 And then, we'll have a focus on evaluation of unsympathies. And you will get a practical exercise to be done with an Excel file that you probably received already by email. Or you are going to receive it later in this morning. And then we'll also address the modeling side of this. You were worried about modeling in different presentations. But we'll have Augustin Collette from Inneris who will present more detail on the modeling side of this type of exercise. OK, so Francesco, please. Thank you. Thank you. Good morning, everybody. As a continuation of our discussion on health impact assessment, today we will address one of the central issue on how to make the impact assessment, which is the assessment of the dose response relationship between the specific exposure and the specific outcome. And as an outline of my presentation today, we will see different aspects, what's a dose response, compare the definition of dose response versus some toxicological terminology, which specific exposure response function we want to quantify, how I do get these functions. A response to a question that came yesterday, how I compare the local estimates versus the systematic review, the issue of double counting, and the issue of the shape of the exposure response, and especially the issue of addressing the high level of exposure, how we can extrapolate our dose response when the exposure is high. So in terms of terminology, you have here one nice link to the EPA documents, where you can find more of this terminology, of course, of the dose response assessment. But I want to just to introduce you some of the toxicological terms, which are very useful to understand what we are speaking about. So in toxicology and in risk assessment, we have some interesting concept. One is the no observed adverse effect level. So this is the highest exposure level at which there is no biological increase in the frequency and severity of the effects. So until that level, we are pretty sure that there are no health effects. And this is the term NOIL, which has been very much used from EPA and other agencies, including the European agencies. On the other hand, this is another term, which is also interesting, is the lowest exposure level at which there is a biological significant increase in frequency and severity. So you may ask yourself, why we have two terms. This is the lowest observed level, and the other one is the no observed adverse effect level. So you could assume that in theory, they should be the same, right? Because you think until a certain level, there is no biological effect. And then after that level, the increase in risk will start. But this is not the case because the evidence sometime is not so clear. So for instance, we are pretty sure that until that level, there is no adverse health effects. But there is a gap of knowledge. And we know that just after a specific level, there is an increase in health effects. So that's why we have two terms. The other terms that the toxicology have been using a lot is the so-called benchmark dose. It's a dose at concentration that produce a defined change in response for an adverse effect called the benchmark response. This is quite difficult if we read. But if we go to this slide, it's very clear. So suppose we define this, so we said, what's the benchmark dose and the benchmark response? So we define that the benchmark response is 5%. So we are interested in 5% increase in risk. And the benchmark dose is the level of dose at which the 5% increase is observed. You see here. And so this benchmark dose comes with a confidence interval. So you are pretty sure that at this specific level, you have a 5% increase in risk of the adverse effect over the baseline. This is the baseline. And this is where the 5% increase is reached. So this concept are quite used in toxicology. But let's go back to epidemiology. And epidemiology try to use more or less the same concept. But the evidence is not coming from animal studies. The evidence is coming from human studies. And coming from human studies and coming not from experiments but from observations, the uncertainty is, of course, much higher. And especially in the air pollution epidemiology, the exposure response function comes from large court studies for the long-term effects or comes from time series for the short-term effects. So what is the exposure response function? And I call here exposure response function. But we will see what's the meaning. It's the slope of a regression line where the health is the dependent variable and the exposure is the independent variable. They come from both from epidemiology and toxicology and they come with confidence intervals. And if you want to see an example of this exposure response function coming from an epidemiological study, this is our court study. It's called the longitudinal study of Rome. This is a large court study that we developed in 2001. So it's a census court of more than 1 million people in Rome. They were enrolled in 2001 according to the census. And they have been following up in this study. They've been following up until 2010. We have now the follow-up, I think, up to 2014 or something. And this publication, we were providing the exposure response function for NO2 and natural mortality. Natural mortality is total