Clinical Prediction Models & The Multiverse of Madness

Hi everybody again, this is Richard, uh, Professor of Biostatistics at the University of Birmingham in the UK. Right, so this is another one of my videos talking about a particular research topic that I work on, and this is clinical prediction models and the multiverse of madness. You'll see I actually published a paper with that title, but really it should be called clinical prediction models and the uncertainty of individual predictions, but that just wasn't as fun as the original title. Okay, let's crack on. So a bit of background. Clinical prediction models, these are mathematical tools which are used to estimate, or if you like, predict the risk or value of a future clinical outcome in an individual. So they use multiple predictors. Some people refer to those as features or characteristics. Bits of information about an individual such as their personal characteristics, their family history, their location, their blood pressure, biological information, and so forth, and they are combined to make a prediction. So we know models in the UK, for example, QRisk, QCOVID, the Apgar score, Nottingham Prognostic Index— these are used, for example, to estimate an individual's risk of cardiovascular disease within 10 years breast cancer recurrence risks, and so forth. Typically, these models are developed using statistical methods, regression-based. Increasingly, of course, we hear about machine learning methods such as neural networks, random forests, and so forth. Broadly, we might think about all these things as artificial intelligence. They are computational tools which are using data to produce a statistical equation or a black box that allows that information to be projected to a new individual to make predictions in them. Okay, let's look at a real example. This is a tool called the CRASH tool, and this is a prognostic model for estimating mortality risk in patients who've had a traumatic brain injury. So for example, been in a traffic accident, had a blow to the head. They'll get picked up by an ambulance, taken to hospital, and at that point they could have the CRASH tool applied to them. So as for any prediction model, we need to have information about their predictors in the model. Here we've got country, age, Glasgow Coma Score, reactivity to light, and so forth. And And for this individual from Denmark, age 54, Glasgow Coma Score of 12, and so forth, the model, which behind the scenes is actually a logistic regression equation, the model estimates for this individual that their 14-day mortality risk is 18% and that their risk of an unfavorable outcome at 6 months is 60%. So what we're seeing here is the front end, but behind it is the statistical or mathematical equation that's being used to derive predictions in this individual conditional on the model and the values of the individual's predictor values. Clinical prediction model research has 3 main phases. So the first phase is the model development, so the production of that statistical equation or black box. This has some— it should have, doesn't always have— it should have some internal validation where The process is subject to some rigor which deals with issues such as overfitting and produces a final model. There's then usually, particularly if the original data was small, some external validation where we examine the performance of the model in new data. So how do the model predictions work? Do they accurately predict outcome risks or not? Often we're interested there in transportability, so we've developed the model in maybe one country and we're examining the performance in another country. And the third phase, which is very rare, is investigations of clinical impact. So when we use the model in practice, is there evidence that actually makes a difference? Does it improve patient outcomes? Does it improve healthcare? And so forth. Now, as you can see from many of my other talks in this YouTube series, that improvements are needed in this process at all these stages. Now today I'm going to focus on model development. So this is the production of the model, the training, the development of the model. Very few developed models in the medical literature are actually fit for purpose. Many models just don't give reliable predictions. They're unstable. They shouldn't be used for guiding individual decision-making in medicine. Yet it's quite incredible that most of the models that are being produced— I would say nearly all of them— never actually reveal the instability, the unreliability, the uncertainty in their predictions. So fundamentally, they would just provide a single estimated risk for an individual, and we never see from those models what the uncertainty is around that risk. And that's the flavor of the talk today. So when is a model reliable? So when I say reliable, I mean that the predictions from the model are in some sense accurate, so helpful and stable in individuals such they can guide clinical decision-making. Now when we develop a model, we need to think about the sample size. So a model is more likely to be reliable when the sample size is large and representative of the target population that you want to apply the model to. We also need to think about how many predictors we're putting into our model. And you'll have seen other talks that I've given about sample size requirements, but the broad issue is that we don't want to be using thousands and thousands of predictors to develop our model when we have a small sample size. So if the sample size is large and the number of predictors is relatively small in relation to that, then the model predictions are going to be more reliable. We also need to make sure that we're using good statistical machine learning methods, so methods that deal with overfitting such as penalized regression, which account for the fact that we know we're going to be overfitting to our data because predictions are going to be picking up noise in our dataset, and therefore we want to try and minimize that problem as best that we can. Part of that is also to do methods such as cross-validation