Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit

Round 1

Reviewer 1 Report

In general, the work done is described properly, although as is highlighted in the Conclusions and Discussion section, the model follows a general approach and does not reflect the variability involving clinical data, which is crucial for decision-making in health. 

There are three paragraphs at the end of the Materials and Methods section that should be removed, and in the Result section appears duplicated a sentence.

Author Response

Comment: There are three paragraphs at the end of the Materials and Methods section that should be removed, and in the Result section appears duplicated a sentence.

Response: We appreciate your comments and pointing out the error. We've now removed the three paragraphs at the end of the Materials and Methods section and duplication issue has been resolved in the Result section.

Reviewer 2 Report

The authors proposed phase-type survival tree(PHTST) in previous work, , This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit.The research has certain significance, but there are still many problems in the paper:

(1) The font format of the paper is not uniform, such as lines 65-68 and 225-226.

(2) At the end of the Introduction, the organizational structure describing the text can be added to enhance readability.

(3) In Materials and Methods, multi-level headings appear continuously, and transition sentences can be appropriately added in the middle.

(4) Some pictures have low resolution, and it is recommended to replace them with vector graphics, such as Figure1. Moreover, the transition rate from state2 to state3 in Figure 1 is , why is it still  after state3 ?

(5) At the end of Chapter 2, there are a number of things that are not relevant to this study, which may be journal template descriptions.

(6) There are missing pictures in the paper, such as Figure 20.

(7) It is mentioned in this paper that the author has proposed the PHTST model in 2010 in his previous work. In the application presented in this paper, what are the advantages of this method compared to existing research?

(8) The title of each chapter is the template content, and the structure of the thesis has not been reasonably modified and arranged according to its own content. In addition, the content in Acknowledgments is the initial content in the journal template, and authors need to modify it according to the actual situation.

Author Response

I appreciate your helpful comments. Here is our response:

(1) The font format of the paper is not uniform, such as lines 65-68 and 225-226.

Response: Thanks a trillion for pointing it out. The paper is thoroughly revised to ensure uniform formatting.

(2) At the end of the Introduction, the organizational structure describing the text can be added to enhance readability.

Response: Thanks a lot for the suggestion. A paragraph on the organizational structure is added at the end of the introduction section.

(3) In Materials and Methods, multi-level headings appear continuously, and transition sentences can be appropriately added in the middle.

Again, I appreciate your suggestion. The multi-level headings have now been improved accordingly in the Material and Methods section.

(4) Some pictures have low resolution, and it is recommended to replace them with vector graphics, such as Figure1. Moreover, the transition rate from state2 to state3 in Figure 1 is , why is it still  after state ?

We have now updated figures 1 and 4 accordingly. The transition rates are placed between two states between which the transition these are representing. We have now removed it after state three. 

(5) At the end of Chapter 2, there are a number of things that are not relevant to this study, which may be journal template descriptions.

Thanks a lot for pointing it out. We have now removed such three paragraphs.

(6) There are missing pictures in the paper, such as Figure 20.

We have made sure all pictures from Figure 1 to figure 22 are there.

(7) It is mentioned in this paper that the author has proposed the PHTST model in 2010 in his previous work. In the application presented in this paper, what are the advantages of this method compared to existing research?

I appreciate your comments. We have described it in the discussion section: "

It models the process dynamics of a care system more realistically by representing the patient journey through the care system as a finite state continuous-time Markov chain. It has better explainability to the healthcare professionals as the blocking state is modelled as a partially-observable state of a continuous Markov chain exhibiting the stochastic nature of discharge delay. Another contribution is the PHTST-based model for analysing the effects of individual clusters and their interactions with the whole stroke care unit. We can also use the model to determine the association between demographic factors and the effects of discharge delay. This information can identify the reasons for discharge delay and develop better solutions to minimise discharge delay. We can also use it to estimate the effects of demographic change in the patient population on discharge delay and its effects and continually review the trends in discharge delay and resolve these. The model helps recognise groups of patients who require attention to resolve the most common delays and prevent them from happening again. The information about the cost of discharge provided by our model helps health managers and policymakers to plan and allocate budgets for alternate solutions.

"

(8) The title of each chapter is the template content, and the structure of the thesis has not been reasonably modified and arranged according to its own content. In addition, the content in Acknowledgments is the initial content in the journal template, and authors need to modify it according to the actual situation.

We have used the template as it is, keeping the same structure that fits the paper contents well. We have now slightly modified the structure following your suggestion (3).

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Editor,

The authors have addressed all the concerns. I think the manuscript can be accepted in as it is form.

Author Response

Thanks a trillion for accepting the revised manuscript.