mortalities minus the accidents and all the violent death. So this is natural mortality. It's basically all-cause mortality. And as you see, there is an increase. This is the slope of the regression line. There is an increase in risk of mortality with increasing level of NO2 in this particular court investigation. I was saying, we have been using the term exposure response function. But we should be clear what we are meaning. Usually in epidemiology, we have the specific emission of pollutants. This emission cause increase in concentration. But as you know, one thing is concentration, and the other thing is the exposure. Because the exposure very much depends on the time activity pattern of the specific person. So we have concentration, exposure, and of course, from the exposure, you have the internal dose, the biological effective dose, and biological effect. So many times, we can speak of concentration response function. We can speak about exposure response function. And we can speak about dose response function. Of course, in many animal studies, we can estimate the dose. But it's very difficult to estimate the dose in human studies. So we think we can estimate the exposure. But even the exposure, you know that in many observational court studies, you actually estimate the concentration out of the residential address of a specific person. So and of course, the person is not sitting outside in front of the door all 24 hours. He is sitting inside during the night, and maybe he goes to work, and he goes to school, or other places. So actually, we measure concentration, outdoor concentration at the residential address, but we don't measure exposure. So the reason for this, so we say exposure response function. But we actually are meaning concentration response function, because it's the concentration estimated outside. So this is due, of course, to the design of the epidemiological studies. And of course, people are making critiques regarding this. You say, how can you imagine that you make a surrogate of exposure just estimating the concentration outside and giving to this specific subject that specific concentration for the annual average. Of course, we know that this is an approximation. What is interesting for us is the ranking. So if I get an exposure outside of 50 micrograms PM 2.5 and someone has an estimate of 30, we know that the gap is probably not 20. This is not the precise gap. There's a lot of uncertainty, but it's pretty much sure that I get a much higher exposure than the other guy. So we know that it's a surrogate of exposure. Can we do better? Of course, we could do better. So in theory, in the future, we should be able to have more data on the time activity pattern of the individuals, including the time spent to commuting and including the time spent indoor at the office or the plant or the workplace. But this is something is a future to come. Up to now, there is no single large epidemiological study that has been able to estimate real exposure, but just the proxy like outdoor concentration. The time activity pattern is, of course, very important. And the time activity pattern is more complicated for the adult population because we know we go to work. But if you are speaking about, if you are interested in elderly, you are more sure that they spend more time indoor, more time at home. So the misclassification is less. And maybe if we are speaking of children, we know there is some misclassification. But they tend to spend their time near the home because they go to school near the home because they play near the home. So the misclassification is less. The most of the misclassification is in the adult period of life. So we already spoke yesterday of the portability on transferability issue we already covered. And it's the issue of transferring the results of different studies to a specific other population and specific other contexts. So the question is, what kind of exposure response function I want to use? And of course, the first question is what kind of outcome I want to estimate? What kind of health effects? We were discussing yesterday of childhood leukemia, of course. If we think that the first outcome of exposure to volatile organic compounds is childhood leukemia, we need an exposure response function for childhood leukemia. We have to be conscious that some exposure response function do exist. And some other exposure response function, they do not exist because there are no enough good studies. And if there are not good studies in epidemiology, is there that toxicology comes? So in a way, there was a discussion yesterday of combining the toxicological and epidemiological evidence. Less evidence we have from human studies, more toxicology we have to use. But of course, there is the need to use more and more human studies and to do more, as was said yesterday, more epidemiological studies to have more exposure response functions. In choosing the exposure response function, we have to rely on the level of evidence. What is the level of evidence? Suppose we want to address the issue of air pollution and someone comes and says, OK, you are saying that air pollution is able to cause an increase in immortality, is able to cause an increase in ischemic heart disease. But we know from two studies that it's also related