and bootstrapping, which will essentially identify issues of overfitting and adjust for them, sometimes called optimism. So good methodology, good sample sizes, being considerate of the number of predictor parameters we're using. So a model is therefore going to be less reliable in the opposite situation. So when the development data is small, not represents the target population, when we're using way too many predictor parameters relative to the sample size, and we'll be using model development methods that don't adjust for optimism or consider overfitting at all. So concerns of an unreliable model, um, we can have some understanding of, of what sort of good practice, but really what we want to see is, okay, we've developed a model or somebody's developed a model, can we expose the issue of unreliability? And one way of doing that is to think about the concepts of model instability, and a related concept is uncertainty. Essentially, what is the uncertainty around predictions for an individual. So that, that's the aim of this talk. I'm going to think about the concept of prediction instability and put this across in the sense of the multiverse, um, and then I'm going to talk about how we quantify the instability and the uncertainty predictions. I'm then going to focus on the pros and cons of providing uncertainty alongside risk estimates, and this is quite controversial. for the reasons I'll come on to. And within that, I'm going to consider the patient perspective. So does the patient actually want the uncertainty around predictions given to them or not? It's always good to have a film quote in the talk. This is a great one from The Naked Gun. Doctors say Nordberg has a 50/50 chance of living, though there's only a 10% chance of that. Well, actually, Obviously that's one of the most famous lines from that film, but there is some truth in this, and we'll come on to it in this talk, that there is some relevance to that statement. Perhaps we'll come on to— right, so instability. What, what do we mean by instability? Instability refers to when a developed model may be very different if it was developed again in a different sample of the same size from the same population. I refer to this as a multiverse of potential models. So you happen to have a development data set, you develop your model, it comes up with a— let's say we use a regression equation— it comes with a particular regression equation with a particular set of predictors. But what if we'd happen to have a different sample of the same size from the same population? That could by chance have led to a very different regression equation, a different set of selected predictors, different predictor effects. If you're not using regression, it may lead to different sets of trees and branches and, and a different black box. What that means is that instability in a model leads to instability in predictions, and really this is the heart of what we're talking about. The predictions at the individual level from a particular model are unstable. If we happen to have developed a different model from the same population using a different sample of the same size, an individual's predictions could have been very different. So if you like, there are multiple models in the multiverse, and each of them are potentially equally plausible and could give different predictions. The larger the instability concern, the greater the threat a model is unreliable. So large instability implies likely that there's going to be poor internal validity. So in the development population, that any one model is unlikely to do well. Now, like I said, this is rarely examined, which strikes me as strange because in statistical— the statistics in medical research, we would always present confidence intervals and so forth. But in this area we often do not see uncertainty presented. So what I suggest is that we should always be examining and reporting instability after developing our models. Now, this is not a new topic as such. There's been many people talk about this over the years. Just very briefly, Frank Harrell— and I've always liked this concept— he's often referred to as a developed model as just an example model. It's just one model. Various authors, Patrick Royston and Willy Saalbrei in particular, have shown instability in models in terms of the set of predictors that they choose and the functional forms of those predictors. Doug Altman and Anderson and Alexander Pate and colleagues have looked at instability using an approach called bootstrapping, which I'll come on to, and both those papers show the variability in individual predicted risks from models is often very, very wide. So I'm very much building on all of these excellent papers that have gone before. In the last few years, we've published ourselves a few papers on this topic. First of all, Gary Collins and I published a paper in the Biometrical Journal called Stability of Clinical Prediction Models Developed Using Statistical and Machine Learning Methods, where we raised the, the potential for bootstrapping to examine prediction instability and presented prediction instability plots and so forth. We then followed that up with a paper in the BMJ called Uncertainty of Risk Estimates from Clinical Prediction Models: Rational Challenges and Approaches. And that's talking about the general issue about how, whether, and if we should be presenting uncertainty of risk estimates from clinical prediction models. Many of the findings I'll come back on to later in this talk. But the main focus of today is this paper that was published in BMC Medicine, Clinical Prediction Models and the Multiverse of Madness. Sometimes I think it's important to try and draw the reader in, and that's what we wanted to do here. We wanted to bring in a wider audience than our typical statistical papers and just raise the issue about the fact that prediction model research is focusing on single estimates, single point predictions, and just to raise the fact that actually there is a multiverse out there of other possibilities. So yeah, let's, let's just unpack that a bit more now. Right, let's