Causal mediation analysis and the promise of alpha-DEspR, a preclinical potential COVID-19 treatment in the ICU

Transcript

• 00:00That's important that is important
• 00:02in this application
• 00:04because there are no untreated
• 00:06outcome data in humans or
• 00:09alpha desperate that is the
• 00:11treatment that I will be
• 00:12talking about.
• 00:14Because alpha despa is still
• 00:15in its preclinical
• 00:17phase.
• 00:18It has been tried out
• 00:19in mice. It works really
• 00:21well in mice, and it
• 00:22has also been tried out
• 00:24on petri dishes, these little
• 00:27plastic thingies that they mess
• 00:28around with in the lab,
• 00:30works very well there too.
• 00:32But there is no authorization
• 00:35to use it in humans
• 00:36yet. So we cannot measure
• 00:38our own treatment outcome data
• 00:40yet.
• 00:41We can, however,
• 00:43think that hopefully
• 00:45the the alpha despa has
• 00:47a certain effect on what
• 00:49are called
• 00:50desperate positive
• 00:52neutrophil meds.
• 00:54And from that
• 00:55effect on desperate positive
• 00:58neutrophil meds, we hope to
• 01:00be able to estimate an
• 01:02indirect effect
• 01:04on the final outcome.
• 01:06And that's caused a mediation
• 01:07analysis for you, but then
• 01:09without splitting up an effect,
• 01:11but focusing only
• 01:13on an indirect effect.
• 01:16Why is that important? Because
• 01:17we don't know how Alpha
• 01:19Dashboard will work in humans,
• 01:21and we wanna get a
• 01:22sense of how it works
• 01:24and what we can expect
• 01:26of alphadespir once it will
• 01:28be used in humans,
• 01:30supposing that the only effect
• 01:32that alphadespir
• 01:33has
• 01:34is through those desperate positive
• 01:36neutrophil nets
• 01:38that are actually the target
• 01:39of alpha despa.
• 01:41So what I am going
• 01:42to estimate is the targeted
• 01:44effect, the effect of what
• 01:46the treatment is targeting. It's
• 01:48targeting desperate and positive neutrophil
• 01:50meds, so we are going
• 01:52to look at the effect
• 01:54through the targeted
• 01:56biopsy.
• 01:59Okay. So
• 02:01my talk is causal mediation
• 02:02analysis and the promise of
• 02:04alpha
• 02:05for a preclinical
• 02:06potential COVID nineteen treatment in
• 02:08the ICU.
• 02:09This is an actual treatment
• 02:11except it has not been
• 02:12tried in humans.
• 02:17So typically,
• 02:18direct and indirect effects are
• 02:20used to separate a total
• 02:23effect. And so I let
• 02:24let me first introduce that
• 02:26to you. It's used because
• 02:28the mediation analysis separates the
• 02:30effect
• 02:31into
• 02:32a part that is oh,
• 02:33this doesn't work. A part
• 02:35that is mediated through covariant
• 02:37m, that's the indirect effect,
• 02:39and the part that is
• 02:40not, and that is the
• 02:41direct effect. It works through
• 02:43other pathways.
• 02:45For example, the treatment could
• 02:46be a blood pressure lowering
• 02:48medication.
• 02:49The outcome could be heart
• 02:51attack, yes or no, maybe
• 02:52within five years or so.
• 02:54And then we can think
• 02:56how much of the effect
• 02:57of the blood pressure lowering
• 02:59medication a is mediated by
• 03:01the effect it has on
• 03:02blood pressure m
• 03:04and how much
• 03:05works,
• 03:06if any, works through other
• 03:08pathways.
• 03:09So also in this case,
• 03:10you see that there is
• 03:12an intended effect, a targeted
• 03:14effect
• 03:15that is the effect of
• 03:16blood pressure
• 03:17lowering medications working through blood
• 03:20pressure,
• 03:20but there may also be
• 03:22other effects.
• 03:25And here is my example
• 03:27that is also my application
• 03:30Alpha desperate,
• 03:31the preclinical
• 03:32pro potential COVID nineteen treatment
• 03:35in the ICU
• 03:36has been shown to eliminate
• 03:39desperate positive
• 03:40neutrophil meds
• 03:41in rats
• 03:43and in petri dishes. Actually,
• 03:44I'm not sure it's rats
• 03:45or mice. I have on
• 03:46my list of to do
• 03:47things to figure it out,
• 03:48but these little small animals
• 03:49that we don't like in
• 03:50our house.
• 03:51So if alpha despera also
• 03:53eliminate despera positive neutrophil meds
• 03:56in humans,
• 03:57What is its indirect effect
• 03:59on the SOFA score ICU
• 04:01discharge and it's her outcome
• 04:03y
• 04:04that is mediated
• 04:06through Desperative Neutrofel
• 04:08NETs?
• 04:09So we have here an
• 04:10outcome that is measured at
• 04:12the end of the study.
• 04:13They also assign
• 04:15a SOFA score,
• 04:17if a person is not
• 04:18discharged alive. So if people
• 04:21die in the hospital, that
• 04:22happens when we're talking about
• 04:24ICU data,
• 04:25and then assign a score
• 04:27to people who died as
• 04:28well.
• 04:32Another application I have been
• 04:34working on also is,
• 04:36there are several potential preclinical
• 04:39HIV
• 04:40cure treatments,
• 04:41and they typically target the
• 04:43HIV HIV
• 04:45reservoir.
• 04:46And there are several measures
• 04:47of the HIV reservoir that
• 04:49they may target,
• 04:50and we can try to
• 04:51figure out what is the
• 04:52indirect effect
• 04:54of HIV curative treatment on
• 04:57long term outcomes
• 04:59mediated by their
• 05:01the HIV reservoir. And also
• 05:03here you see it's the
• 05:04the effect that is targeted.
• 05:07And you see often in
• 05:08causal mediation analysis that that
• 05:11indirect effect that goes to
• 05:12that pathway
• 05:14treatment to mediator
• 05:16treatment
• 05:17to mediator through outcome
• 05:19that is often the intended
• 05:21pathway
• 05:22for which the drug is
• 05:23designed.