to the cognitive function in children. And so the guy comes and says, you have to make an input assessment not only on mortality, not only on ischemic heart disease, but also on cognitive impairment in children. What will be your reaction? Knowing that you have plenty of studies on mortality, plenty of studies on ischemic heart disease, and two studies on cognitive function. What would you do? Any suggestions? No suggestions. Yes. I could choose extreme temperature, for example, or extreme heat or extreme cold. And to see what's happened in the human body, with the health, if they have some problem or some time, fertility, mortality. Yeah, but my question was the following. I have to estimate in a specific situation, suppose in a new power plant, we have a discussion with the stakeholders, we have a discussion with the owner of the new power plant, and we have a discussion with the community group. And they both ask health input assessment, OK? And you have a discussion with them, and they discuss your proposal. And your proposal is, OK, this is a new power plant. This is probably a cold power plant. So what kind of emissions this power plant has as a particulate matter? So you come with your proposal. I can estimate, because I have enough exposure response function, I can estimate mortality from this new power plant, and I can estimate ischemic eye disease. And you have the community group saying, OK, you can estimate this, but we care about our children. Our children are more important than the elderly people. So we know from these two studies that air pollution from this cold power plant will decrease the cognitive function of our children. So you have to estimate the effect of this new cold power plant on cognitive function. Very aggressive, OK? So what you do? I will write a list of caveats, and I will perform the cognitive reduction impact assessment. But we don't have time to, I mean, it's important to be clear about the caveat. OK, OK. This is a good approach. So you say, I will rank my outcomes according to the level of the evidence. And I would say, we are pretty sure that for mortality and ischemic eye disease, we have very high level of evidence. But for cognitive function, this exposure response function I'm getting is from two studies. The level of evidence is much lower. So I will come with some caveats. In your proposal, we will do that, but we have caveats. Some other people would say, I don't do this rubbish, OK? But this is something on the discussion. This is a good point. So ranking, please. Yes, working. A question from Salmanesh is asking, can we check the cognitive capability of children by comparing their ability at the beginning and after exposure? OK, that's a good question. That's the indication that we need more clarification of health impact assessment and epidemiological study, OK? A long term. So I need a response from you to this question. Who wants to respond? Not Isabella. So this question is just asking, can we do an epidemiological study and assess the cognitive ability of the children before the plant and after the plant? Of course, we can do this. This is a nice epidemiological study. Why is it nice? Because we have no exposure before and we have the exposure after. So it's the best of the comparison. But this is not the question we are asked for. So we have one there and one here. I was just wondering if it's really, we're talking about exposure and we're taking into account children. And I was thinking about the ethical aspect of the study. I don't know if we're giving a theoretical example. But when we talk about the exposure to air pollution and taking epidemiological studies or we cannot think about RCTs, let's say, or whatever the design is, that's why I have this question. So this is more into the design of the study and the ethical aspects of study in children, probably. But the question is, what's the value of the epidemiological study? What's the value of a health impact assessment, please? Sorry, I'm probably not going to answer your question exactly. I'm wondering if I could, for clarification, is this after the coal plant goes in? No, this is before. We are in a meeting in the whole of the municipality. You have the industry people there, the community group, and you are the scientists. Right. So they are fighting all the time, and you have to decide what to do. This is before the plant. Yeah, because you can't do a health impact assessment on that community without the coal plant going in. But you can't answer the question. You can answer the question. So why we are here? We are here to respond to the questions before the plant, because we have to make these people agree. Yeah, so no, I was going to say, you can't answer the question without studies from someplace else. OK. OK, sure. You can answer the question. If you have two studies suggesting that it's a relationship, you can come out with a report as he was saying, indicating that there is a solid evidence for some outcome. There is suggestive evidence for other outcomes. But what we are here is that we have a sort of moral duty to respond to the question before the plant. After the plant, everybody is able to do an epidemiological study. But we have to take the responsibility of responding to the request of people before