think about this multiverse in a bit more detail. Um, so the idea is that we're going to develop a clinical prediction model. So that means we're going to estimate the parameters in the model, be a regression model or a machine learning black box approach. We need to understand relationships between predictors and outcome risk. So we're going to take a sample of data and we're going to estimate our model from a set of candidate predictors. Some of those predictors may not be retained in the final model, but some of them will. And then that final model is going to be used to make a prediction. So if we focus in on the bold bit in the middle This is what actually we observe to do. So we take a sample of individuals from the target population. Let's say there are n individuals, and we use that development dataset to develop or train our clinical prediction model. And we're going to use a chosen method, okay, be it regression or machine learning. But I'm not going to consider a multiverse where people are using lots of different methods. I'm just going to say there's one particular method that people are using. That other multiverse is even more diverse. And once the model has been developed, I'm going to use that model to make predictions in individuals from that same target population. So this is what was realized, this is what was actually observed in your research study. But what you need to recognize as a researcher and as people who are consuming prediction models is that this was just one flow that we could have taken. what happens if we actually took— if we'd actually taken another random sample of the same size from the same target population. Um, and you know, it's just a random sample, so it could easily have happened this way as well. We could have taken this route in this random sample where we developed a model in exactly the same way with the same set of candidate predictors. We would have ended up with a different clinical prediction model. Um, and that model was then used to make predictions in individuals, and maybe those predictions could also be very different. And so you can see where I'm going here. We could have another route down there, or it could be some— from somewhere else in the multiverse where we have this, uh, this route here where we have another set of patients of the same size, a sample size. We develop our model, we use that model to make predictions. So we have a multiverse of models and a multiverse of potential predictions for each individual. So each individual has a multiverse of predicted values. So there's a multiverse of models out there that we could have developed with that same model development technique. And if we think about all those models, then we can use each of those models to make predictions in individuals. So this is just an abstract depiction of the multiverse. This might be the model that we develop, but there's other ones out there that we could have thought of producing if we'd happen to have different data than the one that we got. If you like, you can think of this as a distribution of values compatible with the same sample size the same model development approach and the same set of candidate predictors. Okay, so it's always in the context of what model development approach you've used and the predictors that you've considered. I'm not thinking here of a multiverse of, oh, we could have used a different method or a different set of predictors. That's the even bigger multiverse. I'm just focusing in here on something that's compatible with the way that you've actually produced the model with those same set of predictors. Right, let's use simulation to demonstrate the multiverse concept in a bit more detail, and in particular the instability of predicted values even just for the same individual across the multiverse of potential models that are out there. So with simulation we can compare something to the truth, which we can't do in, in real practice of course. But what we're going to do here, and I'm not going to go into the details too much, but I'm going to generate a huge dataset of a million individuals I'm going to specify a true prediction model containing 9 predictors, and on average the outcome risk is 50%. And because I've got the true prediction model, I know the true risks for each individual, so that's my reference point. I'm then going to take a sample of a particular size from this large million dataset, and to that sample, the training data, I'm going to fit a LASSO logistic regression model to these 9 candidate predictors. So I actually, you know, this is quite a stable situation if you like because I've not got any noise variables here. I know that these 9 predictors are important, so I'm going to consider including them. I'm then going to develop my model and apply it to make predictions, and I'm going to actually apply it to everybody in this large dataset, but I'm going to focus for the purposes of illustration on 9 individuals, um, and these 9 individuals have risks from 0.1 to 0.2 to 0.3 all the way up to 0.9. Okay, so 9 individuals across the spectrum of estimated— uh, sorry, of true risks. Um, so that's one clinical prediction model, but I'm actually going to do this 1,000 times. So I'm going to create 1,000 models, I'm going to apply them to the same 9 individuals each time, so I'm going to get 1,000 predictions per model. So 1,000 models in the multiverse 1,000 predictions, and each model is developed using lasso logistic regression with 9 predictors, and crucially, all of the same sample size, but different sets of patients potentially from the large population, but the same sample size. Now, this is my prediction instability plot. What I'm showing you on the left is predictions so estimated risks for each of the 9 individuals across all of those 1,000 models that I've developed. And on the x-axis, I'm displaying the true risk for the 9 individuals. Now what we want to see, of course, is that our predicted risks from the developed models are very, very close to the true risks for the individuals. I'm also presenting you the results across different