• 05:25So what is the effect
• 05:26of an HIV curative treatment
• 05:28a on viral rebound? Why
• 05:30viral rebound is how good
• 05:32the treatment works long term
• 05:34mediated through the HIV repertoire.
• 05:38That's not my application today.
• 05:42The seminal article on mediation
• 05:44analysis that has been cited,
• 05:47a zillion times, not a
• 05:48zillion, one hundred thirty nine
• 05:50thousand something yesterday,
• 05:53in Google Scholar, and many
• 05:54of these are from the
• 05:55last ten years. So calls
• 05:57to mediation analysis has been
• 05:58boy booming. Maybe I shouldn't
• 06:00say causal mediation analysis. Maybe
• 06:02I should say mediation analysis
• 06:05because Baron and Kenny did
• 06:06not exactly
• 06:07popularize causal mediation analysis, but
• 06:10just look at half its.
• 06:13Mediation analysis is very important
• 06:15in the health sciences, psychology,
• 06:17epidemiology,
• 06:18space places like that. And
• 06:21it is very important to
• 06:22know the kinds of assumptions
• 06:23that we're making when this,
• 06:25when we do these conclusions.
• 06:27And I like this citation
• 06:28from Jamie Robinson,
• 06:30Thomas Richardson.
• 06:31They are much my senior,
• 06:32so they can say this.
• 06:34I can't, although I do
• 06:35happen to this happen to
• 06:36agree with them.
• 06:38The nature of the relationship
• 06:39between the senses expressing these
• 06:41causal conclusions
• 06:43and the statistical computer calculations
• 06:45performed on the string of
• 06:47numbers
• 06:48has been obscure.
• 06:50In other words, causal mediation
• 06:53analysis is much more disputed
• 06:56than other
• 06:57types of causal inference
• 07:00and I will tell you
• 07:01why later.
• 07:03There are quite a number
• 07:05of people who like causal
• 07:06inference but who don't want
• 07:08to do causal mediation analysis.
• 07:10You may have met them.
• 07:12So the setting and the
• 07:13notation, randomized treatment a, that
• 07:16can be relaxed, but that
• 07:17is not the subject of
• 07:18this talk.
• 07:20Pre treatment common causes of
• 07:22the mediator m and the
• 07:24outcome y. I'm assuming here
• 07:26we have them all and
• 07:28I call them c for
• 07:29common causes.
• 07:31And I'm assuming that there
• 07:32are no cross treatment common
• 07:34causes of the mediator
• 07:35m and the outcome y.
• 07:37And the reason is that
• 07:39things get complicated in that
• 07:40case. I have some work
• 07:42on it, but that needs
• 07:43to do data sample reports
• 07:44with Ohio Tech.
• 07:47I use as usual a
• 07:49superscript zero to say without
• 07:51treatment. So zero is no
• 07:53treatment. Superscript one indicates under
• 07:56treatment.
• 08:00So then we have the
• 08:01following causal diagram.
• 08:03Wouldn't call it that bad
• 08:04because and then they get
• 08:05in trouble with some people.
• 08:07So we have here the
• 08:08treatment.
• 08:09It may affect the mediator,
• 08:11which in turn may affect
• 08:13the outcome.
• 08:14So this path from a
• 08:16to m to y, that
• 08:17is the indirect effect.
• 08:19And there could be effects
• 08:21through other pathways. Those go
• 08:23around the mediator,
• 08:24and the that is called
• 08:26the direct effect.
• 08:31Effect. And my recurring
• 08:33example,
• 08:34alpha despora,
• 08:36that is the treatment that
• 08:38I'm interested in.
• 08:39And I, that is the
• 08:40mediator that I'm interested in.
• 08:42In this case, it's desperate
• 08:44positive neutrophil nets. It's a
• 08:45mouthful, but they're really pretty.
• 08:47They make really pretty pictures
• 08:49of these nets, and then
• 08:50they are able to count
• 08:51them. And it's a whole
• 08:53big process.
• 08:54So the datasets that I'm
• 08:56using in this project are
• 08:57small. There are like thirty
• 08:58four patients or thirty five.
• 09:01There are few because it
• 09:02takes a ton of time
• 09:03to make these beautiful pictures
• 09:04and then to count all
• 09:06these nets.
• 09:08Final outcome is the SOWFA
• 09:10score and ICU
• 09:12discharge. It's a measure of
• 09:14multi organ failure
• 09:16that is typically used in
• 09:17the ICU
• 09:19and again, they also assign
• 09:20a score if a patient
• 09:22dies.
• 09:24And then there is a
• 09:25common cause of the mediator
• 09:27and the outcome. So the
• 09:28mediator is the desperate positive
• 09:30neutrophil nets. The outcome is
• 09:31the SOWFA score at ICU
• 09:33discharge.
• 09:34And this common cause that
• 09:36we have been using
• 09:38is the SOWFA score at
• 09:40ICU admission or close to
• 09:42ICU admission.
• 09:43It is a measure of
• 09:45how well a person is
• 09:46doing when they enter the
• 09:48ICU.
• 09:49It's also, again, the the
• 09:51score of multi organ failure.
• 09:56So what I'm interested in
• 09:57especially is the effect of
• 09:59alpha desprud
• 10:01that affects the desprud positive
• 10:03neutral film that's in turn
• 10:04the SOWFA score. So I'm
• 10:05mainly going to estimate the
• 10:07indirect effect
• 10:08because it turns out I
• 10:10cannot do the direct effect.
• 10:15I like Baron and Kanesho.
• 10:17I wanted to put that
• 10:18up also.
• 10:20Suppose the model for m
• 10:21given a is a linear
• 10:22model where the mean of
• 10:24the mediator given the outcome
• 10:25is just, you have two
• 10:27different means, one for treated
• 10:28and one for untreated.