the plant. And the health impact assessment is useful before the plant. Of course, because it's prognostic in a way, we want to have a prognosis of the new implant. Of course, we have other health impact assessment which are not prognostic or retrospective. You can do an health impact assessment on what has been the effect of this existing plant in the last 20 years. So please catch this terminology. It's retrospective health impact assessment and prognostic health impact assessment. So we are here, especially for the prognostic one, because we want to be useful for the decision of the policy makers and the stakeholders. OK, so we are addressing the severity of the health response. Oh, sorry, you want to speak? Yeah, sure, sorry. Just, yes, just for me, OK, the posteriori assessment, it depends also who is paying the research. Because if the company that is building the new power plant is saying, no, I need the health impact assessment now, and the community is saying, no, we have to wait for, I mean, it could be something a little bit not really easy to deal with. The other point is the population of children that can be used for the posteriori epidemiological studies is the community, let's say, is a rural area. Then maybe we can use 500 children. Is that a strong epidemiological studies? Or is it just something that we can perform to let the community be more happy, but without the really strength of the study? Yeah, there are several issues, of course, to discuss, and especially if we decide to do an epidemiological study because the community wants. Usually you do the health impact assessment, you do your evaluation, but then in any case, the community will ask for an EPI study after the plant. Francesco, just got a question from the internet from Hannah. Sorry, maybe I should come there. The question is, why don't we compare children in another region with an already established plant with children in a place with no plant? If there is a difference, it will show a possible association. Yeah, this is again a question on the type of the epidemiological study. So we can discuss one day on how to make an EPI study regarding this. And of course, there are several possibilities on the comparison because most of the discussion on the EPI study is the comparison group. It's before after with the comparison group, usually. But this is not our topic today. So our topic today is not the EPI study, it's more on the health impact assessment. So we have been already speaking of the severity of health response because I was concerned on mortality, and the community group is concerned on cognitive function. So we have to discuss which one is more severe. So to me, mortality is more severe, but for the people in the community, they care much more of children. So the severity here goes with what I say here, the stakeholder view. So for the stakeholder view, it's much more important children are much more important than elderly people. But of course, in the assessment, a number of people affected. It's also an important issue. Suppose that the community is very much interested in cognitive function in children. And you discover that your area, your impacted area where the new plant will be this basically elderly population. They don't have many children. There are a few villages with just 50 or 60 children there. So the health impact assessment is not very powerful in that situation. So the size of the group affected is also a matter of discussion. So we have this nice graph showing the severity, but you probably know it's well known. So how I derive my exposure response function, what's the best recommendation? Use what other people have already used. And especially if you have a recommendation from an authoritative organization like WHO, don't spend time. Use that specific recommendation because you are pretty sure you are not going into discussion because you are using WHO estimates. If you are using your estimates, you will get more problems and you will get more questions. Or in some cases, especially when you don't have the WHO and EPA or other organization already establish exposure response function, then you want to do your systematic review and meta-analysis. And I think Carla will address that part of systematic review and meta-analysis in a more formal way. So you want to collect the evidence. And the last one, it's very funny method, but it has been used in the past. Where is the expert panel? So what is the expert panel? You don't have the evidence from toxicological study. You don't have the evidence from the epidemiological study. But people ask to you, what is the effect? And what you can do, the only thing you can do is gather a group of experts and get a guess estimate from the expert. Of course, in terms of the level of confidence, I would go first with this approach. Second, I would develop my systematic review and meta-analysis and it's very rare that we should use this expert panel. But this has been going on for some exposure. For instance, there is an exit panel on ultra-fine particles providing exposure response function for ultra-fine particle as a guess estimate from the expert. So this is also interesting. So I have a story here. So, for instance, we are discussing PM 2.5 and mortality. So how I get the exposure response function? So in 2013, a systematic review was published from Geryl Hook. And this systematic review indicated that the relationship between PM 2.5 and natural mortality, you see, this is the result. It's called the forest plot. It's where we combine the results of the single studies. This each one is a study. The central point is the effect estimates. And then you have the confidence intervals here. So you have the numerical results here. So the first study is 1.06, 1.06, 126. They come with confidence intervals. This is the weight of the study. And the weight is a function of the sides of the study, of course. And this is the overall estimate. So this overall estimate is the weighted pool estimates of all these numbers. So this systematic review came with this magic number. 