Mediation and continuous time to event PreviousNext
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 Jill McClain posted on Monday, January 28, 2008 - 10:18 am
Hi. I'm a doctoral student in nutrition epidemiology. I am relatively new to SEM, but am hoping to use it for my dissertation to test mediation of the relationship between body mass index (BMI) and Coronary Heart Disease (CHD) hazard. I have continuous time-to-event (censored) CHD data, and BMI and all potential mediators are continuous, though I have some dichotomous exogenous covariates, such as gender. I understand this is doable in Mplus, but I've seen no papers testing mediation of a continuous time to event outcome and only a few papers at all on survival analysis in SEM. But I'm more familiar with the medical literature, so I'm probably not doing a very good job of searching other literature. So my questions are: a) can someone confirm that testing mediation of censored continuous time to event is doable (in Mplus), and b) does anyone know of any papers on similar analyses? Any advice would be very much appreciated. Thanks.
 Linda K. Muthen posted on Monday, January 28, 2008 - 12:32 pm
A time-to-event variable can be used as a mediator, for example,

y ON t;
t ON x;

where t is the time-to-event variable.

The regression of t ON x is a Cox regression. In the regression of y ON t, t is treated as a continuous variable as are all covariates.

Continuous-time survival analysis is not part of SEM. It can be carried out in Mplus because Mplus is not an SEM program but a latent variable modeling program where SEM is a special case.
 Jill McClain posted on Friday, February 01, 2008 - 11:53 am
I'm afraid I confused the issue by talking about mediation of my time to event variable. What I meant was that my time to event variable (CHD) is my outcome variable, with body mass index as my exposure and mediators such as continuous systolic blood pressure and glucose. I don't need to model any latent variables, as all of my variables are observed, but I do want to use path analysis to assess mediation with one exposure, one time-to-event outcome and multiple mediators in the model at once. Is that not possible?
 Linda K. Muthen posted on Friday, February 01, 2008 - 2:25 pm
Yes, this is possible.
 Jill McClain posted on Friday, February 01, 2008 - 5:30 pm
Thanks very much. I'm glad to hear it!
 Jill McClain posted on Tuesday, February 05, 2008 - 10:49 am
I have another question on this same topic. If I run the analysis I've suggested above, will I get fit indices such as one normally gets for SEM, such as RMSEA, CFI, etc.? I'm specifically interested in comparing the fit of the same mediation model in race and gender groups (I have Whites and African Americans of both genders). I believe the CAIC and BIC would be appropriate for comparing across different populations, but will they be output with a Cox regression?

P.S. I tried to find the answer to this in the user guide rather than bothering you, but I can't find it. Sorry if I missed it. Assuming I decide to go forward with this analysis, I will acquire Mplus and learn how to use it, which will then prevent my having to ask such basic questions.
 Linda K. Muthen posted on Tuesday, February 05, 2008 - 2:00 pm
No, you will not obtain chi-square and related fit statistics. You will obtain a loglikelihood value, AIC, BIC, and sample-size adjusted BIC. For future reference, the way you could have known this is by looking at the output from the continuous-time survival examples.
 Brian Steinmeyer posted on Thursday, February 14, 2008 - 1:47 pm
Hi Linda,

We propose to test a similar type of mediation model (time-to-event outcome and single/multiple mediators).

A few follow up questions regarding the test of the mediated (indirect) effect:

1) Can Mplus compute the estimate of the indirect effect and its standard error when the outcome is a censored, event time? 2) While the test of mediation is well understood for normally distributed variables, does it make sense to use the product of coefficients (path a x path b) method to test the indirect effect, when these estimates correspond to OLS and Cox regression, respectively?

Any insight or a sense for the appropriateness of the mediation test under this setup would be greatly appreciated!

Thanks in advance,
 Linda K. Muthen posted on Thursday, February 14, 2008 - 2:28 pm
1. Mplus provides indirect effects only for continuous and categorical outcomes.
2. I do not think this would be correct.
 Brian Steinmeyer posted on Tuesday, February 19, 2008 - 8:07 am
Thanks Linda,

I appreciate your opinion.

 Kesinee posted on Tuesday, August 23, 2011 - 2:21 pm
I have a model with continuous survival time (age at diagnosis), m1, m2, m3, m4 are continuous (observed). While case is the event classified as a binary (0,1) or ordinary (0,1,2).
My code:
USEV are case x1 x2 x3 m1 m2 m3 m4 t;
survival = t ;
timecensored = case (0=not, 1=yes);
missing values all (-9);
Model: m1 m2 m3 on x1 x2 x3;
M4 on x1 x2 x3 m1 m2;
T on x1 x2 x3 m1 m2 m3 m4;

1) Is it correct for the code above? What is the estimator?
2) Can we use this model when the event is ordinary?
Thank you very much.
 Kesinee posted on Wednesday, August 24, 2011 - 7:30 am
One more question
Can Mplus 6.11 handle with late entry?