• 10:30And then the model for
• 10:31the outcome given the mediator
• 10:34and the treatment
• 10:36is also a linear model,
• 10:38can depend on the treatment
• 10:39and it can depend on
• 10:40the mediator.
• 10:41And then what, Baron and
• 10:43Kenny say is that the
• 10:45effect
• 10:46that is mediated
• 10:48is first alpha one so
• 10:49that you get the different
• 10:51mediator.
• 10:52And then in the next,
• 10:53you see that the different
• 10:54mediator causes beta two alpha
• 10:57one on average.
• 10:58So that's how they motivate
• 11:01their alpha one beta two.
• 11:03They don't use causal mediation
• 11:06analysis notation
• 11:08with counterfactual
• 11:09outcomes, or even maybe,
• 11:11crossroads
• 11:12counterfactuals.
• 11:13Nothing of that. They just
• 11:15say, look, we had this
• 11:16mediator goes and it makes
• 11:18it alpha one bigger.
• 11:19The treatment goes, makes the
• 11:21mediator alpha one bigger, and
• 11:23then look at this model
• 11:24that causes is beta two
• 11:25times alpha one.
• 11:28And then when they say
• 11:29the direct effect is whatever
• 11:30is left, and you can
• 11:32show in these models that
• 11:33that is just beta one.
• 11:35That's the difference between the
• 11:37total effect
• 11:38you can also get from
• 11:39these things
• 11:40and the indirect effect.
• 11:45Most applications of causal mediation
• 11:47analysis
• 11:48estimate natural
• 11:49indirect effects. Those have really
• 11:52been booming.
• 11:53You see that there is
• 11:54not that many applications
• 11:56of other approaches to causal
• 11:58mediation analysis.
• 12:00Well, they will go on
• 12:01to apply causal mediation analysis,
• 12:04find a package online, and
• 12:06typically say, I want the
• 12:08natural indirect and direct effects.
• 12:11And I will argue that
• 12:12that is not always the
• 12:13way to go, but,
• 12:15let's let's see why.
• 12:18The building blocks for natural
• 12:20direct and indirect effects
• 12:22are the outcome,
• 12:23but under treatment,
• 12:25be the mediator set to
• 12:27its failure without treatment.
• 12:31Okay? So is the outcome
• 12:33under treatment had the mediator
• 12:35been set to its value
• 12:37without treatment.
• 12:40And then the natural direct
• 12:42effect you see here maybe
• 12:44I should stand here so
• 12:45that the people online can
• 12:47also see what I point
• 12:48to.
• 12:50So here you have the
• 12:51mediator under no treatment.
• 12:53Here you also have the
• 12:54mediator under no treatment. Right?
• 12:56Because these are untreated people.
• 12:58They don't know are not
• 12:59messing with their mediator specifically.
• 13:01So it's mediator under no
• 13:03treatment versus mediator under no
• 13:05treatment,
• 13:06but treated versus untreated. So
• 13:08that's the direct effect that
• 13:09works to other pathways that
• 13:11are not n.
• 13:14And here we have the
• 13:15outcome here. The mediator is
• 13:17mediator under treatment because we're
• 13:19not messing with it and
• 13:20we are treating these people.
• 13:21So it's mediator under treatment
• 13:23versus mediator under no treatment.
• 13:27All these people are treated,
• 13:29both these ones are treated
• 13:30and these ones are treated,
• 13:31but it's m one
• 13:33versus m zero.
• 13:35So this is the indirect
• 13:37effect. This goes through the
• 13:39pathway through the mediator.
• 13:42And that's the kind of
• 13:43mediation analysis that most people
• 13:45are applying.
• 13:47It's maybe not
• 13:48the mediation causal mediation analysis
• 13:50that you see the most
• 13:51theory papers on.
• 13:56So suppose treatment is randomized,
• 13:58then estimation of the expectation
• 14:00of the outcome under treatment
• 14:01is very easy. You just
• 14:03did the average in the
• 14:04treated group.
• 14:06So then you need to
• 14:07still for,
• 14:08an indirect and direct effect
• 14:10because, look, they are based
• 14:11on this
• 14:13on this expectation of y
• 14:15one and zero.
• 14:16We still need to
• 14:18estimate
• 14:19the expected outcome under treatment
• 14:22with the mediator set to
• 14:23its value without treatment.
• 14:26And there,
• 14:27is a, what is called
• 14:28the mediation
• 14:30formula.
• 14:31So that says first,
• 14:34the
• 14:35common causes come about.
• 14:37Then the mediator comes about
• 14:39given the common causes
• 14:41according to its distribution under,
• 14:44under a is equal to
• 14:45zero, which makes sense.
• 14:48And then after that, you
• 14:49get the expected
• 14:50outcome
• 14:51given that common calls and
• 14:53given the mediator that we
• 14:54just had had had the
• 14:55distribution of, but they come
• 14:57about under a is equal
• 14:59to one, which also makes
• 15:00sense because you see a
• 15:02one there.
• 15:03So when the first time
• 15:04when I saw this mediation
• 15:06formula, I was like, okay,
• 15:07that's cool. I understand that.
• 15:08That seems nice. And then
• 15:10I was told, well, actually
• 15:11to prove that, you need
• 15:13a lot of assumptions and
• 15:15there's a lot of mess
• 15:16going around behind the scenes.
• 15:21So I will tell you
• 15:22a little bit of that
• 15:23mess that comes around behind
• 15:24the scenes, but not until
• 15:26I say, well, actually, if
• 15:28there is no treatment mediator
• 15:31interaction in the outcome model,
• 15:32so this outcome model, the
• 15:34expectation
• 15:35of y
• 15:36given m and a doesn't
• 15:38have
• 15:39some kind of parameter times
• 15:41a times m. It's just
• 15:44a, parameter times m plus
• 15:46other term parameters times
• 15:48a,
• 15:49then the resulting,
• 15:52indirect effect
• 15:53is actually the same as
• 15:55the one that was proposed
• 15:56by Varun and Kemi.
• 15:59It turns out if there
• 16:00is an interaction between treatment
• 16:02and the mediator in that
• 16:04outcome model,
• 16:05that there there is a
• 16:07difference between the two approaches.
