YSPH Biostatistics Seminar: “The Predictive Individual Effect for Survival Data: A Patient-Oriented Summary Measure for Treatment Benefit”

November 14, 2022

Information

Speaker: Satrajit Roychoudhury, PhD, Pfizer

November 8, 2022

ID9090

To CiteDCA Citation Guide

00:00(presenter faintly speaking continues)
00:05<v Presenter>Dr. Roychoudhury,</v>
00:07(presenter faintly speaking continues)
00:26research institute (indistinct).
00:30He had 15 years of extensive experience.
00:34(presenter faintly speaking continues)
00:43Model based projects (indistinct).
00:47He served as the (indistinct) co-chair
00:51(faintly speaking) workshop.
00:55(presenter faintly speaking)
00:56And he's serving as co-chair for DIA, FDA,
00:59biostatistics (indistinct).
01:04Dr. Roychoudhury was exacted to be a panel
01:07of the American (indistinct) Association.
01:10(presenter faintly speaking)
01:11the country (indistinct),
01:15international (indistinct) society in 2019.
01:20So let's welcome Dr. Roychoudhury.
01:23Now I'm yours.
01:25<v ->[Dr. Roychoudhury] Thank you.</v>
01:28Thanks a lot Dr. (indistinct) for the nice introduction.
01:30Can you all hear me well?
01:34And thank you for the opportunity to present here
01:38and having a chance to interact with all of you.
01:41So today, (faintly speaking) I'm gonna talk
01:45about a problem that is many
01:48of the recent drug development are facing,
01:52and we try to talk about better interpretation
01:55of clinical trial data,
01:57especially bringing the different perspective
01:59as some of you know and some of you don't.
02:02FDA actually specifically started
02:05a patient oriented drug development program,
02:08which kind of how to make the data more understandable
02:12to the patient, more reachable to the patient.
02:14So this was kind of on that theme mostly.
02:18Before I begin, just I wanted to mention
02:21the standard disclaimer, this my own view,
02:25and not necessarily reflect the view of the Pfizer.
02:30So I think many of you have work
02:33on survival analysis as a coursework
02:36or maybe analyzing trial data, research perspective.
02:41So often, in critical trial setting,
02:44we call that analysis over time to event data.
02:47Because we look into the data that up to time,
02:51so we analyze the time up to a certain event
02:54or sensor the data looked at.
02:57And the standard way of analyzing such data,
02:59these are the, more or less, a standard tool.
03:01I'm sure you all have done or are going to do
03:04in your courseworks, that looking into Kaplan marker
03:07which looks into the survival function,
03:10the effect over time.
03:12Log-rank test, which basically tests the difference
03:16between the two curve, that if the treatment is better
03:19than control or control is worse.
03:22And then last, to summarizing treatment of it, right?
03:26At the end of the day, we need to know
03:28how good is the treatment.
03:29And one way to say that was basically hazard ratio
03:32or something we call Cox regression.
03:37Now low-rank p val-
03:38These are very standard reporting techniques.
03:41Any time to event data, if you pick up any medical journals,
03:45are typically analyzed using three (indistinct).
03:48But the question was, and based on some examples done,
03:52we'll dive into the details as we go along.
03:55the question really came up,
03:56are these really good metrics to analyze the data?
04:03So just to give a quick introduction,
04:05I'm sure all of you know it very well.
04:06But just to understand the fundamental assumptions,
04:10what the Cox regression means.
04:13So Cox regression and hazard ratio are the very,
04:17very popular method.
04:18And it started, basically introduced
04:20by Dr. DR Cox in 1972, one of the brilliant statistician.
04:26And it's closely related to mathematically
04:29with the log-rank test,
04:30which actually kind of increases its popularity.
04:33There mathematically, the score function,
04:35the score test for Cox regression is equal value
04:40to the log-rank test under two sample case.
04:44But it has an assumption also.
04:46It assumes that the treatment effect basically is constant
04:50over time, so it emerges at the beginning of the trial
04:53and it remain kind of a constant over time.
04:58Which is a problem when this is not true,
05:01because not all drugs work the same way.
05:03Sometimes, maybe some patient get benefited
05:05after getting treated for longer time.
05:10On such case, such a measure has a ratio,
05:13start to lack its interpretation.
05:16And also there is some problem
05:18regarding causal inference perspective.
05:22Let's look into two examples, two, three examples,
05:25real life examples, and try to understand
05:27where the problem was.
05:28So first, let's start with more simpler
05:31when treatment effect emerges at the beginning
05:34and remained at that (indistinct) over the trial.
05:38So the trial on...
05:39And they're all real trials,
05:41and I added the references in case you want
05:44to look into later.
05:45The one on the left is basically a trial
05:48for non-small cell lung cancer where gemcitabine
05:51and gemcitabine plus erlotinib combination has been
05:55looked into, which is showed the blue curve.
05:58There is experimental combination drug,
06:01which shows superiority
06:03over the standard of care, gemcitabine.
06:06The one on the right is basically
06:09on refractory multiple myeloma disease,
06:12which is a very fatal disease.