Thank yous
 Tihomir Asparouhov posted on Wednesday, August 24, 2011 - 1:45 pm
1) I would say that it all looks correct. The estimator is ML (actually MLR)
for Cox proportional hazard model.

2) If the event is ordinary 0=not diagnosed, 1= diagnosed, 2=?. You might
have to use competing risk for that or simply treat 2=diagnosed as well.

3) Late entry should generally be treated the same way unless at the time of
entry it is already diagnosed which would mean that it is left censored and
that is currently not available in Mplus 6.11
 Kesinee posted on Wednesday, August 24, 2011 - 4:57 pm
1)For the ordinal outcome; 0=no disease, 1= susceptible, 2= definite, so how to use competing risk. I’m sorry I just first use Mplus. Could you please give me some advice where I can find the example for this?
2)I use age at diagnosis as a time scale. However, we recruited participants with different age and all of them free from disease at the time of entry, in SAS or R, we can use some command to account for this different such as use (exit*entry)*disease (0). I do not know that how I can do with Mplus. Since It makes more precise than use a study time and control for age.

Thank you for your help.
 Tihomir Asparouhov posted on Thursday, August 25, 2011 - 8:43 am
1) This is not a competing risk example but a bivariate survival example See section 3.1
So you should have two survival variables in your model I think.

2) I will need the entire SAS or R program to be able to tell you what (exit*entry)*disease (0) means.
 Kesinee posted on Thursday, August 25, 2011 - 11:21 am
Thank you for your kindness.
the code from SAS,

Proc phreg data=new;
model (entry, exit)*disease(0)=x;

entry is age at entry,
exit is age when censored/event
 Tihomir Asparouhov posted on Friday, August 26, 2011 - 11:48 am
This SAS program does implement left censoring but this is not appropriate in your case because ... the "entry" variable specifies when the subject first got exposed to the "risk" (and not the age you enrolled him/her in the study), your subjects were exposed to the risk even before you enrolled them. Here is an example of how to use the SAS option correctly. This is from

"Another useful application of the counting process formulation is delayed entry of subjects into the risk set. For example, in studying the mortality of workers exposed to a carcinogen, the survival time is chosen to be the worker’s age at death by malignant neoplasm. Any worker joining the workplace at a later age than a given event failure time is not included in the corresponding risk set. The variables of a worker consist of Entry (age at which the worker entered the workplace), Age (age at death or age censored), Status (an indicator of whether the observation time is censored, with the value 0 identifying a censored time), and X1 and X2 (explanatory variables thought to be related to survival). The specification for such an application is as follows:

proc phreg;
model (Entry, Age) * Status(0) = X1 X2;

Alternatively, you can use a time-dependent variable to control the risk set, as illustrated in the following specification: "
 Kiarri Kershaw posted on Tuesday, November 29, 2011 - 3:51 am

I have a multiple mediation model with continuous survival as the outcome and dichotomous mediators. I know Mplus uses MLR estimation for Cox proportional hazards models, but is there a way I can use WLS estimation for the mediators in the path analysis? I was hoping to avoid the problem with using logistic regression for the dichotomous mediators. If not, do you have any suggestions for running this analysis? Thanks for your help!

 Linda K. Muthen posted on Tuesday, November 29, 2011 - 11:40 am
The Cox proportional hazards model requires maximum likelihood estimation. It is not clear how mediation is defined in survival.
 Luciana Quaranta posted on Friday, November 16, 2012 - 12:50 am
Dear professors,
I am a doctoral student and I´ve started to test the demo version of Mplus to see if it is the software I could purchase and use for the study I need to conduct.
I would like to do a path analysis, with continuous survival as the outcome and categorical variables (with 2 or more categories) as mediators. I have three questions:

1- Is this implementation correct (for a the test with only one mediator)?

VARIABLE: NAMES = t wc cs tc;
MODEL: t ON wc cs;
cs ON wc;

2- Can Mplus 7 handle left censoring in Cox?
3- Can direct and indirect effects be estimated in Mplus 7 for time-to-event outcomes?
Thank you very much in advance for your help!
 Linda K. Muthen posted on Friday, November 16, 2012 - 12:05 pm
1. This looks okay.
2. No.
3. I don't think this indirect effect has been defined in the literature. See the following paper on the website for related information:

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
 Samuli Helle posted on Wednesday, January 15, 2014 - 4:27 am
Just curious, what's the reason why ordinary model fit indices etc. are not provided in the case of survival analysis?
 Linda K. Muthen posted on Wednesday, January 15, 2014 - 6:08 am
When means, variances, and covariances are not sufficient statistics for model estimation, chi-square and related statistics are not available.
 S. Mason Garrison posted on Sunday, August 23, 2015 - 4:01 pm
Are there any workarounds for handling left censoring for Cox regression, using mplus 7.31?
 Tihomir Asparouhov posted on Tuesday, August 25, 2015 - 11:07 am
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