• 16:09And this has actually been
• 16:11used by causal inference people
• 16:13to say that Baron and
• 16:14Kenny got it wrong.
• 16:16And this is something with
• 16:17which I personally completely
• 16:19disagree with because I do
• 16:21not think I got it
• 16:22wrong.
• 16:23I think we have to
• 16:24think carefully
• 16:25about what we want.
• 16:27And, there I mean, do
• 16:29we want to set the
• 16:31mediator to its value without
• 16:33treatment,
• 16:34or do we want to
• 16:35set the mediator to its
• 16:37value with treatment?
• 16:39And depending on the application,
• 16:41the one is of interest
• 16:42or the other is of
• 16:43interest.
• 16:45If we set the mediator
• 16:47to its value with treatment,
• 16:50suddenly get it right.
• 16:52In other words, if we
• 16:53start missing out with what
• 16:55we call treatment and what
• 16:56we call control,
• 16:58then sometimes Baron and Kenny
• 16:59get it right and sometimes
• 17:01they get it wrong.
• 17:03In other ways, they are
• 17:04after
• 17:05both
• 17:07by causal inference people have
• 17:09been called the pure indirect
• 17:12effect.
• 17:13And then you look at
• 17:14their
• 17:16interpretation
• 17:17that I just showed you,
• 17:18that is also more in
• 17:20line with the pure indirect
• 17:21effect
• 17:22than it is with a
• 17:23natural indirect effect.
• 17:27Okay. So
• 17:28under certain conditions, strong parametric
• 17:30assumptions, linear models, and no
• 17:32exposure mediator indirection, they do
• 17:35get the same as Baron
• 17:36and Kenny. And so they
• 17:38add a causal interpretation
• 17:39to that,
• 17:41line of research, which is
• 17:42very important
• 17:44because you saw how many
• 17:45citations that got.
• 17:48It's important to underpin that
• 17:50also from a causal perspective.
• 17:52Most methods need many quantifiable
• 17:55outcomes. They use the come
• 17:57on their treatment with the
• 17:58mediator set which value without
• 18:00treatment,
• 18:01and I don't haven't seen
• 18:02many causal inference approaches
• 18:05that don't also talk about
• 18:06the outcome
• 18:08on their treatment
• 18:09where the mediator sets to
• 18:11any very particular
• 18:12value of the mediator.
• 18:16And this requires
• 18:17that you can set the
• 18:18mediator,
• 18:20which you can sometimes do
• 18:21but sometimes also not.
• 18:25So the first thing is,
• 18:27so when we talk about
• 18:28these counterfactual
• 18:30outcomes, they are called cross
• 18:31rules
• 18:32counterfactuals
• 18:33because we are talking out
• 18:35about the mediator that is
• 18:36set to its value without
• 18:37treatment
• 18:38while a person is treated.
• 18:41So even if we could
• 18:42set the mediator, we don't
• 18:43typically know how to set
• 18:44it or where to set
• 18:46it because we don't if
• 18:47we treat the person, we
• 18:49don't observe their mediator under
• 18:51under no treatment, so we
• 18:52don't know where to set
• 18:54it. And
• 18:55but this is this is
• 18:56what has been generally in
• 18:58the postural inference literature
• 19:00being attacked
• 19:01to the
• 19:02to the,
• 19:04natural indirect effect approach.
• 19:07But what I find actually
• 19:09more bothersome
• 19:10is that in many cases,
• 19:11we cannot set a mediator.
• 19:14When you look at the
• 19:15first paper that Judea Pearl
• 19:17published on causal mediation analysis,
• 19:20his example is a mediator
• 19:23aspirin
• 19:25and aspirin use was more
• 19:27common
• 19:28under treatment than under no
• 19:30treatment because aspirin use was
• 19:32you, aspirin was used
• 19:34to
• 19:35make sure that the side
• 19:37effects of the treatment were
• 19:38not too heavy because the
• 19:40treatment treatment con
• 19:42resulted in headaches,
• 19:44and so the aspirin was
• 19:46used to treat the headaches.
• 19:48About then, the effect of
• 19:49the treatment was mediated through
• 19:52the aspirin dose, which was
• 19:53helpful,
• 19:54but was not the was
• 19:56not really the intended effect
• 19:58of the treatment.
• 19:59So they wanted to figure
• 20:00out how much of the
• 20:01effect of the original treatment
• 20:03will work through the aspirin
• 20:05use and how much of
• 20:06the treatment effect works through
• 20:08our pathways.
• 20:10But our pathways were in
• 20:11this case actually the intended
• 20:13effect.
• 20:15But there are other settings,
• 20:16and that includes my HIV
• 20:19example,
• 20:20where the,
• 20:21where the
• 20:23mediator is the HIV reservoir.
• 20:26Now if you were able
• 20:27to set the HIV
• 20:28reservoir,
• 20:30HIV research would be down
• 20:33there. We're we're ready because
• 20:35if we can set the
• 20:37HIV reservoir,
• 20:39we're going to set it
• 20:40to zero,
• 20:41and all these patients are
• 20:43suddenly cured of HIV.
• 20:46And,
• 20:48hypothetically,
• 20:49this is awesome. In practice,
• 20:51it doesn't doesn't work because
• 20:52there are no treatments that
• 20:54set the HIV reservoir.
• 20:56People are really trying very
• 20:58hard to reduce it.
• 21:00But even if they can
• 21:01reduce it, they can probably
• 21:03not set it to any
• 21:04particular value. They'll be able
• 21:06to change the distribution,
• 21:08but they are not able
• 21:09to set it to a
• 21:10particular value.
• 21:12So I I don't usually
• 21:14know
• 21:14how to set that mediator,
• 21:16how to how to internalize
• 21:19that.
• 21:20So how to set the
• 21:21mediator is usually left unanswered.
• 21:23Outcomes are undefined in many
• 21:25many practical situations.
• 21:28Colin Frankakis provide an illustrative
• 21:30example.