06:15And they're basically triple combo,
06:17so kRd is a triple combination drug,
06:19where Rd is basically a double combination drug.
06:22I'm not going into the details of that.
06:24Looking into basically kRd,
06:27was the experimental drug of this showing the superiority?
06:30In both cases, the proportionality has assumption,
06:33looks valid, because the effects started and it continued.
06:37But that's not all always the case.
06:39Here are the very few, very recent examples,
06:42especially if you are looking into the newspapers as well.
06:46And I think two years or three years back,
06:49the person from MD Anderson actually got the Nobel Prize
06:52for looking into the immunotherapy,
06:54one of the fundamental research from that area.
06:57So when it does this particular type of therapy,
07:01basically putting people immune system,
07:05basically and they kind of train them
07:08to fight against their cancer.
07:11And CheckMate 141, which is squamous cell carcinoma
07:15on head and neck,
07:16and nivolumab is one of the immunotherapies
07:19of the first (indistinct) cluster for their client.
07:22When they looked into the actual treatment effect,
07:26started to emerge pretty late.
07:27So that means it take the time for the immune system
07:31to actually work.
07:33And then the question is,
07:35the treatment effect is no more constant, right?
07:38Immunity is at three month.
07:40It's even more problematic coming into the example
07:43in IM211 trial, which is urothelial carcinoma
07:47and well atezolizumab, a compound,
07:50and Roche was actually looking into against chemotherapy.
07:54The compound was detrimental at the beginning
07:58and slightly at least compared to the standard of care,
08:01the chemotherapy that how the people are treated.
08:04And then it showed benefit, definitely.
08:08But there is something more interesting in the second ex-
08:10I will concentrate and each of them are interesting,
08:13each of them have a story of its own.
08:15But I just focus on this IM211 trial
08:19to bring in the patient perspective a little bit.
08:22So if you look into this trial, of course the trial
08:25doesn't have a significant amount, right?
08:28The log-rank test, which tested the superiority
08:31of the curve basically said it's nonsignificant.
08:35But if you actually wanna look
08:38into this survival curve a little bit more details,
08:42one can see the survival effect is really emerging
08:46and once it gets into the 18 month,
08:49it started to be pretty significant.
08:52You come in carcinoma.
08:53So this is kind of an 8% survival benefit is for this class
08:57of patient is quite a meaningful benefit on that context.
09:01So the question is, are we evaluating this drug correctly
09:06by these two standard metrics like Cox, hazard ratio,
09:09which doesn't look good here, 0.9, close to one.
09:12So it has a ratio less than one
09:14because we are comparing treatment versus control.
09:17Less than one means treatment is better
09:19and bigger than one means treatment is worse.
09:22So basically doesn't really reflect these angles.
09:25And also, if you look into the hazard function plots
09:29or hazard ratio plots,
09:30you can quickly see they're not constant over time.
09:33They're actually emerging or varying there.
09:41I mean, there was been a working group,
09:44there has been a number of workshop here,
09:46and even FBA and other regulators got interested.
09:50There has been a lot of discussions started in 2016
09:53when nivolumab, the first class
09:56of immunotherapy compound came in in a development phase.
10:01And there has been a lot of research.
10:02People were looking into different tests, okay,
10:05log-rank is not good, because it is most powerful test
10:09under proportionality hazard assumption.
10:11We don't have it, especially for situation like this,
10:14CheckMate or IM211 trial;
10:17or we should do some other test.
10:19This is not powerful, some better test.
10:21So there has been a zoo of tests being came in.
10:24You may have heard about some of them weighted,
10:26so instead of log-rank test, weighted log-rank test
10:29where we selectively weight that separate areas
10:33of the Kaplan-Meier curve.
10:35Then some a little bit more robust, like MaxCombo,
10:38weighted Kaplan-Meier test, restricted mean survival time,
10:42and there are many, many.
10:43I mean, and they try to look into
10:45how to handle different potential.
10:47Because one thing we need to understand,
10:49proportional hazard is a very specific character.
10:54When we say proportional hazard
10:55that these two hazard plots are (indistinct).
10:59But once we set non-proportional hazard,
11:01there could be many, many possibilities.
11:04Drugs can be crossed, drugs can separate the link.
11:08Drugs can first separate and then emerge back.
11:11So it's a no more unique (indistinct).
11:13So we need a set of methodology that's sort of robust
11:16across this different class of alternatives.
11:21But the problem is even having a P value,
11:25suppose once we call about, okay, there's a good test
11:28and we got a good P value for such a curve.
11:31But one can say, oh how can a P value is meaningful?
11:35The beginning of the curve, the patients are getting worse.
11:39Is a P value really meaningful in this context?
11:43So rejecting the null is really a less informative.
11:47You need to know more information
11:50to understand these kind parts of compounds better.
11:54And that's also been looked into.
11:56There are multiple, multiple things has been looked into
12:00with simulation, with datas, lot of meta analysis
12:06with different data looking into the percentile, right?
12:08I mean one part of we're looking,
12:09why don't we look into the ratio of the median
12:13of the compound?
12:14Or we look into the (indistinct) time or percentile, right?