6% increase in mortality for each 10 micrograms increase of PM 2.5. And this result was also taken from the World Health Organization, which recommended in this report the exposure response function. So if you need the exposure response function, go Google Rapier. And you will get a lot of exposure response function for air pollution. So this is quite interesting. So in this report, let's look at all of this. This is the recommended exposure response function. So it's 1.62, which is exactly the results of the systematic review published in 2015. So we got a number from WHO. So my point would be, if I have to estimate for the new power plant, the new coal power plant, what would be the impact on the population after the operation of the plant? I can use this exposure response function. But there are some guys coming from the community group saying, OK, look. This exposure response function is old. It was published in 2013, was using data until 2012, time passes. And just last year in 2017, the large court study on Medicare patients in the United States, 60 million subjects were published. And they had this nice exposure response function. And that function is a little bit higher than the 6% from the systematic review. Why we should use this function, not the old function? So then, what do you do? You have two possibilities. Use the old systematic review, 2013. You get this new, fresh result from the American study. And you have to choose. But then you go and see that after the systematic review in 2013 was not only the American study that was published. You had several studies published. And those studies were published just after the systematic review. So what I did in this case is made a systematic review. So these were the old studies considered up to 2013. These are the new studies. And when I pulled them together in the new systematic review and meta-analysis, my estimate is no longer 6% is 10%. So my approach in this situation would be not to use the old one, but to use the new one, please. The geography? Yes. OK. These studies were basically Europe and North America. Or actually all are Europe and North America. Excuse me. I feel I have confusion. Yeah, sure. You said that the value that you use for a variate exposure was maybe 0 for PM2.5. 0, 5 microgram per cubic meter, or 10. And you choose that 5 microgram per cubic meter. No, no, we are using always 10, always 10. So this, sorry. Yes, yes. This is the old, is 6%. The 1 of 06 is 6% per 10 micrograms PM2.5. And this is also recommended by WHO. This is the function coming from the American study. These are the results. The new studies and all these are for, sorry. These are the increased risk. All are for 10. Because to make this systematic review, we have to have the same unit. And this is the new result, please. Sorry to bother you. But what do you think about the fact that a particular matter in USA, Canada, is different from a particular matter in Europe in terms of composition? I mean, yeah, that's the problem of portability. That's another issue. Also, humidity. Yeah, it's a problem of portability. So we are now trying to find the best way to calculate this exposure response. But of course, you say, we are in Europe. We don't care about this funny Americans. So instead of using, yeah, without diesel. So instead of transferring the information from US, we want to use only the European studies. So you can select from this list only the European study and make a systematic review and meta-analysis of the European studies only. Of course, when you publish that, you have the referee who is the American one and says, oh, you know, the European studies are shaky. So you have to use the American evidence. OK. Yeah, you do both. OK. So this is the way, please. OK. I had two questions. But one was about these, about the American studies and European studies that you already answered. And the other one is just, I'm a little bit confused about the names. One was in one paper. It was a relative risk. Another one is incident risk. And here is a. Sorry, it's increased risk. Yeah, it's the same. It's the same. OK. Actually, the former concept, these are all court studies. And for all court studies, they've been using the Cox proportional model. So from that study, it's the other ratio that comes from those studies. We call that relative risk in a sort of more familiar term. OK, thank you. But the relative risk, if you want to transform the relative risk into an increase, percentage increase in risk, you