• 21:31There are many competing
• 21:33ways to assign hypothetically
• 21:35a body mass index of
• 21:37twenty five kilograms per square
• 21:39meter to an individual,
• 21:41and each of them may
• 21:42have a different effect, causal
• 21:44effect
• 21:44on me.
• 21:47You can think of very
• 21:48extreme ways
• 21:50to reduce their body mass
• 21:52index.
• 21:57So people have been trying
• 21:58to get around these couch
• 22:00the these crossroads counterfactuals.
• 22:03I haven't seen many approaches
• 22:05that also try to
• 22:06get out of,
• 22:08out of these ones.
• 22:10My approach also tries to
• 22:11get out of these ones
• 22:12because I want to apply
• 22:14to these HIV examples, to
• 22:16the COVID nineteen example where
• 22:18we cannot set them in
• 22:19use.
• 22:22So I have been proposing
• 22:23organic direct and indirect effects
• 22:25that I will tell you
• 22:26about.
• 22:27It can be shown that
• 22:28they are a generalization
• 22:30of randomized direct and indirect
• 22:32effects.
• 22:34And they're also
• 22:35most likely, I have the
• 22:37proof for that, but not
• 22:38published.
• 22:39There are also a generalization
• 22:41of separable, direct, and indirect
• 22:43effects that are also around
• 22:44the literature.
• 22:45So I will tell you
• 22:46what those are, the organic
• 22:48indirect and direct effects.
• 22:50So I as an intervention
• 22:52on the mediator that is
• 22:53not that doesn't affect the
• 22:55pretreatment common causes of the
• 22:57mediator m and the outcome
• 23:00y.
• 23:01And then I'm going to
• 23:02talk about
• 23:03the mediator
• 23:05under no treatment but with
• 23:06the intervention
• 23:08and the outcome under no
• 23:09treatment but with the intervention.
• 23:13It's an intervention on the
• 23:14mediator.
• 23:17And then I define something
• 23:19as an organic intervention
• 23:21If under the intervention,
• 23:23the mediator has the same
• 23:24distribution as the mediator under
• 23:26the treatment
• 23:29given the common causes, you
• 23:30have to always respect the
• 23:31common causes.
• 23:34And then the other condition
• 23:36for an organic intervention
• 23:38is that once the mediator
• 23:40comes about under the intervention,
• 23:44then it doesn't matter how
• 23:46that
• 23:47mediator comes about under the
• 23:49intervention.
• 23:50After this, the outcomes
• 23:52follow their natural course as
• 23:55though that mediator equals m
• 23:57came about naturally under no
• 23:59treatment.
• 24:02So after the mediator comes
• 24:04about under the intervention,
• 24:06the system follow its natural
• 24:08course as though the mediator
• 24:10came about
• 24:11without treatment. The expected outcome
• 24:13is the same. I have,
• 24:14in the past, sometimes even
• 24:15have a vaguely sign language,
• 24:16but the distribution
• 24:17is the same. The only
• 24:19thing that you really need
• 24:20is the expected value that's
• 24:21the same.
• 24:23So after I effects the
• 24:24mediator,
• 24:26the system follows its natural
• 24:27course as though the mediator
• 24:29value came about with no
• 24:30treatment a is equal to
• 24:32zero. And for the system
• 24:33to know where it has
• 24:34to go,
• 24:35you need to condition on
• 24:37the common causes
• 24:39because otherwise the system will
• 24:41go wherever it will ignore
• 24:42common causes and then you
• 24:44don't really truly know where
• 24:45it wants to go.
• 24:48For example, a is equal
• 24:49to one is the blood
• 24:50pressure lowering medication
• 24:52and blood pressure by the
• 24:53occurrence of a heart attack.
• 24:55Does a is one have
• 24:56a direct havoc on heart
• 24:58attacks?
• 24:59Well, for example, blood pressure
• 25:00lowering medication, so this could
• 25:02be the distribution of the
• 25:03blood pressure,
• 25:04then maybe it's just a
• 25:05shift of the blood pressure
• 25:08distribution, the treatment.
• 25:09So the intervention also has
• 25:11to be a shift in
• 25:12the distribution
• 25:13of the blood pressure and
• 25:15maybe we could
• 25:17think of this as, as
• 25:19a salt reduction because that
• 25:20also changes the blood pressure
• 25:22distribution.
• 25:24And then
• 25:25after that, it has to
• 25:26be that,
• 25:29the heart attacks follow their
• 25:31course as though that reduced
• 25:32blood pressure came about without
• 25:36the treatment or without
• 25:38the Schult.
• 25:41And it turns out that
• 25:43Schult is believed to have
• 25:44an effect on on heart
• 25:46attacks only through its effects
• 25:48on blood pressure. You can
• 25:49look it up in the
• 25:50CDC website.
• 25:52And so maybe we can
• 25:53affect and we can we
• 25:55can think
• 25:56that once the blood pressure
• 25:57has been lowered by the
• 25:59salt reduction,
• 26:01that after that, it is
• 26:02just as though the blood
• 26:03pressure came about without the
• 26:05salt reduction.
• 26:07So what does salt reduction
• 26:09do? It has no direct
• 26:10effect on heart attacks according
• 26:11to the CDC.
• 26:13It affects blood pressure and
• 26:14the same as a is
• 26:15equal to one does. So
• 26:17its effect should be the
• 26:18effect of a is equal
• 26:19to one mediated through the
• 26:21blood pressure. So that's the
• 26:23idea of an organic intervention.
• 26:25It affects
• 26:26the mediator the same way
• 26:28as the treatment does, but
• 26:29after that, the system follows
• 26:31its natural course
• 26:32as though that mediator came
• 26:34about without treatment.
• 26:39And then you can define
• 26:41the indirect effect. So here
• 26:42we have the mediator distribution
• 26:45is the distribution of m
• 26:47one under the intervention.
• 26:48Here we have m zero
• 26:50itself. So this is the
• 26:51mediated effect.