12:17Things are separating at percentile.
12:19Maybe we can look into percentile
12:21over the time ratios of those.
12:25Then milestone survival and coming into a moment,
12:28which is a sort of a very meaningful
12:31to a patient's restricted means survival.
12:34Basically you average over the area under the curve,
12:39which it has a ratio, because we are doing with a test,
12:42a dual estimator of that is weighted hazard ratio,
12:45piecewise hazard ratio.
12:46Cox model, now, the initial Cox model doesn't have
12:51a time component in it (indistinct).
12:53Only the time component is in the baseline hazard.
12:55We can introduce a time component into that
12:58to make sure the treatment effect is sort of time dependent.
13:03And then there are other things like net benefit.
13:08I won't dive every one of details,
13:10but I just wanted to mention that hazard,
13:12so weighted hazard ratio means hazard ratio,
13:14we were doing a Cox regression.
13:16We were looking into basically the regression coefficient
13:20corresponding to the treatment using
13:21a partial likelihood method.
13:23And now, the whole idea was similar to like testing
13:26where we are weighting different part
13:28of Kaplan-Meier differently, we weight different part
13:31of the partial likelihood differently.
13:33Or there are other type of weightings as well,
13:36like average weights and others.
13:38So basically, the whole idea was not
13:39to treat each event similar,
13:41but differently based on their interest.
13:44But that's the (indistinct) of course,
13:48treatment emerges at the end.
13:50We may be interested more towards the end,
13:52but it adds a subjective choice, right?
13:55And it's not very easy for non-clinicians
14:00to understand on that aspect.
14:06So now then, of course in 2005, people also talk quite a bit
14:12about piecewise hazard ratios
14:15and now still piecewise hazard is still very important.
14:18Like you divide the whole time axis into different intervals
14:23and you basically calculate local hazard ratios.
14:28Which is very meaning 'cause you can look
14:30into the first part when (indistinct) not separated.
14:32The hazard ratio's close to one,
14:34then the hazard ratio emerges.
14:36And there's a natural extension
14:37of that was basically using a regression using a time factor
14:41into the core value.
14:41But really, the power and the performance really depends
14:47on the function that you choose, which is, again,
14:51is difficult to interpret in a practical sense
14:54that if results really value on such a choice.
14:57But one thing was kinda after all,
15:00among all this discussion,
15:02one thing was when we talked to non-statisticians,
15:04specifically clinician, one thing was very clear,
15:07one measure we found.
15:09The measure is improvement in survival.
15:12That means they're very clear about certain metric
15:15that, okay, what is the survival gain at five year
15:18or eight year?
15:19Those metrics seems to be very intuitive,
15:21very clear to to non-statistician patient
15:25and all other stakeholders.
15:28But the only problem is at the beginning of the file,
15:31you just don't know when the curve is gonna be separate.
15:35You don't know that.
15:36So (indistinct) finds such point,
15:38can be very dangerous for you.
15:44The last measure I mentioned was this,
15:46been over and over discussed,
15:47which is called residual, meaning lifetime,
15:50basically (indistinct) lifetime,
15:53residual means survival time.
15:56Which has been over and over discussed recently
15:58in clinical literature, as well as in statistical,
16:00restricted mean people.
16:02When people looking into restricted mean,
16:03that means they're looking for supposed up to a time Tau.
16:08You cut the curve, you compare the area under the curve,
16:12which is in this block.
16:13And you see if you can look into the difference,
16:16you can look into the ratio,
16:17and try to see if the area under the curve is better
16:21on that context.
16:22But remember, the problem is here,
16:24the comparison also very much depends on the choice
16:26of the cutoff, where you choose it, basically.
16:31The Tau and risk of the censoring pattern
16:33of the Kaplan-Meier plays a very big role
16:35in such a such compass,
16:39especially in a setting for such metrics.
16:43Especially, it's very problematic
16:46when in a cancer setting like metastatic,
16:49the one I showed you earlier,
16:50because there is a, the disease is very fit on it,
16:54happens very quickly.
16:55Patient gets multiple therapies.
16:57So censoring patterns are much more aggressive,
16:59whereas there are other disease setting
17:01where RMST seems to be very meaningful.
17:04Because you get lot of follow up much more uniformly.
17:10Now the problem was, okay, all these measures differently.
17:13We apply, we get different results, we get, okay,
17:16one is good right here, right?
17:18We talked about IM211 at beginning.
17:20We saw survival benefit.
17:22We see that the survival benefit coming
17:24into the 12 month zone, but RMST was still showing, okay,
17:30there is no confirmation of such an effect.
17:34So there has been a interesting paper
17:36I came across last year.
17:38It was a patient voice survey in UK.
17:41They basically did a survey on patients
17:45as well as the health practitioners
17:49who are participating in the TACT trial.
17:53Taxotere is a adjuvant chemotherapy drug.
17:56It's a very big trial.
17:57And they surveyed that what patients really want,
18:01how they want the trial results are for.
18:04I mean, because at the end of the day,
18:07the doctors tried to discuss these results
18:09with the patient before they choose as a therapy.
