Survival analysis
Message/Author
 gibbon lab posted on Tuesday, December 14, 2010 - 6:16 am
In a path analysis, can one of the paths be a survival analysis, e.g. cox regression?
 Bengt O. Muthen posted on Tuesday, December 14, 2010 - 8:51 am
Yes.
 gibbon lab posted on Tuesday, December 14, 2010 - 9:46 am
I am using mplus 3.0. It seems that this version is not able to perform survival analysis. Should I upgrade to a newer version of mplus?
 Linda K. Muthen posted on Tuesday, December 14, 2010 - 12:25 pm
If you want to do a Cox regression, you would need to do that.
 gibbon lab posted on Thursday, March 08, 2012 - 2:07 pm
Dear Professors,

I have upgraded to 6.12 and have another question. Let s be a continuous survival time, can s be a mediator if it is modeled with Cox model? Or can it be correlated with other variables using "with" statement? Thanks.
 Linda K. Muthen posted on Monday, March 12, 2012 - 5:54 pm
It can be used as a mediator but an indirect effect cannot be computed for it.

Yes, it can be correlated with another variable but not using the WITH option. You would do it as

f BY survival@1 z;
f@1;
[f@0];

 Richard E. Zinbarg posted on Friday, September 28, 2012 - 10:57 am
I just got a result from a discrete-time survival analysis that puzzles me. There are two predictors in the survival analysis that are latent variables that have been constrained to be orthogonal (and the Teach 4 output confirms their orthogonality). Each of the two predictors has a significant association with the hazard function when the other is not in the model. But the regression coefficients of each are smaller and non-significant when both are included in the model. I expected that as the two predictors were constrained to be orthogonal that the unique effects would have to have been at least as large as the zero-order effects. Thus, my pattern of results makes no sense to me. Was my expectation incorrect? Thanks!
 Linda K. Muthen posted on Sunday, September 30, 2012 - 10:38 am
You are correct in your expectations. What you see points to the model possbly being misspecified in terms of the marginal distribution of the two exogenous factors.
 Richard E. Zinbarg posted on Sunday, September 30, 2012 - 12:08 pm
Thanks very much for the speedy reply Linda! I am not sure that I fully understand it though or know how to correct that mis-specification. I would appreciate it very much if you could elaborate a bit. Thanks!
 Bengt O. Muthen posted on Monday, October 01, 2012 - 8:34 am
The part of your model for the 2 exogenous factors may not be perfectly correct - you can do a CFA of that alone. And the covariances between those factor indicators and the survival outcomes may not be perfectly correctly represented by your model. Either of those 2 matters can throw off your expectation.
 Richard E. Zinbarg posted on Tuesday, October 30, 2012 - 7:59 pm
Thanks very much for your earlier reply Bengt! We have been checking on our model for the 2 exogenous factors and though the fit of that CFA isn't perfect, it is good (CFI = .96; RMSEA = .06; SRMR = .06).

The survival analysis doesn't give us fit indices other than the chi-square so we are not sure how well it fits. Moreover, the output doesn't include the survival outcomes in the covariance matrix so we have no idea what the covariances between the factor indicators and the survival outcomes might be (though to tell you the truth, we are not sure we would know what pattern to expect if they were perfectly represented by our model). We did try testing whether to relax the proportional hazards constraint and that didn't lead to a significant increment according to a chi-square difference test nor did it make our anomalous finding go away. Unfortunately, that is the only modification of a survival model we are familiar with. Any thoughts on how to proceed?
 Bengt O. Muthen posted on Wednesday, October 31, 2012 - 11:37 am
One thing to check is that you can look at how much chi-square improves in your CFA when you let the 2 factors correlate.
 Richard E. Zinbarg posted on Wednesday, October 31, 2012 - 3:51 pm
thanks Bengt. In the CFA, we fit a trait-state-occasion model (following Cole and Steiger). The two factors we are using as predictors in the survival analysis are the Trait factor and one of the occasion factors which are orthogonal by definition (one decomposes the state variance into a trait component and an occasion component).
 Richard E. Zinbarg posted on Friday, November 30, 2012 - 2:57 pm
Hi again,
We have a couple of new survival analysis questions.
1. In one survival analysis, we get the following warning:
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE
OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.
AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE.
THE CONDITION NUMBER IS -0.641D-01.
THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE
MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES
OR BY INCREASING THE NUMBER OF INTEGRATION POINTS OR BY USING THE MLF ESTIMATOR.