• 26:53And here we have the
• 26:55mediator distribution
• 26:57is m one. The mediator
• 26:59distribution
• 27:00is m one, but with
• 27:01or without treatment, so that
• 27:03is the direct effect.
• 27:04And then maybe what you
• 27:06can think of is that
• 27:07maybe this is not a
• 27:08good definition
• 27:10because we are doing it
• 27:11relative to c.
• 27:14But you can show
• 27:17so
• 27:18and so I can my
• 27:19first is, I can be
• 27:20seen as a hypothetical intervention
• 27:22to phrase the question, what
• 27:23if the mediator distribution changes
• 27:25according to treatment a is
• 27:27equal to one? And after
• 27:28that, the system follow its
• 27:30natural course
• 27:31as though the mediator
• 27:33value came about without treatment.
• 27:37And then there's another this
• 27:38is the consistency assumption. When
• 27:40we treat someone, we measure
• 27:41their treatment treated outcome and
• 27:43mediator,
• 27:44and under no treatment, we
• 27:46measure the untreated mediator and
• 27:48outcome. And only under that,
• 27:50so now all these assumptions
• 27:52that natural indirect effects are
• 27:53based on, you own you
• 27:55you need nothing more than
• 27:57the definition of organic intervention
• 27:59and this consistency
• 28:01assumption
• 28:01to write down the mediation.
• 28:05If you're interested,
• 28:06at the end of the
• 28:07talk, I can give you
• 28:08the proof. It's
• 28:10very
• 28:11short.
• 28:14So it's and and and
• 28:17what I try to do
• 28:18here with this organic intervention
• 28:20is read off the results
• 28:21from the mediation formula to
• 28:22get a sense of what
• 28:23we want and also to
• 28:25follow Baron and Kenny
• 28:26before because first, the mediator
• 28:29comes about according to its
• 28:30distribution under treatment. That's my
• 28:32first condition for organic intervention.
• 28:35And then the outcome comes
• 28:37about under treatment.
• 28:38It's the second
• 28:40condition of organic intervention. So
• 28:42it's just read off of
• 28:43the mediation
• 28:44formula
• 28:45because the the first time
• 28:46I saw the mediation formula,
• 28:47I was like, that is
• 28:48really cool.
• 28:49So I wanted that formula
• 28:51but without those extra assumption.
• 28:56So without common including common
• 28:58causes, the system doesn't know
• 28:59where it can where it
• 29:00has to go.
• 29:01I have proven that if
• 29:04you include all common causes
• 29:05of the mediator and the
• 29:07outcome,
• 29:08then these organic indirect indirect
• 29:10effects are uniquely defined.
• 29:14And this is a definition
• 29:15and stuff. So what I
• 29:16want to do now is
• 29:18apply this idea
• 29:21to,
• 29:21alpha despa.
• 29:23So,
• 29:24the organic indirect effects can
• 29:26be estimated with the distribution
• 29:28of the mediator on the
• 29:29treatment
• 29:30and under no treatment,
• 29:32and the expectation of the
• 29:33outcome given the mediator and
• 29:35pretreatment covariates
• 29:37only under no treatment.
• 29:39And that comes from the
• 29:41mediation formula. If you can
• 29:42go back to the mediation
• 29:44formula.
• 29:45Look. The indirect effect is
• 29:47going to be this one
• 29:48minus the expectation of the
• 29:50untreated
• 29:52outcome.
• 29:54The untreated outcome, I can
• 29:56estimate the mean without on
• 29:57treat without outcome beta because
• 29:58it's the untreated outcome. And
• 30:00look at this formula.
• 30:02It has only expectation of
• 30:04y given a is equal
• 30:05to zero. There's no treated
• 30:08outcomes in this formula.
• 30:10People typically
• 30:11model
• 30:12the outcome given the mediator
• 30:14and the treatment,
• 30:16but there's no need to
• 30:17do that. It would be
• 30:18borrowing strength
• 30:20from treated outcomes
• 30:22to make more precision happen
• 30:24under more assumptions.
• 30:26But if you only have
• 30:28untreated
• 30:29outcome data, that's enough to
• 30:31use the negation formula in
• 30:33this case. And that is
• 30:34because I've been working with
• 30:36the outcome under no treatment
• 30:38but an intervention on the
• 30:40mediator instead of the outcome
• 30:42under treatment
• 30:43with an intervention on the
• 30:45mediator.
• 30:46So this is the an
• 30:47analog of a pure indirect
• 30:49effect
• 30:50where I look at untreated
• 30:52mediator
• 30:53under treatment
• 30:55instead of treated
• 30:57and
• 30:58untreated mediator.
• 31:02Okay.
• 31:03So if we do that,
• 31:05we don't need treated outcomes
• 31:07to estimate an indirect effect.
• 31:11And I will show you
• 31:12how that helps in a
• 31:14preclinical
• 31:14stage.
• 31:16So this is the
• 31:17oh, let's take this out
• 31:19of the way.
• 31:20Yeah. So,
• 31:21this is
• 31:23the graph that my clinical
• 31:25collaborators
• 31:26came me first time I
• 31:27met them.
• 31:29They wanted causal mediation analysis,
• 31:31and they had been told
• 31:32by the NIH and by
• 31:33the reviewers of their paper,
• 31:35you need a statistician.
• 31:38And so when they went
• 31:39on the BU website, who
• 31:41is a statistician
• 31:42at BU who knows about
• 31:43causal mediation analysis,
• 31:45There's not.
• 31:47So they ended up with
• 31:48me, and they were like,
• 31:49we want to do causal
• 31:50mediation analysis, and this is
• 31:52what we want to do.
• 31:53The effect of SOFA one
• 31:56mediated by positive
• 31:58neutrophil nets
• 32:00on the SOFA score at
• 32:01ICU discharge.
• 32:04And it took me a
• 32:05while before I could interpret
• 32:07that SOFA score at baseline
• 32:09as a treatment because for
• 32:10me that was a conveyor
• 32:12not a treatment.
• 32:13But they see it as
• 32:14a measure of how much
• 32:16badness
• 32:18each patient has been exposed
• 32:20to.