18:11And then, it's not surprising that actually,
18:16it's coming in that the patients are really want
18:19to understand these results in a very simple term.
18:22I mean, it's not like,
18:23oh, your drug may not be decreased event rate,
18:27but it expected survival going to get really bigger.
18:31But that's not the question a patient is asking, right?
18:34I mean, it's not type of mindset a patient has.
18:37Then of course, the patients are one who have the results
18:41as soon as possible.
18:42It's a very interesting article I suggest to read.
18:44It's a very fun reading article
18:46to look into the patient voice, how patient wanted...
18:51Because most of the time patients are not being
18:53always communicated about trial results
18:56and how they wanted.
18:58It came out to be very nicely in this,
19:00especially most of them actually want still comfortable
19:05to have the results from their nurse or doctors.
19:09Because they're more comfortable to discuss with them
19:11rather than having a big seminar or formal paper.
19:16But really, let's think about the patient perspective,
19:21what question they really ask.
19:22The question they really ask are these, right?
19:25I mean, if we put ourself onto that shoes,
19:29the question is does this drug really work?
19:32What are my chances that I will do better
19:36in terms of survival or in terms of painful quality
19:40of my life if on the new drug compared to no treatments?
19:46So these are the much more simple question.
19:48Unfortunately, many of the well known methods are unable
19:53to address because I mean, you can indirectly address
19:57those question or you may have the study shows you have
20:02a benefit of pharma.
20:04But that really doesn't answer the question
20:07from that patient perspective.
20:10Which actually motivates us a little bit,
20:12that can we dig in?
20:14Can we try to see if we can use
20:17our modern statistical analytic methods
20:20to address some of that question,
20:21especially from peer's perspective,
20:24from a kind of practitioner's perspective.
20:30So one of the thing that is more easier for anybody
20:34to understand the visual graphics, right?
20:36Kaplan-Meier plot is something which is more easy
20:39to comprehend compared to many other metrics.
20:42So that was kind of how our motivation (indistinct) became.
20:45And then the question is really,
20:47it's not like what trial shows.
20:49Now the question, if a new patient is entering the trial,
20:52can we predict their benefits based
20:57on the available data we have?
21:01And this could be an additional metrics.
21:02Of course we are not saying these metrics is gonna change
21:06the trial or the trial practice,
21:08but this is definitely another metric
21:10which can help patient much better
21:12for making their decisions.
21:16So what we introduced is basically this quantity
21:20which is called individual effect, Y minus X.
21:24What is Y?
21:25So Y is a survival time at the treatment arm.
21:30I'm just making simpler, instead of progression survival,
21:33let's have the conversation on survival,
21:35because it's just easier to understand.
21:38So Y is basically if a patient receives treatment
21:45and control, Y means their survival time in treatment
21:49and X is the survival time in control.
21:53But in a real trial, there was never been one patient
21:56who received both treatment and control.
21:59So this quantity is actually counterfactual.
22:03We cannot have that data.
22:05So we somehow have to predict this.
22:09So in order to do that,
22:11we first need to understand the marginal distribution
22:14of Y and X.
22:15And then also understand the need
22:18to take account the correlation in Y and X.
22:23Let's dive in what we need to do in this step,
22:25and I'll go into details of the statistics
22:27in next of my few slides, what technically it means.
22:31Basically, we are trying to find,
22:35so what we are trying to do,
22:36we are trying to find this predictive patient level effect
22:42of a drug.
22:44So what we need to have for that?
22:46We need to have a marginal distribution
22:49of survival for both,
22:52if a patient is independently goes to treatment
22:56or in control, basically.
22:57We need the marginal distribution first.
23:00Then we somehow need to calculate the difference
23:04by considering the association between them.
23:07Because Y and X are coming from a same patient.
23:13So first thing was interest,
23:15first thing was kind of how to do the marginal distribution
23:19of Y and X.
23:20That part is easier.
23:22That part is technically maybe intrigued, but easier.
23:27So suppose any trial data we have,
23:29we can have multiple trial data.
23:31We look into the treatment, and we look into the control.
23:35I just, for simplicity,
23:36suppose we have one one trial in our hand.
23:40And if there are multiple,
23:41we can definitely add more layers to that
23:43and adding trial specific event.
23:45So we can fit a...
23:47Piecewise exponential models are more,
23:50kind of a flexible model.
23:51So of course, one can use (indistinct),
23:53other parametric family.
23:54The reason we are moving into parametric
23:56because we wanted to extrapolate.
23:58We wanted to see the survival in the future.
24:01So that's why we chose basically
24:03piecewise exponential graph where each of the within,
24:08so the whole time axis is divided into different time span,
24:12different time points,
24:15and then we assume the hazard response within that.
24:18But just not, we don't assume any hazard ratio.
24:21We are (indistinct) treatment effect responsive.
24:23We are fitting this piecewise exponential separately
24:26for treatment and control, basically.
24:29So there is no proportional hazard option.
24:32And then here, we assume that alpha and beta (indistinct)
24:35and using the, basically, the gamma prior
24:38for each of the interval specific hazard.
24:41And we assume non-informative practice.
