A Neural Modelling Tool for Non-Linear Influence Analyses and Perspectives of Applications in Medical Research

Round 1

Reviewer 1 Report

In this paper,  the authors mainly addressed the existing applications and possible future applications of their previsously developed tool for improving performance of neural networks. However, there are many defects in the current manuscript. The detailed comments are outlined below.

1. More related works should be investigated and discussed in the introduction section.

2. Applications in the medical field should be tested with the methods in other applications.

3. Efficacy of their NN tool should be verified on the latest deep learning models.

Author Response

Response to Referee 1

Q question/comment by referee

A answer by authors

Q In this paper, the authors mainly addressed the existing applications and possible future applications of their previously developed tool for improving performance of neural networks. However, there are many defects in the current manuscript. The detailed comments are outlined below.

1 More related works should be investigated and discussed in the introduction section.

A In the introduction we have inserted a couple of new references and briefly discussed about deep learning applications in medical research.

Q 2 Applications in the medical field should be tested with the methods in other applications.

A In this manuscript we perform a review of our previous studies (development of a NN tool for analyses in small datasets and its application with innovative methods in climatic and environmental field) and we propose application perspectives of these methods for medical research. It is not an original research paper, but a Perspective, thus we do not present new original results here. Any new investigation will be presented in future research papers.

Q 3 Efficacy of their NN tool should be verified on the latest deep learning models.

A In our previous works we did not compare our results with those coming from application of deep learning models simply because these models are correctly appliable only at large datasets analyses (otherwise they fall into overfitting problems), while our investigations concern just small datasets. We are aware that in the analysis of large datasets deep learning can certainly do better. Nevertheless, in the medical field there are often small datasets to be investigated efficiently, so that we think that our tool and its application methods can be of help.

Reviewer 2 Report

This manuscript presents a comprehensive extension of the neural modelling with an ensemble strategy using three applications and also discuss some potential applications in the medical field. Please see my comment below.

Major comments:

In figure2, the migration rates in black is the true/observed value, if I understand correctly. If so, the blue line and red line seem not so good, while the authors claim success in row 152.

Minor points:

Row 45, should be “hide”, rather than “hidden”?

Author Response

Response to Referee 2

Q question/comment by referee

A answer by authors

Q This manuscript presents a comprehensive extension of the neural modelling with an ensemble strategy using three applications and also discuss some potential applications in the medical field. Please see my comment below.

Major comments:

In figure2, the migration rates in black is the true/observed value, if I understand correctly. If so, the blue line and red line seem not so good, while the authors claim success in row 152.

A You understand well. We add a reference to Table 1 for numerical details. We understand that this performance can seem not so good if compared with those obtainable in hard sciences, but in a human-science application like this, considering also that we lack any social data about causes of migration, this strong impact of climatic drivers is quite impressive. In any case, we change “very good” in “surely good”.

Q Minor points:

Row 45, should be “hide”, rather than “hidden”?

A Of course you are right. Thanks for the suggestion. We have corrected.

Reviewer 3 Report

I can’t say that the methodology described here is innovative. The method that you call pruning is very similar to a sensitivity analysis already used in medicine. In the chapter of capturing and interpreting the non-linear relationships between explanatory variables and the response variable, there are methodologies such as generalized additive models (GAM) or Generalized Additive Neural Networks. In fact, there are variants for longitudinal data, such as AutoRegressive Generalized Additive Models (GAMAR).

The only advantage of using neural networks over GAMs is that in the latter, we need to specify the interactions between explanatory variables and the response, whereas neural networks automatically model such relationships. However, given the interpretative power of GAMs, especially in medicine, they are preferred over neural networks, especially when the number of observations is limited. In situations where a neural network is employed, one can use an eXplainable Artificial Intelligence technique called Local Interpretable Model-agnostic Explanations (LIME). This may involve the interpretation of a neural network through a GAM, thereby establishing a relationship between predictor variables and the response, as well as determining the importance of each variable through the interpretation of their respective partial function.

Another issue I found, which is often repeated in many papers, involves the use of regression models (and here we can consider a neural network with one layer as a regression model slightly more complex than a GAM) in the context of longitudinal or time series data. The more suitable neural networks for such scenarios would be Recurrent Neural Networks (e.g., LSTM, GRU), as they allow modeling autocorrelations. In the realm of interpretable models, one can use models like the previously mentioned GAMAR.

Another issue was the use of R^2 to measure the performance of a neural network, even when it encounters challenges, especially in less flexible models.