• 32:21So for them, it's a
• 32:23measure of exposure.
• 32:25How much badness has this
• 32:27patient been exposed?
• 32:29And they wanted this, and
• 32:30I gave them this. It's
• 32:31a multi it's a continuous
• 32:33exposure, so it's a little
• 32:34bit complicated,
• 32:35but you can do it.
• 32:37But after two or three
• 32:38meetings, I was like, I'm
• 32:40fine.
• 32:41Why?
• 32:42Why do you want this?
• 32:45And it turned out what
• 32:46they wanted actually was, well,
• 32:48if we have this and
• 32:50it's mediated,
• 32:52then that's a measure
• 32:53that also alpha desperate, that's
• 32:56our treatment, our
• 32:57prekinable treatment that we hope
• 32:59to bring on the market
• 33:00someday, that actually affects
• 33:03the
• 33:04the despa positive neutrophil nets.
• 33:06And if it me if
• 33:08the despa positive neutrophils fit,
• 33:10neutrophil mediate
• 33:12so far so far too,
• 33:14then that's an indication that
• 33:16maybe our treatment does something.
• 33:17And then I was like,
• 33:19ah, but I know a
• 33:20thing or two about false
• 33:21remediation analysis.
• 33:23So why don't we look
• 33:24at this graph?
• 33:27And they were like, can
• 33:28we?
• 33:30Yeah, we can. I published
• 33:32something on this
• 33:34similar
• 33:35for HIV curative treatment in
• 33:37epidemiology in twenty twenty one
• 33:39together with a collaborator and
• 33:41we looked at hypothetical,
• 33:44interventions on the HIV reservoir,
• 33:46hypothetical
• 33:47reductions
• 33:48of the HIV reservoir.
• 33:50But in your case, it's
• 33:51not even hypothetical,
• 33:55effects on the on the
• 33:57desperate positive movement from that.
• 33:58You actually have done this
• 34:00in animal studies and feathery
• 34:02dishes, so you have a
• 34:03clear hope for what that
• 34:05effect on the mediator is
• 34:07gonna be.
• 34:08So yes, we can do
• 34:09causal mediation
• 34:10causal mediation analysis
• 34:12really for alpha desperate itself
• 34:14as well and that got
• 34:16them excited so we added
• 34:17this to their paper.
• 34:19So we have alpha desperate,
• 34:21it affects desperate positive neutrophil
• 34:23nets in turn, hopefully, the
• 34:25SOWFA score and ICU discharge.
• 34:28Now this made it very
• 34:30easy to come up with
• 34:31a common cause because,
• 34:33look,
• 34:34there is a common cause
• 34:35of MMI. You see that?
• 34:37It's it's so far one.
• 34:38It now becomes a common
• 34:39cause.
• 34:40Not a treatment anymore. It
• 34:41becomes a common cause. So
• 34:43we need that common cause
• 34:44because that's what they started.
• 34:47Okay. So the indirect effect
• 34:49is here,
• 34:51and the direct effect is
• 34:52something that I cannot get
• 34:53my hands on until they
• 34:55get permission to actually try
• 34:57this treatment out in human
• 34:58beings.
• 35:02So we investigated the progress
• 35:03of alpha despa by estimating
• 35:05its indirect effect mediated
• 35:07by despa positive neutrophil nets,
• 35:11assuming,
• 35:12as was shown in animal
• 35:13studies and peckerly dishes,
• 35:15that alpha despa
• 35:18eliminates
• 35:18this propositive
• 35:20looping terms. Completely invented.
• 35:22We can do it otherwise.
• 35:23We can say it has
• 35:25or whatever kind of stuff,
• 35:26but I really think it
• 35:27will eliminate, so we will.
• 35:31So what can we expect
• 35:32if alpha desperate eliminates this
• 35:34positive neutral film nets and
• 35:36after that the body
• 35:38system follows its natural course
• 35:40as though alpha desperate was
• 35:42not the cause
• 35:44of the absence of desperate
• 35:46positive neutrophil mats.
• 35:49And this is something that
• 35:50we can estimate.
• 35:52And this was published
• 35:54in,
• 35:56in in, in a paper
• 35:58together with,
• 35:59in my clinical collaborate.
• 36:03So we don't have alpha
• 36:04and s for outcome measures
• 36:06net
• 36:07yet.
• 36:09So what we did is
• 36:10just use the core the
• 36:12mediation formula.
• 36:13We get the expected
• 36:15outcome with it. So we
• 36:17get the expected out the
• 36:18mediation for maybe oh, we
• 36:20don't have one. So
• 36:23let's go back to mediation
• 36:24form.
• 36:27So we need to do
• 36:28this. So first, the common
• 36:30goal is that it's the
• 36:31SOFA score. Right?
• 36:33And then we need the
• 36:34distribution of the mediator
• 36:36under,
• 36:37under alpha dash prop zero
• 36:39zero zero
• 36:41zero zero. So that's that's
• 36:42fine. It's a it's a
• 36:43point mass.
• 36:44And then we get the
• 36:45outcome,
• 36:46the SOFA score given that
• 36:48there is no that's proper
• 36:50positive filter fill nets, given
• 36:51the SOFA score and under
• 36:54a is equal to zero,
• 36:55then we do have outcome
• 36:56data under a is equal
• 36:57to zero. It
• 37:01back.
• 37:06So the outcome under no
• 37:07treatment, that's just their outcome
• 37:09because they don't have treatment.
• 37:11And the other one, we
• 37:13need
• 37:14to
• 37:14do average over the distribution
• 37:16of the c. So we
• 37:17just get mass one over
• 37:18m to each of the
• 37:19c's.
• 37:20And so that is the
• 37:22empirical
• 37:23distribution function of the c's.
• 37:24Just get mass one over
• 37:26m to each of them.
