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Let T i = min(T i*, C i*) be the observed time and let δ i = I T i* ⩽ C i*) be an indicator for uncensored observation.
Let X i denote the baseline predictors for ith subject and T i = minimum(D i, U i ) be the observed time, where D i was the time to POAG and U i represented the censoring time independent of D i. Let Δ i be the corresponding event indicator, with Δ i = 1 if POAG is observed and Δ i = 0 otherwise.
Let Ti = min(Zi,Ci) be the observed time, where Zi is the time to event (development of disease) and Ci the right censoring time, δi the censoring indicator (δi = 1 if Ti = Zi and δi = 0 if Ti = Ci) and Xi the biomarker value for subject i. Independence completely at random between Z and C is assumed as in the classical framework of survival analysis.
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We then observe z i = min(t i,c i ), where t i is the observed time to the event and c i is the observed right-censored, for i=1,…,m.
which t n and t n−1 (t n >t n−1) are the observed time.
where Δt k = Δt(k) is the observed time between the ED wake-up and the reception of k th beacon message.
In the physical models, we can express the physical propagation from transmit array and receive array by using the double-directional impulse response, h t,τ,θ t,ϕ t,θ r,ϕ r ), where t is the observed time, τ is the delay, and (θ t,ϕ t ) and (θ r,ϕ r ) are the (elevation,azimuth) angles of departure and arrival, respectively [20].
Let s t be the observed normalized time for time point t.
A second limitation that has to be mentioned is that the observed time effect found in healthy volunteers will need to be confirmed in ICU patients before assuming that the time effect would lead to equivalent results in this population.
One potential explanation is that the observed time is not long enough to allow calendar factors to emerge.
Let the random variables X and C be the failure and censoring times, and T = min X, C) be the observed follow-up time.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com