Reviewer 4 Report

This manuscript applies survival tree analysis to hospital discharge and bed blocking.

The authors correctly identify delayed discharge (and length of stay) as a major issue for health care sustainability.

 

The introduction identities well the  common operational issues behind this issue, such as out-of-hospital bed availability, and appropriately terms these ‘discharge delay’. The fact that an ageing co-morbid population means that medical issues requiring longer in-hospital management will increasingly be an issue in the future also warrants a brief mention, if only to identify this as not being in scope for this study.

P2, l78 requires units of currency.

In general, the background around causes of discharge delay could be briefer, in the interests of space, without loss of messaging.

Much of the latter part of the introduction belongs in methods, as it describes the nature and origin of the data to which modelling was applied.  

 

The methods section describes and illustrates the Markov chain, and its transitions, well.

In this model, the states appear not to be hypothetical, but are locations/types of care. Both phases and states are described, and physical locations/types of care are really only mentioned in detail in p11 l317 – 319, and could be clarified earlier in the manuscript as it provides clinical relevance to the model. The absorbing state covers both death and discharge. This makes the model focussed on the institution (e.g. capacity, costs), as patient-centred and community care-centred perspectives would consider these differently. This warrants mention.   

The PHTST clusters patients according to specific criteria, patient characteristics. The reasons behind the criteria chosen could be clarified. The basis of the survival tree, with splits based on WIC minimisation, appears sound, and is well outlined in Table 1.

The addition of a blocking state appears logical. It appears to align with the clinical state of ‘awaiting, or ready for, discharge’. If so, this might warrant mention. 

 

The results section includes some data which belongs in the methods, such as how delays were specifically modelled: p11, l313 – 329.

Figure 5 illustrates the modelling output without clustering, and is well described in the text. Figure 6 illustrates the impact on the institution (numbers awaiting discharge) clearly. Figure 7 illustrates numbers awaiting discharge from each from each phase. If these phases are the physical states (eg Phase 1 = acute care) then this figure would be clearer if this were apparent from the stand alone figure, and legend. This would resonate better with clinical/hospital administrative readers, for example. Subsequent figures illustrate nicely the implications of the modelling for this group.

 

The discussion mentions explainability to healthcare professionals, which I agree is important. Note the comments previously on figure labelling to better explain phases and states. The utility of the model to project impacts of population changes, and to identify groups for whom greater attention would provide institutional benefit, is well described. The authors might consider adding some scenario analysis, for example what might happen in 10 years if population ages have increased, or the impact on bed block if more out-of-hospital beds were made available.

The limitations of this model are also well described. The conclusions are sound

Author Response

Dear Reviewers and Editors,

 

We profoundly appreciate your time and efforts in handling the manuscript and providing an opportunity to improve it based on reviewers' suggestions and addressing their comments. We have thoroughly revised the manuscript accordingly and responded to each reviewer's comment. We've attached the revised manuscript for your consideration in both word (with changes highlighted) and Pdf format and hope the updated manuscript will meet all your expectations. Here is the commentary on the revisions responding to reviewers' comments.