• 37:27They have to do given
• 37:28the mediator is zero because
• 37:30everything what alpha desperate will
• 37:31do, that's a point mass
• 37:33at zero,
• 37:34and we get the expected
• 37:35outcome on,
• 37:37expanded so far two score
• 37:39under m is equal to
• 37:40zero, c is equal to
• 37:41c, and a I is
• 37:42equal to zero. So what
• 37:43we still need to do
• 37:45is make,
• 37:47outcome model under no treatment.
• 37:49But we have outcomes under
• 37:51no treatment so that we
• 37:52can
• 37:56we we took a regression
• 37:58model for that, simple regression
• 38:00model.
• 38:02And here is the correlations,
• 38:05and here is
• 38:07the fit.
• 38:08They wanted the interaction between
• 38:10the SOFA score and the
• 38:12best proposal.
• 38:14They thought it was important,
• 38:15so I included.
• 38:17And they were right. You
• 38:18see that the PBL is
• 38:20quite
• 38:22standard residuals
• 38:23looked a little bit all
• 38:24over the place, so we
• 38:26decided to not go with
• 38:27parametric models.
• 38:29Parametric semi parametric models where
• 38:31we don't want to assume
• 38:32that the distribution of these
• 38:33things is normal
• 38:35because there's only thirty four
• 38:37observations and three fall out
• 38:39of the boundary.
• 38:41So here's my zeros.
• 38:43I made sure I had
• 38:44enough of them. I needed
• 38:45enough of them, so I
• 38:46counted them. And so you
• 38:48see they they have the
• 38:49we have the model. There's
• 38:51the model. Here. Yeah. Yeah.
• 38:53Here's the model sofa score,
• 38:56and then the t one
• 38:57sofa that is the predictor
• 38:58and then the post it
• 39:00both. And the there's prepulsive
• 39:01neutrophil nets and the interaction.
• 39:05So we need to,
• 39:08do the predicted
• 39:09values
• 39:10of that
• 39:11model,
• 39:13but with the new data.
• 39:15And the new data have
• 39:16all the positive the positive
• 39:18the all the desperate and
• 39:19positive neutrophil nets equal to
• 39:21zero. That's that m zero
• 39:22that I have there, all
• 39:23zeros.
• 39:24So we can just do
• 39:25this, and we find
• 39:28a pure indirect effect or
• 39:31an organic indirect effect relative
• 39:32to a is equal to
• 39:33zero,
• 39:34a decrease in time to
• 39:36SOWFA score of zero point
• 39:38seventy one. They were a
• 39:39little bit bit disappointed, the
• 39:41doctors, and then they were
• 39:42like, ah, but there are
• 39:44people actually that we don't
• 39:46expect
• 39:47to have a big effect
• 39:49because they already have a
• 39:51pretty good SOWFA score once
• 39:53they come in. So we
• 39:54cannot expect a much of,
• 39:56of an effect in those
• 39:58people because they're already pretty
• 39:59healthy.
• 40:00So they said, let's also
• 40:02figure out how it is
• 40:03in people who come into
• 40:04the ICU
• 40:05with the score with the
• 40:06SOFA
• 40:07score below two.
• 40:09And there we found an
• 40:10indirect effect of zero point
• 40:12ninety eight.
• 40:13And the ICU doctors told
• 40:15me that's a meaningful clinically
• 40:17meaningful,
• 40:19difference.
• 40:21A clinically meaningful defect.
• 40:24So normality and constant variance
• 40:26may not hold, so we
• 40:27use the bootstrap for the
• 40:28conference interval. You see that
• 40:29there we create a.
• 40:35Okay.
• 40:39So COVID nineteen in the
• 40:40ICU, the effect of SOWFA
• 40:41one of SOWFA two mediated
• 40:43through this proposal neutralness that
• 40:45was the question that came
• 40:46in first,
• 40:47but we can also use
• 40:48the same data to estimate
• 40:50the indirect effect of alpha
• 40:51desperate
• 40:53on SOFA two
• 40:55mediated by this positive neutral
• 40:58film
• 40:59without on treatment outcome data.
• 41:01And I have not seen
• 41:03other applications
• 41:04where people do that, that
• 41:06they estimate indirect effects
• 41:08without on treatment outcome data.
• 41:10It can be done. We
• 41:12did it. We get it.
• 41:13We call it public.
• 41:16I also looked at the
• 41:17effect of HIV cure for
• 41:18these treatments out in the
• 41:19HIV reservoir. There are several
• 41:21papers on that, and I
• 41:23looked at causal mediation and
• 41:25loss of neuroprotection
• 41:26of
• 41:27APO gene
• 41:28through lipid pathways. He wanted
• 41:30to do natural indirect effects.
• 41:32It can be done.
• 41:36I'm working on including measurement
• 41:38error in the mediator, not
• 41:40in these models because here
• 41:41we don't really model the
• 41:43mediator. We just may assume
• 41:45that the effects of alpha
• 41:47despais is making it zero.
• 41:49But in the HIV application,
• 41:50there is an HIV reservoir,
• 41:52and that is measured with
• 41:54error.
• 41:55I am also working on
• 41:57relating,
• 41:58causal mediation analysis on surrogate
• 42:00to surrogate markers
• 42:02because you can if you
• 42:03don't need on treatment outcome
• 42:05data, if you have the
• 42:06effect on a surrogate, you
• 42:08can estimate its indirect effect
• 42:10through the
• 42:11server without long term data.
• 42:15I've been looking at post
• 42:17including post treatment common causes
• 42:18of the mediator and outcome.
• 42:20If you have a good
• 42:21applied application and are interested
• 42:23in dealing with it because
• 42:25it's difficult to deal with,
• 42:26please send me an email
• 42:28because maybe we can make
• 42:29a team because I have
• 42:30theory
• 42:31but no good data example,
• 42:32and I don't wanna publish
• 42:34that without the good data.
• 42:35So if you have, please
• 42:36let me know.
• 42:38I am looking for other
• 42:39applications
• 42:40as well,
• 42:41and thank you so much.
• 42:52Question?
• 42:53Yeah. I have a question
• 42:54about the how you calculate
• 42:56your or any,
• 43:00Since based on your owner.