Author Response

Response to Referee 3

Q question/comment by referee

A answer by authors

Q I can’t say that the methodology described here is innovative. The method that you call pruning is very similar to a sensitivity analysis already used in medicine. In the chapter of capturing and interpreting the non-linear relationships between explanatory variables and the response variable, there are methodologies such as generalized additive models (GAM) or Generalized Additive Neural Networks. In fact, there are variants for longitudinal data, such as AutoRegressive Generalized Additive Models (GAMAR).

A We have inserted the following text in the Conclusions: We are of course aware that there are other methods, such as sensitivity analyses and Generalized Additive Models (GAMs), that do similar things to our tool. However, what we consider 'innovative' here is the set of features of our tool, including ensemble runs, attribution analysis and forecasting activities for small datasets available. Obviously, we also know that the neural networks used by us are quite simple (MLPs) and it is our intention in the future to include more powerful networks in this tool. In this Perspective, we only wanted to show the application potential of the current tool in the medical field.

Q The only advantage of using neural networks over GAMs is that in the latter, we need to specify the interactions between explanatory variables and the response, whereas neural networks automatically model such relationships. However, given the interpretative power of GAMs, especially in medicine, they are preferred over neural networks, especially when the number of observations is limited. In situations where a neural network is employed, one can use an eXplainable Artificial Intelligence technique called Local Interpretable Model-agnostic Explanations (LIME). This may involve the interpretation of a neural network through a GAM, thereby establishing a relationship between predictor variables and the response, as well as determining the importance of each variable through the interpretation of their respective partial function.

A We have inserted the following text in the Conclusions: Furthermore, our method should obviously be tested against standard models used in medical research, and this will be done in our future works.

Q Another issue I found, which is often repeated in many papers, involves the use of regression models (and here we can consider a neural network with one layer as a regression model slightly more complex than a GAM) in the context of longitudinal or time series data. The more suitable neural networks for such scenarios would be Recurrent Neural Networks (e.g., LSTM, GRU), as they allow modeling autocorrelations. In the realm of interpretable models, one can use models like the previously mentioned GAMAR.

A This is true, but one does not always have long time series and sufficient amounts of longitudinal data to apply these neural networks effectively. In any case, as written before, we are of course open to future improvements of our tool, with the inclusion of other algorithms.

Q Another issue was the use of R^2 to measure the performance of a neural network, even when it encounters challenges, especially in less flexible models.

A In this Perspective, we have referred to this performance measure for simplicity, but in the original papers we also used others, e.g., ROC curves. We have inserted this information in the text before Table 1.

Reviewer 4 Report

The paper describes how smaller neural networks with non-linear transfer functions can be used on datasets with limited numbers of cases, and how to analyze the contribution of certain variables to the predicted output. Examples are shown from climate studies.

While the models can capture non-linearities easier than deep neural networks and are probably more robust, the conclusions are a bit too strong. The models allow quantification of the effect of variables on the predicted output, but they are built on the assumption that the given variables are causal and complete. Drawing conclusions from analyses of these models on the causality (e.g. lines 245-246, line 258) would be a form of circular reasoning: you already assumed these variables to be causal. In that sense, the conclusion section, stating that the tool can be used for causality analysis, is too strong in my opinion.

It would also be good to show the non-linear contributions of variables better, e.g. in the example discussed in Figure 2, to make very clear that contributions are not just linear.

Furthermore, it would be good to show the improvement of the method over deep neural nets for the given examples.

Some more detailed comments:

- In Figure 2, I assume the same model is applied to all data points from all countries? Could you include the results of the linear multiple regression model, for comparison?

- Lines 171-186: if you leave out one variable, but the remaining ones still have a strong non-linear contribution, the performance of your NN and the linear multiple regression may still differ a lot; would it be better to look at drop in performance?

- Line 189: could you show a graph in which one variable is varied while the other ones are kept constant, to show that it indeed contributes non-linearly to the output variable? Is the relation monotonous?

- Lines 220-223 seem counter-infuitive (I was expecting something like my previous comment), and the rationale only became clear after reading the  next paragraph and looking at Figure 3.

- Line 258: this proves that there must be more than only the sun, but it does not necessarily prove that the other model variables _must_ have caused the increase in temperature (you assumed causality before building the model).

- Section 4 is fairly speculative; it would be better to show how your NNs do better than deep neural nets or linear regression.

Maybe good to have a native speaker read the manuscript for some smaller edits.

Author Response

Response to Referee 4

Q question/comment by author

A answer by authors

Q The paper describes how smaller neural networks with non-linear transfer functions can be used on datasets with limited numbers of cases, and how to analyze the contribution of certain variables to the predicted output. Examples are shown from climate studies.