sample sizes. So here we've got a development sample size of 50, 100. This is the so-called Riley et al. minimum sample size, 385. Please see my other talks for how to derive that minimum. Uh, 500, 1,000, all the way up to 5,000. So let's just focus on the 5,000 because that's obviously a very big sample size. In fact, we've only got 9 candidate predictors, and with a 50% outcome proportion Obviously that's 2,500 events, so we've got huge data here really. And because of that, we see, um, stability. There's very little variability in predicted values from the models compared to the true risk. So on average, all of those models are getting the right value. So somebody whose risk is 0.1, their estimated risk from the models on average is 0.1. Similarly, 0.2, 0.3, that's the bold line. Um, what we're mainly interested in though, in terms of stability and instability, is, is the variability around that. So across all the models in the multiverse that could have been developed, what's the variability in the predicted risk? And we can see that it's very narrow. So somebody whose true risk is 0.1, the variability is tiny around 0.1. Somebody whose risk is about 0.5, the variability again goes from what, 0.45 to 0.55? So very, very narrow. So what that means is that we'd anticipate that any one model that we would have developed in the multiverse would be pretty good in terms of estimating precisely and reliably the true risks for each individual. Of course, what happens when the sample size becomes smaller is that the instability starts to increase, and so we see wider variability of estimated risks from each of these 1,000 models compared to the true risks. So even though the true risks on average are pretty close to the— sorry, the estimated risks on average are close to the true risks, the actual variability is enormous. Look at this for n= 50. For every one of these individuals from 0.1 to 0.9, any multiverse of models could have produced an estimated risk of 0 or 1. So let's just think about that a bit more. So somebody whose true risk is 0.1 If we took one random model from the multiverse, that model might have estimated a, a risk of 1 for that individual. Conversely, somebody whose true risk is 0.9, one model from the multiverse might have estimated a risk of 0. Now, why is that important? Well, it's important because we don't have 1,000 models. When we develop a prediction model using a set of data, we only develop one model. So what we need to know is that that one model that we do pick out from the multiverse is likely to be close to the actual truth for that individual. Um, think about the consequences. You know, you're telling somebody who's actually got a very high risk that their risk is low or zero. The consequences for clinical decision-making in that patient could be catastrophic. So this is serious business. This is not just like a Netflix recommendation or Amazon recommendation. This is very, very important to understand the robustness of predictions that we're getting out. Um, if I just zoom in a little bit more, you can see that in a little bit more detail there. Look at this scatter, it's just hugely unstable, but people are not presenting this. So this is not exposed at the moment in prediction model research. People develop a model and they tell you what it outputs, a single prediction for each individual, but they don't tell us the uncertainty, the instability. And I think that's something that we should, should now change with plots like this, prediction instability plots. Okay, that was using simulation, but in reality, of course, we wouldn't know the truth. But we, we do want to look at instability and uncertainty. So how do we do that? Well, we can use an approach called bootstrapping. Bootstrapping is an idea where we, we have our original dataset and we sample from that original dataset with replacement until we get a dataset of the same size as our original dataset. And then in each of those bootstrap samples of the same size, we can develop another model. Again, we would use exactly the same model development approach as before, but this would lead to— for example, if we use 1,000 bootstrap samples, we would have 1,000 models. So just like in the simulation where I was generating 1,000 models, here I'm doing exactly the same thing based on 1,000 bootstrap samples. We can then apply each of those 1,000 models back to our original data so that every individual in our original data has 1,000 predictions, one for each of their bootstrap models. So I can then do my prediction instability plot that I showed you on the previous slides, where on the y-axis I've got my predictions for each of the bootstrap models, and I can plot that against the original prediction from my original model in the original sample. Um, yeah, so I've got the variability displayed on the y-axis against the original model, and clearly when a model is more stable going to have less variability on the y-axis, but when it's unstable, there's going to potentially be that huge variability and maybe even going from 0 to 1 that we exposed before. Related options which we'll come back onto are Bayesian modeling, getting posterior distributions, and if we use maximum likelihood estimation, particularly if we don't use a penalized approach, we can use Fisher's information matrix, but that would tend to work best when the sample size is reasonably big. Okay, let's look at a real example now. I'm going to develop a model for 30-day mortality risk after, after a myocardial infarction. I'm going to use the GUSTO-1 data. This is freely available thanks to Duke Clinical Research Institute. Those of you that work in this field will have seen this data being used quite a lot of times. The full data has 40,000 participants, about 3,000 deaths by 30 days, so the overall risk is about 7%. I'm just going to focus on 8 predictors listed here. For reference, if you just fit a logistic regression to this equation— to this dataset, you get a C-statistic of about 0.8. So a measure of discrimination performance. So I'm going to examine the instability when I use all my data