Reviewer's comment	Summary of response	Location
This manuscript applies survival tree analysis to hospital discharge and bed blocking. The authors correctly identify delayed discharge (and length of stay) as a major issue for health care sustainability.   The introduction identities well the  common operational issues behind this issue, such as out-of-hospital bed availability, and appropriately terms these 'discharge delay'. The fact that an ageing co-morbid population means that medical issues requiring longer in-hospital management will increasingly be an issue in the future also warrants a brief mention, if only to identify this as not being in scope for this study.	We appreciate your suggestions, and following these, we have now updated the introduction section accordingly on the second page, the first paragraph, lines 85-87, mentions as follows: "Elderly patients experience delayed discharge more as an ageing co-morbid population, so medical issues requiring longer in-hospital management will increasingly be an issue in the future."	The second page, the first paragraph, lines 85-87
P2, l78 requires units of currency.	Thanks a trillion for noticing and pointing it. The currency unit £ is now added accordingly.	Page 2, Line 78
In general, the background around causes of discharge delay could be briefer, in the interests of space, without loss of messaging.	Again, we appreciate your suggestion and have now shortened this section accordingly.	Pages 2-3, lines 90-106.
Much of the latter part of the introduction belongs in methods, as it describes the nature and origin of the data to which modelling was applied.	Thanks for your suggestion, and we have now moved this latter part to the Materials and Methods section.	Page 3, Lines 108-149.
The methods section describes and illustrates the Markov chain, and its transitions, well. In this model, the states appear not to be hypothetical, but are locations/types of care. Both phases and states are described, and physical locations/types of care are really only mentioned in detail in p11 l317 – 319, and could be clarified earlier in the manuscript as it provides clinical relevance to the model.	Thanks for your suggestion. We have now also mentioned on page 5 in lines 142-144.	Page 5 in lines 142-144.
The absorbing state covers both death and discharge. This makes the model focussed on the institution (e.g. capacity, costs), as patient-centred and community care-centred perspectives would consider these differently. This warrants mention.	Following your suggestions, we have now mentioned on page 4, lines 163-166 as follows: "This single absorbing state might cover both death and discharge, making the model focused on the institution (e.g. capacity, costs) as patient-centred. Therefore, the community care-centred perspectives would consider multiple absorbing states in sections 2.3 (extended PHTST) and 2.4.2 (multi-absorbing state)."	Page 4, lines 163-166
The PHTST clusters patients according to specific criteria, patient characteristics. The reasons behind the criteria chosen could be clarified.	Thanks for your suggestions. We have now clarified it on pages 3-4, lines 156-159, as follows: "These covariates represent patients' characteristics such as gender, age at admission, and disease (diagnosed) available in the dataset used and have previously been identified in the literature and anecdotally as useful (Garg et al. 2011, 2012, McClean et al. 2009, 2011)."	Pages 3-4, lines 156-159
The basis of the survival tree, with splits based on WIC minimisation, appears sound, and is well outlined in Table 1. The addition of a blocking state appears logical. It appears to align with the clinical state of 'awaiting, or ready for, discharge'. If so, this might warrant mention.	Thanks a lot for your suggestion. We have now mentioned it on page 8, lines 253-254, as follows: "This special state is called the 'blocking state', which represents the clinical state of "awaiting" or "ready" for "discharge"."	Page 8, lines 253-254
The results section includes some data which belongs in the methods, such as how delays were specifically modelled: p11, l313 – 329.	Thanks a lot for your observation and suggestions. We have now moved the following contents to the Material and methods section (page 3, lines 138-144): “We have used our model to understand the effect of delay in discharge from the stroke unit of the Belfast City Hospital. Patients can be discharged to either private nursing homes or other destinations such as their usual residences. Also, some patients can eventually die during their treatment. The estimated daily cost of care is calculated using estimates from Saka et al. (2009), adjusted from 2005. We attach unit costs of £164.80 per day for a stay in acute care (phase 1) and £114.80 per day for a stay in rehabilitative care or long-stay care (phase 2, phase 3 and phase 4).”	Page 3, lines 138-144
Figure 5 illustrates the modelling output without clustering, and is well described in the text. Figure 6 illustrates the impact on the institution (numbers awaiting discharge) clearly. Figure 7 illustrates numbers awaiting discharge from each from each phase. If these phases are the physical states (eg Phase 1 = acute care) then this figure would be clearer if this were apparent from the stand alone figure, and legend. This would resonate better with clinical/hospital administrative readers, for example. Subsequent figures illustrate nicely the implications of the modelling for this group.	The phases are latent but do represent hospital care.	Figures 5-7
The discussion mentions explainability to healthcare professionals, which I agree is important. Note the comments previously on figure labelling to better explain phases and states. The utility of the model to project impacts of population changes, and to identify groups for whom greater attention would provide institutional benefit, is well described. The authors might consider adding some scenario analysis, for example what might happen in 10 years if population ages have increased, or the impact on bed block if more out-of-hospital beds were made available. The limitations of this model are also well described. The conclusions are sound	Thanks for the suggestion. Figures 8-14 are already considering such scenarios, i.e. after 1000 days. These can be extended to any number of days or years. We have also added these scenarios in the conclusion section on page 19, lines 528-529, as follows: “We can forecast the impact of discharge delay after a given period, such as after 10 or 20 years or the result of adding more resources, such as extra beds.”	Figures 8-14 and page 19, lines 528-529.

 

We are looking forward to hearing from you,

Best regards,

Lalit Garg, Sally McClean, Brian Meenan, Maria Barton, Ken Fullerton, Sandra C. Buttigieg, Alexander Micallef

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit. but It is necessary to increase the comparative experiments with related research to enhance the persuasiveness.

Author Response

Dear Reviewers and editor,

We hope you are doing superbly well and appreciate your comments and suggestions to improve the manuscript. We have thoroughly revised the manuscript addressing your concerns and incorporating your recommendations. We have attached the revised manuscript and a commentary on the revision, responding to the reviewers' comments. We hope that the revised manuscript will meet your expectations.

We are looking forward to hearing from you,

Best regards,

Lalit Garg

Author Response File: Author Response.docx