(F j (t, x;β)) , z α is the (1-α/2) quantile of the 1 standard normal distribution.

We could also use the 1 −F j (t, x;β) instead to avoid issues with the denominator. Fig. 3 : ICU -specific hazard ratios with confidence intervals based on the full cohort (using Cox and FRM) and separately for Kuwaiti and non -Kuwaiti population (using FRM). 

Absolute risk: methods and applications in 2 clinical management and public health

Data analysis with competing risks and intermediate states

Estimation of the adjusted 6 cause-specific cumulative probability using flexible regression models for the 7 cause-specific hazards