24:44Most often we only have the trial data,
24:45not much information,
24:47but if they have more information from early trials,
24:49you can use informatic (faintly speaking).
24:51But one of the major challenge always
24:54for piecewise exponential is
24:55how you choose cut points there.
24:59There's like the cut choice of cut points,
25:01people often do eyeballing, right?
25:03They look into the plot, eyeball the times,
25:05but those are mostly subjected.
25:07That means one prediction to another prediction,
25:10it can vary there, which is problematic.
25:13We need a a little bit more uniformal way
25:17of selecting these cut offs.
25:19The second more easier one can think, okay,
25:22I use the person notes there.
25:24But here the problem is when we fixed the personnel,
25:27maybe from one plot to another,
25:30there may be intervals which doesn't have much event.
25:33So (indistinct) may not be basically calculated
25:37in a right way.
25:40So not stairwise.
25:41There is no event within that interval.
25:45So what we did, we basically looked into
25:47a optimal cutoff points searching algorithm.
25:50So we basically first divided the cut,
25:54the axis based on the person health.
25:56So you have 10 intervals to...
25:58So basically, at most, 10 intervals.
26:00So then we consider all possible models.
26:03So one component, two component,
26:05to the power 10 component model.
26:08Of course, if some of intervals doesn't have very few event,
26:11we basically merge them
26:12so that you have a reasonable estimate
26:15for (indistinct) basically.
26:17And we chose the best model based on the DIC
26:20among those two to the power, N number of models.
26:22Of course, there's not always 10
26:23beause some of the intervals may be empty, so we plot them.
26:28And one can actually do a k-fold cross validation as well,
26:32which is we also looked into kind of a giving more
26:35or less similar result.
26:36But if you have a long term data,
26:38one can also do a k-fold validation
26:40in order to choose the hard points.
26:44Now the second part is prediction, right?
26:47So prediction, so what you got from the model now
26:51is that distribution of (indistinct).
26:53That's parameter.
26:54But when you go to prediction,
26:56we are talking about sampling space now.
26:58So we are talking about a new patient's survival time.
27:02So that needs to take account uncertainty of the new sample.
27:07That's the beauty of the Bayesian distribution,
27:09the posterior predictive distribution
27:11automatically does that.
27:12And the setting, the reason we took this setting,
27:16because the predictive posterior parameter distribution
27:19is again, a piecewise (indisitinct) distribution,
27:22which is basically closed form,
27:24that first hour computation quite a bit.
27:27And then we basically use, as I say,
27:30it's can easily done with this Beyesian computation.
27:33But if you want to do more complex model,
27:36we'll one, need to move into a little bit more
27:38MCMC algorithm or kind of writing and way of sampling it.
27:45Now the third aspect, which was actually the more,
27:48most interesting aspect.
27:50Now we got the marginal distribution.
27:52We predicted the marginal survival times.
27:56Now the question is, it's the same patient, right,
27:59we are talking.
28:00So they're correlated, X and Y.
28:02How we most are correlation structure, which is meaningful?
28:07Now that thing was actually the idea was came
28:11from a very old paper by Lehmann and Doksum in 1974,
28:16which we were looking for a scale shifting distribution
28:20I'm going into in a moment.
28:21Which actually brings up a very important property.
28:24And that property is very important
28:27because this methodology, it depends on that property.
28:30And we can talk about in the setting
28:33where you think this property is not true.
28:36So the property is basically a rank preserving property.
28:39What that means, that means if a two population,
28:42so if one fail earlier in control,
28:49they will fail also earlier in treatment.
28:51That's a rank preserving property.
28:53That's a very important property for this.
28:56But one can also question that, okay,
28:58for targeted therapy, that may not be true.
29:00Somebody with a biomarker that order may change, right?
29:03So we need to do appropriate adjustments
29:06to make that assumption.
29:07I'm going into that.
29:08That was one of the referee comments, by the way.
29:12But before going into that,
29:13this paper was really fascinating.
29:15I mean, it was very simple paper in actually 1974
29:20and also of statistics, very simply written paper.
29:24And what they were saying that they were looking
29:28into distance between two normal curves there.
29:33And the property they introduced was scale shifting,
29:36a shift function, which basically makes that,
29:41so your X and Y, what you just mentioned,
29:43we said X plus delta X,
29:45which is one can interpret as gain also,
29:49and Y kind of have a same distribution.
29:54That was the main property.
29:56But it's very, basically, that means you project this curve
30:00to other curve.
30:01There is a path to project all.
30:05And the solution of delta X is,
30:07I mean, what can easily cost start that it's not unique.
30:10But they actually, this is how they constructed it
30:14using the shift function.
30:17But what did that means for our case?
30:19Why we need that, right?
30:20So this means that, so if we,
30:23if I know marginally, the (indistinct) tells of X,
30:26I can project the same content into the Y distribution,
30:30that basically we'll coordinate ourselves.
30:32So that means if we build, if the ordering of X remain,
30:37ordering in Y will remain too.
30:38That is what the rank preservation property's coming in.
30:43I'm sorry, I'm going to revisit the...