We followed the recommendation to use MLF - it did make the model estimation terminate normally but the standard error of the parameter we are most interested in changed from 1.371 using ML to 360.598 using MLF (none of the other SEs changed very much from ML to MLF). Should we trust the MLF output given this huge change in SE? We are also wondering if the results from that MLF model can be compared with other models we have run using ML or if we want to make comparisons should we rerun all of our models using MLF.

Thanks!
 Richard E. Zinbarg posted on Friday, November 30, 2012 - 2:57 pm
and here is our second question.
2. In another survival analysis, we got the following message before our output:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE
INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE
MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT
DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL.
THE FOLLOWING PARAMETERS WERE FIXED:
60

(Parameter 60 is a threshold of one of our categorical DVs in case you need to know that info.) Should we trust this output? For the parameter we are most interested in - the regression of the survival function on a particular predictor, it gave us a regression coefficent estimate that seems nonsensically large (=43.491, SE=4.075).

Thanks!
 Tihomir Asparouhov posted on Friday, November 30, 2012 - 3:44 pm
1. It sounds like the model is not identified. Huge MLF standard errors usually mean that a parameter is not identified.

2. A fixed parameter usually is not a problem, but in this case may be it is. You should look at the standardized regression value for that survival coefficient.

 Richard E. Zinbarg posted on Friday, December 14, 2012 - 12:36 pm
Thanks again for all the help thus far! A now have a general question about survival analysis. If we run one survival analysis on outcome A and a second survival analysis on outcome B, can we test whether a predictor has a significantly different association with the survival function for A than its association with the survival function for B? By running models that includes both survival functions and in one version constrain the two regression coefficients to be equal and another version allow them to be freely estimated? Or are the two survival functions on different metrics such that a comparison like this isn't valid?
 Linda K. Muthen posted on Friday, December 14, 2012 - 2:28 pm
I think they are on the same metric. Be sure to covary the two processes.
 Lewina Lee posted on Saturday, April 13, 2013 - 11:27 am
Drs. Muthen,

In Cox regression models, is it possible to have individually varying times of observations *and* test for mediation?

I am interested in modeling the hazard of mortality over age. Right now, my dataset is set up so that each observation represents the interval between 2 study visits (and has a "starting age" and "ending age" for that interval). What type of manipulation is needed to set up the dataset for doing Cox regression in M+?

Thank you,
Lewina
 Bengt O. Muthen posted on Saturday, April 13, 2013 - 3:26 pm
I don't know what you mean by individually-varying times of observation with Cox regression (continuous-time survival). The survival times naturally differ among subjects. Or do you mean that you combine Cox with a growth model?

Perhaps you are saying that your intervals between the 2 study visits differ between subjects with the survival taking place in that interval? So that subjects are studied during time intervals of different lengths?

Mediation with continuous-time survival can be modeled as described in VanderWheele (2011) in Epidemiology.
 Lewina Lee posted on Saturday, April 13, 2013 - 9:37 pm
I would like to do a Cox regression with a time-varying predictor and several time-invariant predictors. I also would like to test for mediation. How can I set up the dataset to include the time-varying predictors when there are individually-varying times of observation?

E.g., Data were collected from ID=1 at ages 50, 52, 56, 58; from ID=2 at ages 70, 74, 76. Each person has a different # of visits and different interval between visits. I would like to model risk over age (rather than time since baseline).

Thank you,
Lewina
 Tihomir Asparouhov posted on Monday, April 15, 2013 - 2:51 pm
These three papers could help

see section 3.3

also

 Hanjoe Kim posted on Thursday, January 21, 2016 - 2:54 pm
I am studying a mediation model (X -> S -> Y) with a survival variable (S) as a mediator. In my model, I am using a Cox-regression specification for X -> S and since Y is a continuous variable, I assume that X,S -> Y is like an OLS regression.

For the X -> S (a-path) interpretation, I would interpret it as the change in log(h(t)) as a one unit increase in X.

My question is how should I interpret the S -> Y path (b-path)? Since the outcome in the Cox-regression X -> S is log(h(t)), should the b-path be interpreted as the change in Y as an "e" (Euler's number, 2.73) increase in the hazard rate h(t)? I am trying to figure out the metric of the b-path.

Thanks,
Hanjoe.
 Tihomir Asparouhov posted on Thursday, January 21, 2016 - 4:32 pm
It is the observed metric. X,S -> Y is like an OLS regression where we use S directly from the data.
 Hanjoe Kim posted on Thursday, January 21, 2016 - 6:31 pm
Very interesting. Then if my S variable is in years, the b-path would be interpreted as the change in Y as a year increases, right?

Thanks,

Hanjoe.
 Tihomir Asparouhov posted on Friday, January 22, 2016 - 9:08 am
Yes