to develop my model, but I'm also going to compare it to taking a random sample of 500 patients. I'm going to use LASSO logistic regression for my model development. And I'm going to use bootstrapping like I described before to examine instability. So these are the results. On the left here we've got our plot which is from the models that were developed with the full dataset of 40,000 individuals, and what we're looking to see is whether the estimated risks across the bootstrap models are quite stable compared to the estimated risk from the developed model. So I've got all the individuals in my data here, and I've scattered all their 1,000 predictions from the bootstrap models against the estimated risk from the developed model. And we see that it— they, they hug the line of, um, of equality, um, pretty perfectly, don't they? The dashed line is my 95% interval around the, around the, um, line of equality based on the variability that I'm seeing here. We see that that's tiny. So for example, somebody whose risk is estimated to be 0.2 from the developed model, their risk from the bootstrap models, you know, the maximum risk goes from about 0.17 to 0.25, but the 95% range of values is much tinier, like 0.19 to 0.21. So huge stability in this setting, but you would expect that. You've got 40,000 patients, 2,800 events, 407 events per predictor. So huge data, stable models. So any one model from the multiverse is likely to be reliable here, and this is exposing, exposing that. If we though go on to look at the 500 patient sample size situation, we see that the instability starts to get a lot wider. For example, this individual, individual whose predicted risk is 0.2 from the model, now we see that the range goes from, well, maybe up to about 0.6. 0.6 down to 0 across the bootstrap models, and the 95% range of values from the bootstrap models is down to about, what, 0.1 to about 0.4. So now we're going down to low risk up to moderate to higher risk. So there's starting to be instability that's causing some concern here about whether this model might, might not be quite as reliable as we would like it to be to be making clinical decisions. decisions when people are, you know, estimated low risks, but actually the risk could be a lot higher. There's a lot of uncertainty about it. I mean, even right at the top here, with predicted risks of about 0.7, you know, the uncertainty around that, you know, it's coming down to 0.4, 0.3. You know, does that change the decision? Well, this is context-specific, but I'm just raising the point that I'd like to see these plots because I think it's telling us something that the original just single point estimates are not telling us. At this point, you know, people sometimes say to me, well, this is because you're using LASSO and you're using regression statistical methods which are a bit outdated now. And that's absolutely nonsense because it doesn't matter if you're using the most sophisticated machine learning method, you're still restricted by the sample size. So let's have a look at how a random forest does. So this is— I'm going to use 500, my dataset of 500 people. So you've seen this one on the left already. This is the, the LASSO instability. If we use a random forest, I'm just going to use the defaults in a particular software package, uh, which has got essentially 100 trees. The stability is much— instability is much worse. So that individual with the predicted risk of 0.2, now we're seeing the range going up to I don't know, 0.8, 0.9, down to 0. Those at high risk, again, huge range from 0 to 1. And you can see that the 95% interval is much wider for the random forest than the lasso model. So, you know, just because you're using a machine learning method doesn't mean that you don't have to worry about these things. You really do. If you did something more sensible and reduced the number of trees down, you may end up with something very similar to the left-hand side. side, but the defaults often tend to allow for large complexity. So just be very careful. This is not a statistical issue, this is a general issue whenever you're developing a prediction model, that there's going to be instability and uncertainty. And I think we should, we should be exposing that, for example, using bootstrapping. Okay, so I focused on bootstrapping, but really a more general concept is actually just wanting to be able to quantify the uncertainty around an individual's risk. So their sampling distribution, or a better term is a posterior distribution, and really bootstrapping is, is, is a way of approximating an individual's posterior distribution. And this is naturally invoked by thinking of things in terms of a Bayesian approach. What's an individual's uncertainty around the parameter of interest, for example their outcome probability, their risk, conditional on the development data, the predictors that you've included in the model, and some prior beliefs. Now in a, in a prediction model context, those prior beliefs are just aspects that help you deal with overfitting, so they're shrinkage priors. So that's very natural. The pink here is my likelihood, the data, well, the data is telling me about their predicted risks, and, um, the, the turquoise, the green here, the posterior distribution is an amalgamation of the prior and the likelihood. And we see that for this individual, we have this posterior distribution which is fully conveying all the information from the data and the prior that's helping us then make decisions about that individual in terms of their risk. This is on the logit scale. Let's just focus in on one individual now, and let's focus in on just thinking about absolute risk, and that's the scale that we want to think about. So for this individual their absolute risk is, is summarized by their posterior distribution here. Okay, so we've developed a model and this is conveying all the uncertainty. So traditionally what we would focus on is a point estimate. So that might be the mode or the mean of the distribution, a single point estimate that we then use to make decisions or convey information about risk. What