topic Re: Is there a method using longitudinal data to do survival analysis? in Statistical Procedures

Is there a method using longitudinal data to do survival analysis?

Season — Thu, 08 Dec 2022 14:26:04 GMT

To the best of my knowledge, current methods of doing survival analysis, including those that compares survival curves (log-rank or Wilcoxon) and Cox model, does not have the capability of analyzing variating exposures. For instance, one can divide a group of patients into those with hyperlipidemia and those without hyperlipidemia at baseline. After that, the researcher follows-up for a period of time to see if the end point (e.g. death, stroke) occurred. Next, he can plot the survival curves of the two groups via Kaplan-Meier of life table method and compare to see if there were any difference between the two survival curves by using log-rank or Wilcoxon method. He can also use the Cox model to see if hyperlipidemia at baseline was a risk factor of developing end points like death and stroke during follow-up.

It can be easily observed that not considering the change of blood lipids during follow-up is a huge defect of the methods mentioned above. It can be easily understood and verified that blood lipid levels change every day. Therefore, taking the blood lipid level of a single day into account when analyzing an event that might happen anytime during a long follow-up period (usually more than a year) is far from enough. However, to the best of my knowledge, current statistical methods analyzing longitudinal data does not have the capability of analyzing time-to-event data, especially when lost to follow-up, which is common in time-to-event data, has to be considered.

So here is my question: is there a statistical method using longitudinal data to do survival analysis? If there is, can SAS perform this? Many thanks!

Re: Is there a method using longitudinal data to do survival analysis?

StatDave — Thu, 08 Dec 2022 16:01:15 GMT

It sounds like what you have is a time-varying covariate - an explanatory variable that can change over the course of the study. This can be handled in PROC PHREG. See mention of this in the Overview section of the PHREG documentation. An example is titled "Model Using Time-Dependent Explanatory Variables" in the Examples section of the PHREG documentation.

Re: Is there a method using longitudinal data to do survival analysis?

Season — Fri, 09 Dec 2022 16:03:05 GMT

I missed a word in one sentence in the fourth paragraph. "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates" should be "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously". I missed the word "simultaneously" when I was typing.

Re: Is there a method using longitudinal data to do survival analysis?

ballardw — Fri, 09 Dec 2022 16:49:22 GMT

@Season wrote:

I missed a word in one sentence in the fourth paragraph. "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates" should be "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously". I missed the word "simultaneously" when I was typing.

As the author of a post you can edit it. Under the avatar/icon at the head of a post are three horizontal lines. If you click on them you should have "edit reply" as an option. That will bring up your original post with the message in a window where you can edit it.

Re: Is there a method using longitudinal data to do survival analysis?

Season — Sat, 10 Dec 2022 04:27:09 GMT

Thank you for the help you have offered. In a respect, yes, what I want to put in the model is a covariate that changes over time. Actually, I have used the Cox model with time-dependent variable using PROC PHREG before. After receiving your reply, I revised the theory of the model and found that it does not fully satisfy my expectation. The reasons are as follows. First, using Cox model with time-dependent covariates is not unconditional. Violation of proportional hazards assumption of the covariate(s) is a prerequisite of using the model. Were the assumption not rejected, the Cox proportional hazards model is preferred. In this case, the change of hazard ratio over time cannot be observed. Second, explanatory variables in Cox model with time-dependent covariates are "considered" only once. To make my ideas clearer, let me compare Cox models with ANOVA of longitudinal data. Let us suppose that we are dividing a sample into two groups by their age: senior citizens and youngsters. The variable I am interested in is called "X". By using ANOVA of longitudinal data, data from each and every time point can be considered, eventually reaching conclusion like "the curve of the variable X of the population where the sample was from follows a quadratic pattern", "in the second time point, the level of X is 'statistically different' between senior citizens and youngsters", "the mean of X of the entire population in the first time point is 'statistically different' from that of the entire population in the third time point". However, Cox models with time-dependent variables cannot accommodate levels of X in each and every time point. You can put the baseline level of X when in the model, you can put the level of X when the follow-up terminates in the model, you can put whether X changes a threshold during follow-up (e.g. X rises more than 50% from baseline) in the model, but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously. Moreover, it cannot deduce the pattern of the change in covariates as time passes by, let alone reaching conclusions like "if the level of X rises exponentially, then a patient will have an extra 50% of risk of developing stroke during follow-up, compared to those whose level of X rises in a linear pattern". It may be hard to deduce the pattern of the curve of change, but what I am actually looking for is a model that can put virtually all of the data I collected inside, just like ANOVA of longitudinal data. But since a major defect of ANOVA of longitudinal data is its inability to consider loss of follow-up, which is quite common in time-to-event data; I am looking for a "blend mixture" of methods dealing with longitudinal data (like ANOVA) and methods dealing with time-to-event data (like Cox model). I wonder if that kind of model exists and if there really is one, if I can perform this on SAS. Many thanks!

Re: Is there a method using longitudinal data to do survival analysis?

Season — Sat, 10 Dec 2022 04:28:34 GMT

Thank you for the tip you have offered. Actually, I opened the editing page by following your instructions. But I had been doing something else at the same time and left the page unchanged for some time. When I edited my sentences and clicked the "Post" button, the system refused to let me change the contents I had posted, saying that I had run out of time. I tried to enter the editing page again, but failed to find the "edit reply" option this time. So I simply deleted my original reply and posted my corrected version.

Re: Is there a method using longitudinal data to do survival analysis?

Season — Wed, 18 Jan 2023 08:48:13 GMT

After searching for literatures in the past month, I successfully found out that there currently is a model using longitudinal data to do survival analysis. To be more explicit, a joint model of longitudinal and time-to-event data, which in many cases is abbreviated as "joint model") has been proposed, with a few monographs pertaining to this joint model having been published, including those that only introduces statistical theory and those that also introduces the method of building joint models via statistical softwares (such as Rizopoulos, D. . (2012). Joint Models for Longitudinal and Time-to-Event Data). But almost all of the literatures currently published discussing the way to build joint models via statistical softwares are performed via R.

So, my question is: can I perform the building and correction of joint models via SAS? If so, via what module (PROC XXX)?

Many thanks!

Re: Is there a method using longitudinal data to do survival analysis?

Ksharp — Wed, 18 Jan 2023 12:07:45 GMT

Then you need some help from SAS/IML to write a new PROC .
Maybe @Rick_SAS could give you a hand .

Re: Is there a method using longitudinal data to do survival analysis?

Season — Wed, 18 Jan 2023 12:41:17 GMT

Thank you, @Ksharp, for your suggestion!

Re: Is there a method using longitudinal data to do survival analysis?

sbxkoenk — Sat, 25 Feb 2023 20:38:19 GMT

Hello @Season ,

So, you want to analyze two types of outcomes produced usually in longitudinal studies, particularly :

a set of longitudinal response measurements and
the time to an event of interest, such as default, death, etc.

These two outcomes are usually analyzed separately, using a mixed effects model for the longitudinal response and a survival model for the time-to-event.

Geert Verbeke and Geert Molenberghs (two Belgian bio-statistics professors) discussed , somewhere in the 2000s, how you can analyze them jointly.
i.e. ** Joint Models for Longitudinal and Time-to-Event Data **
See

https://gbiomed.kuleuven.be/english/research/50000687/50000696/geertverbeke/cursuskort/ldasc10jsm-cursusversie.pdf

Re: Is there a method using longitudinal data to do survival analysis?

Season — Sun, 26 Feb 2023 04:01:01 GMT

Thank you very, very much, Koen, for your wonderful and helpful reply!

I will investigate the information you provided in depth.