Survival analysis, survival (time to event) estimate probability not accessible

[#1]

Background: Looking at a progressive disease process on which we intervened surgically. All but 2 patients (out of 50) went on to experience disease progression while the remainder had resolution and/or halting of their disease progression at time of follow-up (i.e. successful surgical outcome). I am attempting to obtain a KM curve for the success of this surgical intervention with respect to time. My goal is to provide a meaningful outcome that describes how successful the surgery is in halting disease progression and for how long and with what level of confidence can we report this. I recognize lack of control group but this is separate conversation and innate limitation of the disease process which will be discussed in our paper.

Currently I have my data setup as: Event = disease progression. Since all but two subjects experienced the event, it means the group is composed primarily of right-censored subjects. Very few were lost to follow-up or deceased, but of course they too were censored. Is this setup correct? My resulting KM curve is essentially two small steps early in timeline followed by a flat line through to end of the study period. It just appears strange having so many right-censored subjects. Is there a more appropriate way to represent this data? If this is in fact correct, I would like to provide "survival probability estimate" at given points in time (i.e. what is probability of being progression-free (successful surgery) at x point in time). However on JMP this feature is for some reason grayed out/inaccessible from the red triangle drop down. Any reason this is the case? How would I perform that calculation?

THANK YOU FOR ANY HELP! 

[#2 · Accepted solution]

Yes, your setup is correct. One could argue that the patients who left the study constitute truncated, not censored, data.

The two steps are also correct. The non-parametric estimate remains constant until another exact life observation is encountered.

You must fit a model to obtain the probability versus time. I recommend a Weibull or a Log Normal distribution model. JMP can do all the models and use a criterion to select the best model, but this data-driven approach is risky when you only have two exact lifetimes.

Here is an example. I used the :weight data column in the Big Class data table and pretended it was lifetime data. I added a Censor column with 1 in all but two rows, so only two exact lifetimes. I launched Life Distribution and selected the Weibull model and scale. You can use the distribution profiler to the right to estimate failure probability for a given time.

[#3]

Thank you, this was incredibly helpful! Using the above, I was able to provide progression-free estimates at 1, 3 and 5 years using the Weibull model and scale.

I have an additional question regarding this same data set. My time to event data can be grouped by disease stage (Stage A, B and C). I am able to comment that the distribution of the time to event data did not differ across groups based on logrank test. A reviewer has asked that I "report the difference in time to event as a function of stage with Hazard ratio as the effect size and 95% CI around the HR for Stage B and Stage C". I personally interpreted this as a request for Cox regression hazard ratio analysis with stage A as the reference group. I used the Fit Proportional Hazards module for this and selected "risk ratio" (which based on a quick search is equivalent to hazard ratio in JMP). Is this setup correct? If this is correct, the primary issue is that my Stage B group did not have any events. As such, I am getting an HR of 0.00 and CI with minimum 5.48E-06 and maximum 3.38E+266!! Clearly this is a degenerate estimate but not sure if any workaround or how I would go about interpreting or reporting this value? With so few events in each group (n=1 for Stage A, and n=1 for Stage C), I recognize that it is hard to draw meaningful conclusions from any of these values but any help would be greatly appreciated!

[#4]

@Mark_Bailey brought this thread to my attention. Before I continue, I need to disclose that I don't have experience in medical or clinical fields. My opinion is based on my experience in a related field, reliability data analysis. Here are some thoughts:

1. In the field of reliability data analysis, if there are two few events, there are two approaches to address the situation: (1) obtain a conservative estimate which means the reliability (equivalent name to survival in a different field) is likely underestimating the truth (2) use Bayesian approach to incorporate additional information. But I don't see either options are feasible to you, since they are both parametric approaches in JMP. KME is a nonparametric model. If there are nonparametric approaches to address few events in the field of medical and clinical, that is beyond my current expertise.
2. Proportional Hazard model is a semi-parametric model. But if you have too few events, you face the same difficulty. And I don't see what JMP currently offers can address the challenge.

Please conduct a research on situations like this in the relevant fields. If we have experts on this subject in the community, I hope they can spot this post and chime in.