30:45I mean, like I said, sometimes simple papers give you
30:48very nice ideas as I find.
30:51So now the job is simple, right?
30:52Now we have marginal distribution in hand.
30:56We get the predictive distribution,
30:57how to predict the marginal, and now we know
31:00how to link them using the quantile function
31:03from one to another, how to project.
31:05So basically what we did,
31:06we simulated from this posterior distribution
31:10and then we simulated this uniform numbers.
31:13And then what we did in order to bring X and Y to related,
31:17we basically from same quantile,
31:20we obtained the X for given US,
31:23we obtained the quantile XS and YS for each case.
31:27So they're related by that way.
31:29We project it from X to Y
31:31and then that gives us a pair XS YS for them
31:35and we can make the distribution.
31:41But of course, this is questionable, right?
31:44I mean, we are saying the order remains,
31:46which is not always true.
31:48Suppose this is a very classic example
31:52from the nivolumab trial.
31:55So it's attacking the PD1 inhibitor.
31:58So people with PD1 expressed, it's supposed to work better.
32:03So if you pick two subject,
32:05one is PD1 expressed and PD1 expressed not,
32:08if in control, PD1 expressed one actually works worse
32:12than the PD1 non-expressed treatment that can reverse.
32:15Because PD1 is the line, the target of the truck.
32:19So on such a case,
32:21our solution is basically divide the groups
32:24into the homogenous biomarker class.
32:26And then, the (indistinct) still works.
32:28And that can be easily done adding it as a regression
32:32into the model.
32:35So then finally, we summarize this
32:42with a survival gain and out the loss of tests,
32:45I mean basically using the posterior, sorry,
32:48the predictive distribution of Y minus X.
32:52And then also, we summarized the median
32:56and the 95% prediction intervals.
32:59And also to us, the Kaplan-Meier plot is still important
33:03because that's where the whole story begin.
33:06That's the data which generates our marginal distribution
33:09where we actually...
33:10So we should compare that side by side on this.
33:16Let's see how this method works then.
33:18I mean, so we started, does it improves anything
33:20after all doing fancy things,
33:23make things complicated, making lot of mathematical names.
33:27Did you improve anything?
33:28So did you gain more insight into this?
33:32So let's go back to this trial
33:34where begin the urothelial cancer trial of atezolizumab,
33:37which is basically the low-rank test says
33:41it was basically...
33:43The survival curves are not separated.
33:46Basically significance that doesn't reach.
33:50The Cox has a ratio, upper bound is about one,
33:54even the median, because it's very interesting.
33:56Because the curve actually is separated after median.
33:59So even somebody looking into the median,
34:01the treatment is worse than that for the standard of care.
34:05So the question is really, how can we...
34:08But when we look into the survival differences,
34:11we see a significant survival gain by the patient
34:14who remain on the therapy for a longer time.
34:16But the question is, can we somehow communicate
34:24that better with this individual event?
34:29So the one on the left hand,
34:32one on the left side is basically the probability plot.
34:37So it is basically the first column.
34:40We looked into the gain of survival bigger than zero month,
34:45one month, two month, six month.
34:48And the plot on the right side is basically median
34:51and then predicted interval.
34:53So as you can see, there is an initial setback.
35:00There is a significant probability
35:03that atezolizumab can actually improve the survival
35:07in the problem.
35:08At least you have,
35:09if you're looking to this plot,
35:11the improvement of three month or higher,
35:14which is urothelial cancer is pretty good,
35:16you have 30 to 40% probability,
35:18which needs to be considered for these patient.
35:20Because they don't have,
35:21they only have chemotherapy as a treatment for that.
35:25The most interesting thing comes actually
35:28on the right hand side.
35:30If you look into that, the patient as we talked about,
35:34the benefit actually emerges as the patient went long term
35:38into the therapy.
35:41It start pretty much, much (faintly speaking) to others,
35:45compared to others.
35:49Let's look into another.
35:50So okay, non-proportional hazard,
35:52this may be useful.
35:53But can we still use that for proportional hazard?
35:56Do they have any value?
35:57Actually, do they add anything?
35:59'Cause they're log-rank has a ratio are more popular, right?
36:02Our argument is no,
36:04but maybe this measure can help you there too.
36:06So I go back to this lung cancer PA3 example
36:09of gemcitabine and gemcitabine plus erlotinib,
36:13which is statistically significant
36:14with a very marginal hazard ratio.
36:17But statistically significant
36:20and the media advantage was also not very good
36:24by only .3 months of advantage.
36:27The question is really,
36:29does the survival effect is meaningful in that way?
36:34Always.
36:37So again, we started to plot these two.
36:42So the one here is basically the plot
36:47for the survival gain, X minus Y, once again, control.
36:51Same patient treated in treatment
36:53versus same patient treated in control.
36:55What is the survival gain?
36:57And the one on the right is basically the median
37:01and the corresponding interval.
37:03As you can see here,
37:05especially the patient who discontinued
37:09or there are some questionable benefit on that question.
37:12So just having a proportional hazard
37:14and giving a hazard ratio may not be giving the full point
37:19that we are looking for.
37:20There may be some more to it,
37:22which can be further investigated.
