August 25, 2014 Dear Editor, We want to thank the reviewers for

advertisement

August 25, 2014

Dear Editor,

We want to thank the reviewers for their thorough evaluation of the manuscript and their valuable comments. Please find the answers/comments to the remarks made by the three reviewers in a point-by-point list below and with line references to the edits made in the manuscript. Changes in the manuscript are also highlighted in yellow in the text and tables the resubmitted, revised version. In addition two figures were changed as suggested by reviewer 3.

Reviewer 1 ( Álfheidur Ástvaldsdóttir)

Minor Essential Revisions:

The paper “A retrospective analysis of caries treatment and development in relation to assessed caries risk in an adult population in Sweden” comprises an interesting validation on effectiveness of population based prevention strategies in Västerbotten county, Sweden.

Title: The title is informative and concise.

Abstract: Does give relatively good overview of the work, although I find the conclusions somewhat unclear. QUESTION: Do the results support the following conclusion: “Adult patients classified with high versus no/low caries risk represent two distinct populations who accordingly need different strategies in disease treatment” ?

Answer: Table 2 and Figure 2 substantiate that the two risk level groups represent two clearly different populations based on their caries status and other factors, and figure 6 that within each of these two populations there are distinct subgroups, i.e.

those who stay at the same risk level and those who change it. The cited statement intended to reflect both these findings. We have edited the text to clarify this. It now reads “(i) adult patients with high or no/low caries represent different populations, that each contain distinct subpopulations, those who improve/impair or maintained their caries risk and disease progression. These groups need different strategies in disease treatment ” (lines 37-40).

Introduction:

Well formulated and relevant. The aims could though be more clear: QUESTION: Were the aims of the study to a) evaluate the effectiveness of different caries preventive strategies according to caries risk? or b) evaluate the caries risk assessment made by the treating dentists?

Answer: The aim was to evaluate the accordance between recommended treatment and a patients risk to develop caries. That is if dental personal provided patients preventive counselling and care to meet the needs associated with a scored caries risk. We have clarified this (lines 82-83).

Methods:

This chapter could have better structure and following should be more thoroughly description

Examiners

Answer: The text has been edited to clarify that three experienced dentists performed the record examinations (lines 140-148).

Which data were collected from dental records and how

Answer: Information has been added as requested (lines 140-148).

1

Study design: Clear

Caries scoring and risk assessment: The authors state the following:

“These examinations took place in fully-equipped dental offices and included, at the minimum, bitewing xray”

QUESTION: Was the radiographic examination routinely carried out at every recall visit for all patients?

Answer: A radiographic examination is always based on clinical indications in the Public

Dental C are in Västerbotten. In the present perspective this means availability to register caries on approximal surfaces. Thus, the only situations where x-rays would not be taken are a medical contradiction or if all approximal surfaces can be visually fully inspected. The present two study groups both had many teeth meaning that x-rays were needed for caries diagnosis. That any substantial proportion should meet the contradiction criteria is highly unlikely. Information on this was added (line 107).

The followi ng sentence should rather be incorporated in the “Study population” Chapter “In

2005, 35 896 adult patients (84.9% of all recall visits that year) had caries risk scored. In total, 44.3% of these patients were estimated to have no or low caries risk, 43% were estimated to have moderate caries risk, and 12.7% were estimated to have high caries risk.”

Answer: The text has been moved as suggested (lines 125-128).

Study population: Clear

Data retrieval from dental record

•This chapter is unclear and needs more thorough description of what kind of information was collected. QUESTION: Were the three examiners calibrated? How? Can the interexaminer agreement be described for the three examiners?

Answer: Basic calibration among the three examiners on what and how to search for information was achieved during the discussions while construction the data retrieval protocol. In addition, the results from independent search of 10 high and 10 low risk records were compared. The calibration did not include caries scorings and diagnosis decisions, but information retrieval and how to interpret text in the notes from each visit. We have expanded the text to clarify this (lines 144-148).