I'm really saying is But there's more about uncertainty here that we should be conveying as well, or could be conveying as well. Um, so for this individual, we cannot just think about the mode or the mean, we can think about conveying the whole distribution. So for example, the most fundamental thing is a credibility interval. So we could present a range here that goes from about 0.05 to about 0.45. conveying 95% of our information about where somebody's actual risk lies. So Bayesian approach is really, really natural to do that, and that's something I would encourage to do. But let's just think now, from now on, just a bit more broadly about what we actually do with this information and whether it's useful. I really like this quote, coming back to the Multiverse of Madness, that madness is not a consequence of uncertainty but of certainty. So the idea really is that just pretending that we're very certain about our prediction is not actually helpful. And really, to be clear and scientific, we should be presenting the uncertainty around that too. So I think we should embrace that. So let's embrace the uncertainty. So that's my recommendation, is that when people develop models, that we shouldn't just be allowing these models to give a single estimated risk for an individual. We should be allowing them to present the whole uncertainty distribution, either from a bootstrap approach or from a Bayesian approach, to give measures such as 95% uncertainty intervals, confidence intervals, compatibility intervals, credible intervals. Let's go back to our LASSO model, and I'm going to apply that concept here. I'm going to go to applying that with 40,000 people for my development, or on the right here, 500 people with my development. And I've got 5 individuals, the same 5 individuals in each graph. And what I've done is I've added in the uncertainty distribution for each of those individuals based on my models. So let's just home in a little bit what I mean. So let's focus on this individual here. So this individual, their risk estimate from my model, which I developed in that smaller sample size of 100 people, their best estimate of risk is 0.24. That's my best guess. So if I was to make decisions, I had to make decisions, that would be the risk that I would take. But still, I think there's important information to be conveyed Not just about that point estimate, but about the whole uncertainty distribution. So the 95% confidence interval, compatibility interval, for example, around this risk for this individual is 0.08 to 0.58. And I think that's important to convey because it tells us something about the strength of information from the model that we developed. So across all the potential models in the multiverse that we could have created, risks range from about 10% up to about 60%. So low risk to a pretty high risk. Now that may help you understand as a clinician, as a patient, as a guideline developer, somebody critically appraising a model, that maybe there's a lot of uncertainty about these predictions and maybe this model is not fit for use. And again, that stems from the small sample size. here, but it's exposing that. In contrast, of course, on the left-hand side of the huge data, the uncertainty around predictions is very, very narrow. Let's go back to our CRASH model that I introduced at the start. One thing to note, which I didn't say at the time, we actually see uncertainty intervals being presented. So for this individual from Denmark, their risk of 14-day mortality is 18%. And a 95% interval for that risk is 11% to 27%. So this is one of the few models that actually does present uncertainty intervals too. I would like the whole distribution to be conveyed in some way, um, but a 95% interval is a good start. Now this is the big turning point of this talk. In current practice, like I said, presenting uncertainty around predictions is rare, and there's much debate actually about whether this is a sensible thing to do. If you speak to people, some people will say absolutely not, we should never be presenting uncertainty intervals to patients. But you have people like me who suggest that sometimes It might be something that patients want, but as a methodologist, I think it's something that we should always be having on the table if we need it. Let's have a think about this a bit more. So pros for uncertainty. Number 1, providing uncertainty around predictions and estimated risks, it provides a more complete picture than just a point estimate. Hopefully I've conveyed this. I think it's, it's a sort of measure of performance, a performance metric It tells us the strength of evidence behind a model's prediction. Now, it's not the only thing. We'd want to know other things like calibration and clinical utility and so forth, but I think it's an important metric and measure that shouldn't be dismissed. Um, he says that although a point estimate tells us which decision to make for now, we also may want to know how much confidence we should have in that decision. And if we are insufficiently confident that we are right, further research is warranted. And this is this concept that we can use uncertainty as a, as some sort of metric of strength of evidence. There's also a really nice paper by Dorana Thomason talking about effective sample size in that context too. Think about it this way. Let's say we have a scenario where we, we're going to say we're going to initiate treatment if an individual's risk is above 5%. Now, what if an individual's uncertainty distribution falls on either side of that threshold, um, and maybe there's 60% above that threshold and 40% below it? What would you do? Um, what if the upper value of the confidence interval was 90% and the lower was 0%? So there's a lot of uncertainty. Would you be happy using that model, or would you need more evidence required? And this comes closely back to decision theory and clinical utility, evidence from validation studies, and so forth. But again, I'm just raising the point of why this is of interest. The second one is that understanding uncertainty helps people reviewing models, so