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In this study, measurement was done on each subject at 3 time points (0, 4 and 80 hours). Each subject was then checked for some event. The data is in following form:

Subject    Time    Value   Event
     1       0h      100     Yes
     2       0h       55     Yes
     1       4h       54      No
     2       4h      116      No
     1      80h      117     Yes

Question is whether higher (or lower) value is related to occurrence of event?

Since this is repeated measurement, it will have to be mixed regression. Since outcome is binary, logistic regression is needed.

How do I analyze above data?

Edit: To clarify the role of time: Value may be related to time. Amount/level of Value affecting Event may vary with time. Hence, lower Value may lead to event at time 0 than at later time. Hence, time affects value and value affects events. Time does not directly affect events. How can this be incorporated in analysis?

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Assuming you have enough subjects then a logistic linear mixed model should work in this scenario. Eg:

glmer(Event ~ Value + (1|Subject), data = mydata, family = binomial(link=logit))

The estimate for Value will be the association of a 1 unit change in Value with the log-odds of the probablity of the event occuring. You can exponentiate it to get the actual odds.

If time is just the index for repeated measures and isn't of interest then there is no need to include it. You might want to allow for Value to also vary accross sujects with

glmer(Event ~ Value + (Value|Subject), data = mydata, family = binomial(link=logit))
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  • $\begingroup$ What is the difference between (1|Subject) and (Value|Subject) since there is no other predictor variable? $\endgroup$
    – rnso
    Commented Aug 11, 2020 at 10:54
  • $\begingroup$ Also, time may affect value. How can that be detected? $\endgroup$
    – rnso
    Commented Aug 11, 2020 at 10:58
  • $\begingroup$ If time affects value and the proability of the event then it is a connfounder and you should include it in the model as a fixed effect. If it does not affect the event then you should exclude it. $\endgroup$
    – Robert Long
    Commented Aug 11, 2020 at 11:10
  • $\begingroup$ I have seen it being used at some places as (1|time/subject) or (1|subject/time). What is that for? $\endgroup$
    – rnso
    Commented Aug 11, 2020 at 11:26
  • $\begingroup$ That would be where time is a factor and either subjects are nested within time ((1|time/subject)) or time measurement are nested within subjects ((1|subject/time)). If time affects value - AND the event - then you could try the 2nd model, or just include time as a fixed effect. $\endgroup$
    – Robert Long
    Commented Aug 11, 2020 at 11:31

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