37:25When it's prescribing a patient,
37:28maybe there are certain characteristics
37:30why the patients may be continuing early
37:34and some kind of (indistinct) and some kind of special...
37:37So those patient may not be the benefit is as good,
37:40as prominent as the patients who are long term treated.
37:46So we also investigate CM.
37:48I just don't want to show all the plot just not
37:51to bore anymore, but messages are very similar.
37:53We also look into CM141.
37:57We also look into that ASPIRE trial
37:59as I explained you earlier about multiple myeloma
38:03and the CheckMate141 is basically squamous cell carcinoma
38:08in head and neck.
38:10And we also looked into the CheckMate057 trial
38:14where there's a significant subgroup
38:17that means the one group with PDL-1 expressed
38:23has a significant survival.
38:25But PDL-1 non-expressed has no survival benefit
38:33with the (indistinct).
38:36So we looked into all these examples
38:38into the export data and our codes are also relevant
38:42in public if you want to play with that.
38:44Basically the message we got,
38:46so the one on here is that this table
38:49toward the mean survival gain,
38:52median survival gain, the predictor interval.
38:55And what is the chance that probability
38:57that Y, which means your time,
39:02if a subject is receiving treatment
39:05and X if a subject is receiving control,
39:08what's the time Y is bigger than X,
39:11is basically we started to see some interesting feature.
39:15It gives us much more quantification of benefit compared
39:19to our P value or a hazard ratio in that way.
39:22Of course there are uncertainties in all of them
39:25as well as the clear cases
39:26where we saw statistical significance.
39:29We see some uncertain situation, that patient may
39:33or may not be benefit in some cases.
39:37So the quick conclusion with the increasing complexity
39:42of the drug and the different complex pathways
39:45we are talking, it is very important.
39:47And different patterns of treatment effect,
39:51it's very important to have a simpler language
39:55with the patient.
39:56I mean, because we're all telling what they're answering
39:59their question at least directly.
40:01We find predicted individual effects sort of a step towards
40:05that, which answers the patient's question more clearly,
40:11kind of a clinically relevant.
40:12And also it step forward,
40:14and as well as it supports this 21st century cure act
40:19of patient centricity.
40:21Especially find very useful in where your standard is
40:26of proportional hazard fails.
40:31I just wanted to quickly thank my collaborators
40:34whom I collaborated with and here is outpatient
40:39along with the software is available
40:41in case you want to try out.
40:43And the references that I mentioned
40:45including actually the...
40:47I just wanted to always mention,
40:50if you are reading the famous Lehmann book,
40:54it's actually there as well.
40:55I just find out last night it's there as well.
40:59And not only (faintly speaking) statistics people.
41:03And I just want to thank you for your attention.
41:06Thank you.
41:18<v Presenter>Does anybody have any questions?</v>
41:22<v Attendee>Sure.</v>
41:23Is there a notion of why you get that kind of culling effect
41:27with the treatment groups you were showing
41:30in the survival curves that the,
41:31basically the treatment arm looked worse at first.
41:33<v ->[Dr. Roychoudhury] Yes, I think for a (indistinct),</v>
41:38I think there was a certain group biomarker.
41:42It's again, a heterogeneity of treatment effect.
41:45Certain biomarkers did, I mean,
41:46most of the non-proportional hazard are the same story.
41:49I mean, the certain groups didn't function well
41:51at the beginning until they basically received the treatment
41:54follow up as well.
41:55They actually worse, they were quite a bit.
41:59<v Presenter>Okay, so do you think it's a treatment effect,</v>
42:01not a property of the population that was in it?
42:04<v ->[Dr. Roychoudhury] I think it's, I mean,</v>
42:06it's more of a safety of words I guess I believe.
42:09But of course, it's a road we don't know all the details
42:13inside of it.
42:15But the compound, which is the results which is available
42:17in that paper, it seems like there is an effect
42:20where it's really detrimental, the treatment effect.
42:23(faintly speaking)
42:37<v Presenter>Any other questions?</v>
42:43All right, anything from Zoom land?
42:56<v Attendee>Yeah, I have a question.</v>
42:59So it's interesting to model non-proportional patterns,
43:03but I think maybe another interesting question
43:07is to why there was non-proportional pattern
43:10(faintly speaking), right?
43:11So maybe (faintly speaking).
43:15So say for example if we owe something
43:18like a random voice or like classification,
43:21(indistinct) then we'll be able
43:23to see each subgroup benefits from the treatment
43:27or like why this (faintly speaking)?
43:32(indistinct) comment something else,
43:34like the modeling, the causes or figuring out
43:38why there's non-proportional patterns.
43:40<v ->[Dr. Roychoudhury] Sure, I think what you just said,</v>
43:43that was basically the method, some of five star,
43:47some of the method that more people develop.
43:50(indistinct) and their group did.
43:52They basically looked into a elastic net
43:57to find out the sets were basically you have,
44:01which is heterogeneous.
44:03They divided the group,
44:05this heterogeneous clusters, basically, into that.
44:08And then tried to interpret treatment of problems.