What information was collected for each patient?

Answer: Information has been added as requested (lines 140-142).

Were the examiners blinded concerning the patients’ caries risk?

Answer: The examiners were not aware of what group the participant had been allocated to, but since risk scores at each visit were retrieved from the dental records further blinding was not possible.

Did the examiners make their own caries risk assessment according to the information retrieved from the dental records?

Answer: No. the information noted in the dental records was used.

Did the examiners view the radiographs? How?

Answer: No.

Data handling and statistical analysis. Difficult to identify the specific statistical test used for each analysis.

Answer: This has been clarified in the Statistics section (lines 155-159).

Results: Generally well described and clear

2

Figure 1 is only used to verify the normally distributed data of the included population and do not serve any purpose to my opinion.

Answer: We have included figure 1 (and prefer to keep it) to illustrate that in opposite to the generally highly skewed caries distribution seen in most study samples, distribution was acceptably normal in the present setting.

Caries prevalence and incidence 2005-2011

The chapter presents difference in caries prevalence between the two caries risk groups over the 7 year period.

QUESTION: Why was the secondary caries lesions excluded? This could be clarified in the

Methods chapter.

Answer: In accordance with the criteria for the DMFS sore secondary caries is not included in the score, but handled separately. Please, see also comment by reviewer 2 on diagnosis validity for secondary caries.

Conclusions somewhat unclear – see abstract

Answer: Please, see edited text presented above. The same change was also done in lines

(lines 385-388).

Tables and figures

• Figure 1 – not needed to my opinion

Answer: Please, see answer above.

Table 1: “overview of risk categories and criteria for risk assessment” is this the criteria in

Västerbotten county

Answer: Yes, and this has been clarified in the Table legend

Table 3 : the following footnote does refer to all groups in the table and therefore no need to specify: “ Data are presented as mean (95% CI) adjusted for sex, age, and clinic for the seven-yearstudy period”. Could be incorporated in the table legend.

Answer: The text has been moved to the table legend as suggested

Table 4: difficult to interpret. The groups 1) to 5) specified in the footnote are not referred to in the table.

Answer: We apologize for missing to delete footnotes 2-5 from a previous version. This has been corrected.

In the table legend is referred to odds ratio but in the table it is #-coefficient. Could be clarified.

Answer:

We have added the term β-coefficient to the figure legend to clarify this.

Reviewer 2 (Dan Ericson)

Reviewer's report

This is an interesting report that should have a significant impact on how treatment programs are designed for individuals relating to their caries risk. However, some point need to be clarified before this paper is suitable for publication:

- Major Compulsory Revisions

1. Methods, first paragraph:

Please provide reference for “the larger cohort study”.

Answer: We cannot provide a published reference for the larger cohort study as the first paper is just to be submitted for evaluation. The study is the GLIDE project granted by the

Swedish Research Council. If the submitted paper is accepted by the time of proof reading of

3

this paper (if accepted for publication) we may add the reference.

2. Methods; Caries scoring and risk assessment, first paragraph:

Please clarify if bitewing radiographs were at all recall visits for all patients. I would expect that this is the not case for the low/no caries risk group.

Answer: Please, see answer to reviewer 1 and new text in line 107). For clarification there is no difference in x-ray indication in relation to caries risk score.

3. Methods, Study population, first paragraph: On what characteristics were matching of the no/low caries “control group” made?

Answer: We have misused the term matched. Indeed,

the no/low caries risk participants were not recruited in a proper ‘gender-age-etc matched’ way, but the groups were identically balanced (equal numbers)

for sex, ten-year age groups, coast (more urban)

areas, and inland (m

ore rural) areas as in the high caries risk group. This has been corrected at various places, i.e.

lines 24, and 133.

4. Methods; Data retrieval from dental records, first paragraph:

“After calibrating an independent selection of ten high caries risk and ten no/low caries risk subjects, three experienced dentists examined the dental records of the selected subjects.” a.-The sentence needs clarification : Do you mean that: “Three experienced dentists examined a random selection of ten high caries risk and ten no/low caries risk records”?