just take out the one. So multiply by 100. So for instance, in this case, 1.1 is 10% increase risk. Please. No, no, no, wait a minute. Thank you. I want to ask about the portability of this data because I'm concerned about the pollution in Asia, especially in Indonesia. Just like Isabel asks about the composition in PM 2.5 is different in its country. And in my country, even the PM 2.5 in several cities is low, but the heavy metal content in the PM 2.5 is very high. What do you think about that? Thank you. Yeah, this is one of the most important issue in this estimate of the global impact of pollution. One is the transfer of information from one population to another population, and the other is the transfer of information from one kind of exposure to another kind of exposure. So the assumption that we make here is that PM is toxic everywhere in the world the same way, independently from the source. But this is this very strong assumption. We know that this is not true. Desert dust is probably different than anthropogenic dust. And within the dust, it's different whether the emission come from a steel plant or they come from a diesel or they come from a smelter industry. So you're perfectly right. So in the future, in 30 years, we will need exposure response function source specific. If we have source specific exposure response function, then we solve the transferability problem of the source, not of the population. We need exposure response function that are population specific. OK. But nevertheless, we go back to the example. We have to do the anti-impact assessment now. Not in 30 years. So we have to respond. OK, so OK, I have another example again of transferability. And this is a example of not a long-term exposure on the short-term effects. So for the short-term effects of particles, we had in 2001, we had this wonderful study that was called the AFIA study, was conducted in 29 European cities, was published in epidemiology in 2001. And that one was providing the percent increase risk immortality for short-term exposure to PM10, in this case. As Italians, we are always proud to be up here. This is the ranking of the effects. Athens is the first with an effect size of 1.5%, Lyon then, and then Rome, Milan, and Turin with effect size of about 1%. And then all the others are much lower. So as Italians, we are very proud to have very toxic air pollution. But my question is, I have to make an anti-impact assessment in Rome in effort. What kind of exposure response function I can choose? Let's go here. So I read here is, so the effect estimate is 1.5% for Rome. It's 0.4 for Helsinki, and minus 3% for airport. And the total estimate is about 0.5%. So which one I should use for Rome, Helsinki, and effort? I have this option. We are in Rome. We use the Rome data set, use the effect estimate from Rome. We are in effort. We want to be German. We want to use the local estimate, so the effect size is minus 0.3%. So I choose the city specific, or I know that combining all the studies, the effect estimate is 0.5%, which is an average of all the studies. So what I should do, city specific or the pool estimates? Do we have any indication here, any idea? I'll go with the local, or I'll go. If I go with the local, of course, I should go with the local, both in Rome and in effort, because I cannot change my criteria. Because in Rome, I will get a positive number. In effort, I would get a negative number. But on the other hand, I have the information from the pool estimates. So what do you think? Which one is stronger? Is the pool estimates or the single city estimates? What do you think? You have a lot of information here. You have a lot of information here, a lot of points. These points are specific for each city, but also you have an overall. What do you believe? The pool one. Why the pool one? Because the pool one is the synthesis of the evidence across the different populations. So even though in effort, I get this negative result with this large confidence intervals. I have this information from effort, but I also have this pool estimate. So I have to make a sort of compromise. The best choice would be to use the pool estimates. But you have people here saying, okay, it's okay with the pool estimates, but I have information from my city. So there's a tension there. And there's a nice solution that, yeah, there is another possibility to try to understand why there is a difference. But the best solution it was invented, try to estimate a weighted average between the local estimates and the pool estimates. So in a way, give some weight to your local estimate, but don't forget the pool estimate. And it's a matter to do this. So now this is just to say in this specific study, they were able to evaluate the fact that these estimates were different, whether the N02 level was low and high. You see there is big difference in the estimate where the temperature was low or was high and the geography was of course very important. So this was a way to explain the heterogeneity. But this is the method. You know, it's very difficult in Bayesian approach, but in simple term is the weighted average of the local estimate and the pool estimates. Okay, it's very simple. You know, the mathematicians and statisticians, they make it difficult. So to run that, you