[Adam Mitchell]

Ok, I was actually considering it from a stata perspective as having never ran an analysis like this coded this way. But I can make my decision to adjust how I see fit now I have the added information on potential confounders. I am not sure if it is something you often do but I have to thank you very sincerely for the amount of help and detail you have gone into on your responses to this topic. It has been very educational and practically helpful to run an analysis like this in stata.

[Adam Mitchell]

This is a linear probability model. It suggests that a within-patient change of 1 unit in the y_FGF23 variable is associated with a 0.05 (i.e. 5 percentage points) increase in probability of diabetes, 95% CI 0 to 0.1 (i.e. 0 to 10 percentage points). (Rounding to 2 decimal places.)

Dear Clyde, just returning back to this model above your quote here, do we not also consider the time 5 and 10 in this model and if so, how is that interpreted from such a model?

[Clyde Schechter]

No. The model does not include any interaction between y_FGF23, and it is a linear model. So the effect of y_FGF23 is the same regardless of time. If that is not appropriate for the real-world process you are trying to model, then you have to change the model to include an interaction between y_FGF23 and the time variable(s).

[Adam Mitchell]

You not only attempted to run it, you ran it successfully. If I am correct in believing that the *_BL variables represent baseline values, those are omitted from within-person models because they do not change within-person and therefore carry no information for the value of y. If you think that the *_BL variables might have important effects on the y:x relationship (your earlier models explicitly preclude that possibility, but perhaps you did not intend that), then that must be modeled by interacting them with x. If you're going in this direction, you might want to also interact x with the time variables, since the time span over which x changes might well affect the y:x relationship. If you want to go that route, the code looks like this:

mi estimate: xtreg y c.x#(c.education_level_bl c.bmi_BL i.smoke_status_BL i.time) i.time, i(Patient_ID) fe

When you run this, the "main" terms for the *_BL variables will still drop, but the interactions will be retained, which is what you want. The time variables will not drop, and the interactions with x will be added.

I have assumed in the above code that education_level_bl and bmi_BL are continuous variables, but smoke_status_BL is discrete. If that is not the case, change the c and i. prefixes accordingly. It's important to get that right.

If that's not the direction you are going, we can just interpret the results you have. First we notice that the passage of time is, itself, associated with changing values of y. All else equal, y increases by about 0.58 between years 0 and 5, and by about 0.86 between years 0 and 10. On top of that, if we look at people who start at x = 0 and go to x = 1 sometime later, the mean difference in y between those time periods will be about another 0.5.

Ok, is that because of the binary outcome now? As in the previous model as quoted above, we used both continuous exposure and outcome and we did interpret the time 5 and 10 estimates...

[Clyde Schechter]

This thread has gotten long, and has evolved over an extensive period of time. So it is becoming a bit confusing. I thought your question was in reference to this model, found in #27:

mi estimate: xtreg x_FS y_FGF23 bmi_change vitD_change i.education_level_bl i.smoke_change i.time, i(Patient_ID) fe

Apparently you are thinking about a different model from an earlier post in the thread. In that model, you do have an interaction between y_FGF23 and the time variable, so the interpretation of the coefficient of y_FGF23 would be that it is the marginal effect of y_FGF23 on x_FS conditional on time = the base category of the time variable (which, if memory serves, is time = 0). In a model like this there is no such thing as "the effect of y_FGF23 on x_FS." Rather there is a separate effect at each time. The effects at the other times can be calculated with -lincom-, but quicker and less error prone is to use the margins command:

margins time, dydx(y_FGF23)

[Adam Mitchell]

Yes my apologies for using different terms I will try to be specific. What I was referring to was a simpler model #17 where we ran the following code
[/CODE]mi estimate: xtreg y x education_level_bl bmi_BL smoke_status_BL i.time, i(Patient_ID) fe[CODE]

Here y and x were both continuous measures with y being a protein biomarker value and x being a frailty score ranging from 0 to 1.

from this analysis the interpretation was stated as

All else equal, y increases by about 0.58 between years 0 and 5, and by about 0.86 between years 0 and 10. On top of that, if we look at people who start at x = 0 and go to x = 1 sometime later, the mean difference in y between those time periods will be about another 0.5."

When we say all else equal, is this referring to x also? Or how do we report the association between x and y over that 5 or 10 year period?