examining, for example, for publication, or people examining for whether a model should be used in practice. So peer reviewers, journal editors, systematic reviewers, people working for organisations like WHO and NICE regulators. People looking at the quality models have to do risk of bias assessments, for example using the ProBus tool. Maybe that could be informed better if we understood the uncertainty, the instability around predictions. Like I said, wide intervals flag high risk of bias potentially, especially we don't have any validation studies. Also uncertainty aspects might help us think about model in terms of model fairness. Now fairness is a broad topic But if you think about models having predictions with large uncertainty for one group, for example, they may be very certain for, for whites but very uncertain for non-whites if the development sample size included mainly whites and not non-whites, then this may flag— help flag fairness issues, that the model is more reliable in whites than non-whites. So this will help us to expose models with that potential issue. Otherwise, if you just provide point estimates, we wouldn't know. Fourthly, it may inform shared decision-making. So some patients may ask health professionals, okay, you've provided me my estimated risk, but what's the evidence behind that? Where's that coming from? And in such situations, information about uncertainty I think should be readily available if patients ask for that information. Then I think we should be telling them that. Knowing that predictions are precise and of course well calibrated and there's some evidence of clinical utility should, you would hope, improve a patient's confidence and trust in using the model. It may reduce their anxiety and may enhance management, so it may improve adherence to treatment and monitoring. Conversely, if doctors and health professionals and patients know predictions are very uncertain, That may lead to an individual abstaining from using that model. Health professionals say, I don't want to use that model because I don't believe— trust the findings. And it may motivate obtaining more information and more evidence to inform clinical judgments. At this point, it's very important that I don't just speak for patients. We also need to hear from them themselves, and we've done some research that's published in our BMJ paper, which I'll come on to. But a general note from the literature is that patients do tend to want information that's available to them. So in the Standing Together initiative, the reference is at the bottom there, PPI, patient and public involvement and engagement groups, expressed generally wanting the uncertainty in their own prediction to be communicated to them. We spoke to a PPI group in Ewing sarcoma, and they told us clinicians should discuss with their patients that this is the most likely case for you, but the most likely case still has uncertainty around it. And indeed, one representative suggested that it was ethically mandatory to provide patients with all the knowledge available to them about a model's predictions, including the uncertainty, if they request it. So I think this is really important to So bear in mind that if you're developing a model, you need to understand the people who are going to use it and what their requirements are. Here are some quotes from our research that we published in the BMJ from patients. When I think back to the comment from our consultant that a particular patient had a 70% chance of survival, I now wonder how reliable that figure could possibly have been. Had it been possible to tell us what the uncertainty was Around that figure, it might have led to changes in their treatment. It would certainly have left us feeling better informed. Even now, I'm not sure that this data exists and how reliable that 70% figure is at the individual level. I believe in the old adage, knowledge is power. To make patients aware of the inherent uncertainty in any predictive model is, in my mind, ethically mandatory. To give them the opportunity to get some idea of how uncertain the prediction is, is arguably just as important. I think most patients want to be given the best available information and to have explained to them how that information may or may not be completely useful in that particular case. However, I do acknowledge that there are instances when patients may not wish to be given this information. Some may choose not to access it. Some may reason that the knowledge would not change their decisions. If there is only one treatment path available, does it matter if you have absolute or any partial confidence of the outcome? That is ultimately a decision for the patient. So some really good pros and cons here given to us by patients themselves about, yeah, actually they would want this information, but not everybody would, and sometimes it just wouldn't be useful. Cons for uncertainty, and this is where the strong arguments come from for people saying this should never be given to patients. So number one, a single estimate of risk is already difficult to communicate and interpret. So, right, an individual's risk of death, um, let's say it's 0.3 from the model. And so the health professional might say to that individual, in a group of 100 individuals with similar characteristics to you, the model expects 70 of them to be alive at 5 years and 30 not to be alive at 5 years. Okay, that's a good statement, a clear statement, but there's already uncertainty in that statement. is this individual going to be one of the 70 that's alive, or are they going to be one of the 30 that's not alive? We can't tell them. So there's already uncertainty. Of course, that's a probability. There's uncertainty representing some uncertainty. So if we present an uncertainty interval around that measure of probability, is that just going to confuse them? And a related conflict is, of course, that an individual— no individual has a risk. You could strongly argue that an individual will only have an outcome of yes or no. They do or do not have the outcome, so they are or are not alive by 5 years. Risk