have to go to a statistician. But in terms of understanding, it's very simple. It's a weighted average of the two. And you know, this is a graph, you know, let's see for Rome. So for Rome here, I have five minutes almost done. For Rome here, you know, that was the old estimate, you know, the original local estimate. And this one is the reduced estimates. So you see it's much closer to the pooled estimate, but it's in between the pooled estimate and the local estimate, where as you see it's closer to the pooled estimate. So the pooled estimate is stronger than the local one. But in any case, you have some elevation here. In the case of airfoot, where this airfoot is here, you see the local estimate is down here and the adjusted estimate is here. It's lower than the pooled estimate. So this estimate is very well-influenced by the local one, but it's not extreme as the local one. So this is a way to address the issue of having sort of compromise between the local and the overall estimate. Do you have a question regarding this? This was... One for the moment, it's going to be quite rapid. What is the meaning of negative increase in mortality? It's a decrease, sorry. Yes, but I thought about it, okay. Thank you so much for your questions, what I thought about it. Thank you. Sorry, Francesco, just a quick question. I have the impression that the error bars are more similar from one city to another. So say again, sorry. The error bars, the uncertainties. They're not identical from each city on this plot, but they're much more similar compared to the plot you were showing before. So how the shrunken estimate affects the error bars? They should increase the error bars. But, Francesco, the increase compared to the previous one, compared to the local error bars. Let's see, let's see, I don't have the answer. So for instance, let's look at Rome here. So Rome goes from, let's say, 08 to 1.9, right? Let's go. And here goes from one, it's much smaller, it's much smaller, actually. It's much smaller, yeah. So this method is also shrunken the confidence and interval. And it remains city specific. Yeah, it remains specific. Yeah, the reason why, this is a good point, the reason why it reduced the confidence intervals is because it's using the pooled estimate. You know, the pooled estimate has a very narrow confidence interval. So since we are using that with very narrow confidence intervals, this will reduce also the local one. Okay, so other questions? I have one, Francesco. So there is a kind of discussion to know what kind of estimate you have to use and you have to discussion with the people you work for. So what is science, what science must keep because finally discussion can go very far on to the what kind of estimate we use, what kind of weighted estimate we use, what are the weights, what, so what, where is the science, hard, hard. Yeah, the hard science, yeah, there is no hard science here. But it's a general principle, which I think is inherent in the Bayesian approach. And I think the Bayesian approach is very similar to our way of thinking. You know, in our way of thinking, you have a priori, okay? So no one will convince you that your priority is wrong. No, but the only thing that will try to move you from your a priori is the evidence. But then when you have to make a judgment, you have your a priori, you have the evidence and your next step is to make an average from your a priori and average with the evidence. So your a priori will be much closer to the evidence but you still keep the a priori in a way. And you are moving, you have more evidence, you are a priori which was modified from the previous a priori and you move and you change your judgment. So this is how our mind works. No problem, this is our mind. You know, if you don't agree, no problem, but this is what I think. That's the way we go on. We change our mind according to the evidence but gradually, not suddenly. Okay, so the way we have to approach this, this is weighted average between the pool estimate and the local one is in a way approaching our way of thinking. You know, our way of thinking is we have some evidence there. We have a large evidence here. So I think that the large evidence is correct but I cannot ignore the fact that there, they add that specific effect. So there's no, you know, there's an open discussion but I think the Bayesian approach is the right way to go. I agree, but it works if just only if your a priori is based on evidence. So it's a circle and because the judgment should be evidence-based. Against sometimes the a priori. But if your a priori is evidence-based, it comes from other, you know, it's maybe the crucial is the definition of a priori. That's a good point, that's a good point. Although, you know, I think the a priori should come from the evidence but it's a collective evidence. It's not only the evidence from facts, it's also the evidence from, you know, other information that you have from biology, other information you have from toxicology. So the evidence that form your a priori is not only based on facts, is also based on several aspects related to the mechanism. So it's much more reach in a way than a single experiment. That's my, okay. So they say it's time to close. Thank you, thank you. It was a good pleasure to be here.