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I have a research question where I investigate the links between a continuous changing variable X (taken as a log of a variable) and mortality. This variable X is measured every three years and in my research question, I wanted to see if the increasing/decreasing nature of this variable (the fluctuations/changes) predict mortality.

I opted out against using the Cox Proportional Hazards Model with time-dependent covariates because of the complexities it carries and as it doesn't quite fit my research question. I want to produce a single measure of change in this variable in time for every participant (designated as sortnr below) and I tried that using the mixed models approach in R as:

model.1=lme(X~time,random=~1+time|sortnr,data=Y)

The output of the model gives me random effects for both the intercept and the variable time. Now, is it correct to consider the random effects for time variable is the individual change over time by in my dependent variable X? Or is it proper to think that the change in variable X in time is the fixed effects of time added with the random effects of time. I have also seen that there is a coef(model.1) function that gives a different set of values than the ranef and fixef function.

I am not sure how to produce this change estimate definitively and whether the approach I am attempting is viable. I am very new to mixed models analysis and still learning some of its theoretical underpinnings so I would really appreciate any help regarding this. Thank you!

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  • $\begingroup$ Since you are modeling time series data, you may wish to (1) test whether your data are stationary, and (2) if they are not, to select a good time series modeling approach to account for it. For an approachable introduction, see De Boef, S. and Keele, L. (2008). Taking time seriously. American Journal of Political Science, 52(1):184–200. $\endgroup$ – Alexis Dec 26 '17 at 17:41
  • $\begingroup$ The consequences to the validity of inference for ignoring nonstationarity in one's data can be quite severe. $\endgroup$ – Alexis Dec 26 '17 at 17:46
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The model you have fit is indeed a special case of a growth model. The random slopes will tell you about growth, or rate of change, of $X$ over time. You can lookup the code for coef.merMod to see how exactly the output is generated. Basically, it predicts the cluster-specific effects as constrained by the model statement. If you somehow extrapolated a fixed effects model, it would repeat the slope and intercept term for each cluster. Recall the cluster specific effects are calculated as the sum of predicted random and fixed effects.

However, I don't understand exactly how you will feed such output into a survival analysis without allowing for time varying covariates. In a survival analysis, you cannot "peer forward" in time and create calculated variables as baseline, time-invariant exposures. I don't see how the Cox model with time varying $X$ fails to answer your question, as you say, nor how complexity is any rationale to discredit a method.

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  • $\begingroup$ Thank you for the reply. So basically, my research question is entitled Changes is X and the relationship with mortality and the reason I wanted to produce a single estimate for the change in X, that can later be used in a Cox PH regression model is: 1) My event (mortality) is defined at the end of follow-up period in 2016 and not in during each follow-up period. $\endgroup$ – guaguncher Dec 27 '17 at 10:32
  • $\begingroup$ In tutorials about Cox PH models with time-dependent covariates for R (like this one cran.r-project.org/web/packages/survival/vignettes/timedep.pdf), I have noticed that the event is defined at each time point together with the covariates. In my case the time-dependent covariates are collected from 1965 till 1990 every three years and I want to define my followup period from 1990 till 2016. That is why I wanted to produce a measure for change for the variable X in the years between 1965 and 1990 and use this value as I believe it is more fitting to the research question. $\endgroup$ – guaguncher Dec 27 '17 at 10:35
  • $\begingroup$ I wanted to be certain that I avoid any major flow in this approach. If I define my event time in this way, would it be then wrong to use a change estimate for each person from 1965 till 1990 and then use this in a survival analysis? $\endgroup$ – guaguncher Dec 27 '17 at 10:41
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    $\begingroup$ @A.Teferra As long as nobody is censored, you can look at relative risk models, but there is some loss of power in not knowing the actual event times. If there is censoring, this is a major flaw because you did not observe a censored person for the full duration of follow-up. Your requirement that surveillance begin in 1990 also introduces possible survivor bias: what of those who died prior to then? $\endgroup$ – AdamO Dec 27 '17 at 20:15
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    $\begingroup$ @A.Teferra It is excellent that you have accounted for censoring in some way. The implication however is that you must use a model which accounts for censoring. Cox models are actually the easiest way of doing this. $\endgroup$ – AdamO Dec 28 '17 at 15:15

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