44:11I mean, the major problem is sometimes
44:15those groupings are very hard to interpret.
44:18Because it's so much data driven, right?
44:21And secondly, specify such a method as an analysis
44:25and this is a great method to exploration.
44:27I fully agree.
44:28But if you think about a drug
44:29and kind of a reporting of a drug,
44:32that could be a very risky method to do.
44:34But definitely, they are thinking down on that avenue.
44:37The only reason I think the five star was
44:39a very interesting idea, the only problem really came
44:43in is the estimation of treatment effect
44:45at the end of the day.
44:46Because now, you have a selection, right?
44:49Now you have to have the selection probability incorporated
44:54into the treatment effect.
44:56Some clusters are so small when you put the adjustment
44:59to the selection probability,
45:01it's not very intuitive to non-status station anymore.
45:05But it's been done.
45:07I mean, there are an example,
45:08I think in (indistinct) medicine,
45:10if you search by five star, you can see that.
45:13I think that the major got hit by the interpretation
45:16of the treatment effect.
45:17But you know what they did?
45:19They actually fit a parametric...
45:22First, they did three things.
45:24They looked into each set,
45:26because those population are homogenous.
45:28So they fit the Cox regression model there.
45:31And also they looked into a parametric regression model.
45:35But the only problem is,
45:37as soon as you adjust for your selection probabilities,
45:42if you have a huge effect, right?
45:44The selection probability somehow do a tool on that,
45:50which is clinicians don't find very intuitive, that case.
45:54Because at the end of our regular...
45:56I mean, how do you put such a thing on a drug level?
45:59That is a problem.
46:01But I think such a thing should be done for our...
46:04If we have already face data, we should explore this.
46:07I really think that should be the case.
46:24<v Presenter>Okay, so we don't have any questions.</v>
46:27Let's thanks again.
46:29<v Attendee>Yeah, I have one, just one quick question.</v>
46:32When you're predicting your why,
46:35why not augment that data with publicly available data
46:40based on features like comorbidity, age,
46:43some of the known predictors in terms of survival rates?
46:49<v ->[Dr. Roychoudhury] Absolutely, absolutely.</v>
46:52Sorry, I skipped that.
46:54But that's a great question.
46:57Actually, if we see that, I just wanted to go...
46:59We actually said if you have such a thing,
47:01we just convert this into a regression.
47:04So you can actually,
47:05instead of having just a unstructured model here,
47:08we can actually plug in all the rigorous (indistinct).
47:10But of course then, you don't have (indistinct)
47:13in your family anymore.
47:14It'll be conditionally extensive.
47:16But that's a very easy extension of this.
47:18Yes, absolutely.
47:20Absolutely.
47:27We actually did that for, sorry.
47:31We actually did that for this example
47:33where there's heterogeneous effect by the biomarker.
47:37You basically fill in the regression,
47:40and that's how we operate.
47:42Sorry, I interrupted.
47:43Somebody was...
47:45<v Attendee>Great, thank you.</v>
47:47<v Attendee>Oh, I have another question.</v>
47:50So when you tell the patients
47:51about their predictive treatment effects,
47:54if that affects I'd say how patients attach
48:02to the assigned treatment,
48:07that some way actually affects how you estimate your,
48:14for example, the first step for the estimates.
48:18And does that actually affect the way how you...
48:24Because I think estimation
48:26and also the following steps are actually the different,
48:30for example, the purpose of clinical trial
48:33will be estimation.
48:35But the purpose of, like say telling patients
48:38the individual treatment effects,
48:40a predicted individual treatment effects will be
48:43like a different purpose.
48:44It's not really the estimation for the clinical trial.
48:47Those two can become comfort when you, for example,
48:52using a patient algorithm to update your,
48:54like say marginal distribution.
48:58And then the next step is telling like say patients
49:02about prediction.
49:04And for new patients coming in,
49:06you do the marginal distribution estimation again.
49:13And does that actually pose a little bit of a problem
49:17when prediction actually change people's mind
49:20about their, like say how they attach
49:24to the assigned treatment?
49:25<v ->[Dr. Roychoudhury] Yeah, I think yeah.</v>
49:28That's a very valid question.
49:30I think that's the main reason we needed
49:33this algorithm, right?
49:34And we did not stop just marginally.
49:37But if you look into the new data that's coming in,
49:41of course we need to be careful
49:42because that's not coming from a clinical trial data.
49:47And this one is a more simplified
49:49because the third step was calculated
49:52from clinical trial data,
49:53which is a randomized study.
49:55But if you add more observational data to it,
49:57if I understand how they're touched
49:58and we continue to update that,
50:01it just need to be more careful
50:03about using two different quality of data in that way.
50:07Does that answer your question?
50:11<v Attendee>Sure, thank you.</v>
50:15<v Presenter>Okay, so we are running out of time,</v>
50:19so let's thanks Dr. Roychoudhury again.
50:22Wonderful talk.
50:24<v ->[Dr. Roychoudhury] Thank you.</v>
50:28<v Presenter>Please make sure you sign</v>
50:31the admit sheet.
50:33(attendees chattering continues)
50:53(attendees chattering continues)