is only a concept we can think about when averaging across individuals. So again, a little bit of tension there. Secondly, communicating uncertainty actually may increase anxiety and reduce trust. And this is research not done by me, but others have shown this. So, for example, the International Patient Decision Aid Standards Collaboration recommends to be cautious about presenting uncertainty of risk estimates. This uncertainty may be psychologically aversive and difficult to understand, and that optimal methods of communication remain to be determined. Politi performed a review and concluded that both patients' and physicians' interpretation of and responses to uncertainty may depend on their personal characteristics and values and may be affected by the manner in which uncertainty is communicated. So this is a very nuanced area. Thirdly, the interpretation of uncertainty of risk is context and individual specific. So let's say an individual risk of prostate cancer is 0.005 and the confidence interval goes from 0.001 to 0.1, okay, so up to a 10% risk. Should they have a biopsy? Now Think about the concept. The context is dependent on the patient. So somebody who's aged 85 years with many existing comorbidities might conclude that this interval here is all suggestive of a low risk for them to justify no biopsy. However, somebody that was aged 40 years with no comorbidities and for which interventions early may dramatically improve and extend life if prostate cancer is there might be more concerned that actually my upper risk is 10%, and so they might request more information to make better decisions for them. Again, I'm not saying that we should be basing decisions on upper values of the confidence intervals. I'm just demonstrating that understanding the uncertainty may have an impact on your decision-making, and it's context-specific, so it depends on who you are as an individual in terms of what your thresholds are and how you view things. In summary, I've given some pros and cons, and I want to emphasise that what I'm saying is from a methodological perspective, we should always be allowing presentation of uncertainty, posterior distributions, and credible intervals, for example, around risk estimates, but I'm not saying that this should always be given to the patient. If it is given to the patient, it needs to be tailored, so it needs to be a tailored patient-specific approach. Not all patients are going to benefit from this or want it, and we need to be very careful. If you think about decision analysis theory in particular, this tells us that we should be basing decisions on expected values, so posterior mean risks, for example. Or not for example, that the posterior mean risk is our best guess at the decision, and that's the— based on the current information we have available, that's the best thing we can do. Therefore, given decision analysis theory tells us that, do we need to tell patients or doctors about uncertainty? Well, I think it should be available if they want it, and I think particularly, like I said, for people critically appraising models, we should be, we should be having that information available. So Vickers et al., coming back to this quote about the fact that, okay, point estimates tell us what decision to make for now, but we may also want to know how much confidence we should have in that decision. And if we are insufficiently confident we are right, further research is warranted. So at the point before we get to giving a model to patients and doctors, having understanding about the uncertainty around it may say, okay, there's too much uncertainty, this model is not right yet, it's not ready for use yet. And so we'd actually get to the point where patients need to worry about the uncertainty around a model, and maybe any of those models that we give to patients are the ones that we, you know, are very confident about anyway. But again, we need to think about situations of rare diseases, and there's always going to be uncertainty there. So this is a complicated issue, and it needs a lot more research, and I'm looking forward to, to contributing to that in the future. Okay, in summary, let's bring this to a close. I hope this has been useful. Um, there's some controversial aspects to it, but I think the general premise is important and something I would stand by, is that most models at the moment only give a single-point estimate of risk. Different models that you could have developed from the multiverse may have given very different predictions. And I think we should be exposing that. Yeah, so we think about those instability plots from earlier where instability showed that risks for an individual could be very different, that could go from 0 to 1 depending on the model I produced. We should know that information, shouldn't we? That gives a more complete picture, exposes strength of evidence behind a particular— one particular model's predictions, helps those critically appraising a model, contributes towards assessments of model fairness, and may Like I said, may enhance the doctor-patient conversation. And even if we did go down the road of conveying this to patients, effectively communicating that uncertainty with patients is going to be challenging, shouldn't always be done, and the best approach is going to be context-specific and needs to be tailored to the individual at hand potentially. Thanks so much for listening. I'll leave you some key references. I've also littered the talk with references, so you might want to go back to particular slides to look at those references, but particularly to note the BMJ paper on uncertainty of risk estimates and our BMC paper on clinical prediction models and the multiverse of madness, all building essentially on aspects to do with sample sizes and small sample sizes in prediction modelling research, some of which are listed here, like our paper in Lancet Digital Health on the importance of sample size on the quality and utility of AI-based prediction models for healthcare. Right, I'll stop there. Like I said, I hope it's been useful, and thank you so much for listening.