While the models can capture non-linearities easier than deep neural networks and are probably more robust, the conclusions are a bit too strong. The models allow quantification of the effect of variables on the predicted output, but they are built on the assumption that the given variables are causal and complete. Drawing conclusions from analyses of these models on the causality (e.g. lines 245-246, line 258) would be a form of circular reasoning: you already assumed these variables to be causal. In that sense, the conclusion section, stating that the tool can be used for causality analysis, is too strong in my opinion.

A We understand your concern and partially agree with this. In fact, for datasets and therefore small neural networks like ours, one must always make a choice of a few variables to input. Sometimes they are the only ones available, sometimes they are chosen after a preliminary analysis involving linear and non-linear bivariate correlation analyses, sometimes there are physical reasons for these choices, which come from our previous knowledge of the dynamics of the system studied. There is always a choice dictated by our prior knowledge, unless we consider a huge amount of variables available with a deep learning method, but this is not our case. In any case, our analysis allows us, within the few input variables, to understand which are the most ‘influential’ on the target variable. For this reason, and according to your comment, we decide to substitute the word ‘causality’ with ‘influence’ in the title and in other places of the manuscript, even in the Conclusion section.

Q It would also be good to show the non-linear contributions of variables better, e.g. in the example discussed in Figure 2, to make very clear that contributions are not just linear.

A Here, and in the original paper, we have not burdened the figure with another line, which would have made it difficult to read, and have preferred to give the information of the better performance of the network compared to the linear multiple regression in the table.

Q Furthermore, it would be good to show the improvement of the method over deep neural nets for the given examples.

A In our previous works we did not compare our results with those coming from application of deep learning models simply because these models are correctly appliable only at large datasets analyses (otherwise they fall into overfitting problems), while our investigations concern just small datasets. We are aware that in the analysis of large datasets deep learning can certainly do better. Nevertheless, in the medical field there are often small datasets to be investigated efficiently, so that our tool and its application methods can be of help.

Q Some more detailed comments:

In Figure 2, I assume the same model is applied to all data points from all countries? Could you include the results of the linear multiple regression model, for comparison?

A See above.

Q Lines 171-186: if you leave out one variable, but the remaining ones still have a strong non-linear contribution, the performance of your NN and the linear multiple regression may still differ a lot; would it be better to look at drop in performance?

A If you look at previous rows, you can see that the first thing to do in this influence analysis is precisely to look at the drop in performance, as you suggest here. This is the first thing that we have done and, in fact, avoiding temperature leads to the major drop in performance, so that we consider it as the most influential variable (see the statement after the table). Only after this analysis we go to consider the difference between performances of linear and NN models.

Q Line 189: could you show a graph in which one variable is varied while the other ones are kept constant, to show that it indeed contributes non-linearly to the output variable? Is the relation monotonous?

A This is not a research paper but a Perspective, so that you can find more details in our original papers cited here. However, this way of acting is similar to a bivariate analysis which we performed preliminarly.

Q Lines 220-223 seem counter-intuitive (I was expecting something like my previous comment), and the rationale only became clear after reading the next paragraph and looking at Figure 3.

A We are sorry. Now we add: ‘(see the following example)’, so that the reader can know that a further explanation follows.

Q Line 258: this proves that there must be more than only the sun, but it does not necessarily prove that the other model variables _must_ have caused the increase in temperature (you assumed causality before building the model).

A We substitute ‘caused’ with ‘more deeply influenced’.

Q Section 4 is fairly speculative; it would be better to show how your NNs do better than deep neural nets or linear regression.

A We are aware of this. As a matter of fact, our tool has been widely applied in the medical field, as shown by the many citations of the article presenting the tool itself (A. Pasini, 2015, Journal of Thoracic Disease), but without the methods of application reported in this Perspective. This Perspective aims to fill this gap and provide medical researchers with new ways to apply it. As far as we are concerned, in future studies we will certainly apply our methods by comparing them with those already used in medical research (including deep learning) and publish them in original articles. At this time, however, we thought we would anticipate the possibility of these applications with a Perspective.

Round 2

Reviewer 1 Report

None.

None.

Reviewer 3 Report

My suggestion is to be carefull with the use of R square in context of neural networks. It can be only used if we have just a simple perceptron (with just one neuron), due to the fact that it is the only structure equivalent to a Gneralized Linear Model.

Reviewer 4 Report

Thank you for the adaptations and the arguments to the discussion.

One final remark about the example in Figure 2 / Table 1. The difference (and drop) in R^2 is an indication of a non-linear influence, but still a fairly indirect one. If you see room to show how the output indeed varies non-linearly with one of those variables in a figure (with the other variables staying fixed), that would be appreciated.