Following on this I tried a separate model where now y was a binary outcome and x continuous which was #27 .

mi estimate: xtreg x_FS y_FGF23 bmi_change vitD_change i.education_level_bl i.smoke_change i.time, i(Patient_ID) fe

the interpretation from these results was

This is a linear probability model. It suggests that a within-patient change of 1 unit in the y_FGF23 variable is associated with a 0.05 (i.e. 5 percentage points) increase in probability of diabetes, 95% CI 0 to 0.1 (i.e. 0 to 10 percentage points). (Rounding to 2 decimal places.)

If we look at the results in #27 we do not interpret the results of time 5 and 10. Is this correct, if not how is it reported?

I want to try and keep it simple without the interaction terms for this.

[Clyde Schechter]

If we look at the results in #27 we do not interpret the results of time 5 and 10. Is this correct, if not how is it reported?

The model in #27 does not contain an interaction term. Consequently, the interpretation of the coefficient of y_FGF23 is entirely unrelated to the interpretation of the time effects. You can interpret each of those without regard to the other. And their effects are additive. That is, if between times 0 and 5, say, y_FGF23 changes, then the associated expected change in the outcome probability is the sum of the y_FGF23 effect and the effect of the change in time from 0 to 5.

[Adam Mitchell]

But in #17 and #18 we did interpret the time effect direct from the result table.

All else equal, y increases by about 0.58 between years 0 and 5, and by about 0.86 between years 0 and 10. On top of that, if we look at people who start at x = 0 and go to x = 1 sometime later, the mean difference in y between those time periods will be about another 0.5

All that changed between the models #17 and #27 was the continuous outcome to to the binary outcome, so I am just confused on exactly what I should be reporting from these models and what is the correct interpretation of the results from the statistical perspective.

[Clyde Schechter]

What I was trying to say in #37 is that the interpretation of this model should be done in the same way as in #17 and #18. You can see the effect of the passage of time by itself in the coefficients of the time variables. You can see the effect of change in y_FGF23 from its coefficients. To see the net effect of both things happening, you just add those. That's what was done in #17, and that's what you should do with this. The change to a dichotomous outcome doesn't make any difference here because you used a linear probability model.

[Adam Mitchell]

Ok, but when we talk about the effect of change in time say from 0 - 5 years, and y increases by 0.58, we make no reference to any change in x here. It is purely just the effect of time?

[Clyde Schechter]

we make no reference to any change in x here. It is purely just the effect of time?

Yes, that is correct for this model. This is the expected difference in outcome probability due just to the passage of time from 0 to 5 years, in the absence of changes in anything else.

[Adam Mitchell]

But is that conditional atall on x as it was in the regression model? Or can we only discuss the role of x away from specific time. We can only report the the change in x from 0 to 1 and the estimate of the outcome?

[Clyde Schechter]

But is that conditional atall on x as it was in the regression model?

The model in #17 contains no interaction terms. Consequently, the effect of time is not at all conditional on x, and the effect of x is not conditional on time. They are two separate effects that occur independently of one another, and when both occur together, the net effect is the sum of the separate effects.

We can only report the the change in x from 0 to 1 and the estimate of the outcome?

This sentence is slightly incoherent and introduces a different matter, which is about the outcome. The change in the outcome associated with x changing from 0 to 1 has nothing to do with time: it is the same at all times. However, the level of the outcome is a different thing altogether, and it depends on both x and time. So I'm not sure what you're referring to in this sentence. The only really useful way to get the levels of the outcome for given values of x and time is with the margins command. Actually, I would probably get all combinations of all time levels with x = 0 and with x = 1:

margins time, at(x = (0 1))

[Adam Mitchell]

Ah I see, yes you suggested the use of the margins command previously which I think was perfect to show the outcome at certain levels of x at 5 or 10 year follow up.

I think what I was trying to articulate was that I am fundamentally trying to asses protein biomarker (Y) change over time relative to changes in frailty (x) using some form of longitudinal mixed model approach, and I think I have gotten a little confused with the different estimates gathered from the different methods.

[Clyde Schechter]

Longitudinal data analysis has a lot of moving parts, and it's very easy to get confused. If you continue to do this kind of thing long enough, it will eventually become second nature. But there's a pretty steep learning curve at the beginning.