Answer: Please, see answer above to reviewer 1. The term independent refers to that those records were not part of the 400 study subjects. We have edited the text to clarify this (line

146). b. - Also clarify: Did then one examiner only examine each case if no ambiguity?

Answer: Yes. We have not edited the text further on this matter.

5. Methods; Data handling and statistical analysis, last paragraph: The sentences:

“Multivariate principal component analysis (PCA) was used to search for clustering among the study participants by caries risk group allocation or alteration in caries risk level from

2005 to 2011. The former model included measures for 2005 only, and the latter included the same variables as used in the logistic regression.”

Please clarify (expand) explanation in the first sentence.

Answer: The text has been edited to clarify what the data swarms were in the three different

PCA models (lines 172-177).

Please indicate more clearly what is meant by former and latter model.

Answer: This text was omitted as the edits described in the previous point were made (lines

172-177).

6. Results; Study group characteristics at baseline, first paragraph:

Please define criteria for secondary caries lesions. The reason for this is that the diagnosis is often not so accurate in many clinical situations and might contain a substantial number of fractures and other defects not caused by caries. See also below (fig 4b).

Answer: The definition of secondary caries communicated to the examining dental personal in the County is caries adjacent to a filling. The reviewer is correct that this diagnosis may, however, be biased by other conditions. Since we used the County Council statistics for our evaluations the correctness of the diagnosis could not be evaluated in each situation. This is part of why secondary caries was evaluated separately.

Please see comment below too.

7. Results; Preventive and non-operative treatment measures, first paragraph:

4

It is advised to be correct about what is measured in the paper, therefore I suggest that a few words are added [ ]: The text: “At baseline, [it was documented that] approximately half of the participants received counselling on the use of fluoridated toothpaste (basic prevention), but no significant difference between the two groups was found (Table 2). Furthermore, 35% of the high-risk subjects were [according to records,] told to use additional fluoride compared to

12.5% in the low/no risk group (p<0.0001). Over the seven-year study period, counselling on caries preventive measures was significantly more frequent [ly documented] in the high than in the no/low caries group (Tabl e 3).”

Please change the description as indicated above.

Answer: We appreciate this comment and have changed the text as suggested (lines 239,

242, 250).

8. Discussion; first paragraph.

Please see 7 above, and similarly, use statements that indicate that data from records were used for analysis (so that the reader not is lead to think that records describe a full clinical reality).

Answer: This was corrected in accordance with was is described above (line 291).

9. Discussion; general:

Please add comment to the fact that the number of visits to the dental hygienist did not differ between high and low caries risk groups.

Answer: We have added a comment on this on lines 340-341.

10. Table 4. Heading: “Logistic regression Odds ratio and 95% CI for an impaired caries risk score in 2011 compared to at baseline (2005) and 2011; reference group in parenthesis.”

What is an impaired caries risk score? – Please use increased or decreased score for clarity.

Similarly: “Odds ratio to have an improved caries risk score in 2011 if high risk in 2005

(n=200)”. – Please use increased or decreased score for clarity.

Answer: The Table heading and text for section A, Table 4 has been changed to “lower” for clarity.

11. Figure 2b

The increase of secondary caries at 2011 for the high caries risk group does not follow a decreasing trend. Please comment on this fact in discussion and relate it to what could be included in the clinical diagnosis “secondary caries” among un-calibrated dentists. It might be very plausible that the diagnosis would include marginal defects and fractures of restorations to a significant extent.

Answer: We assume the reviewer refers to Fig 4b where it is seen that the incidence of secondary caries had increased from 2009 to 2011. We agree that it cannot be fully distinguished between true caries lesions and confounding by other conditions. We have added a reflection in the discussion as suggested (lines 320-329).

Minor Essential Revisions

Results; general.

A more detailed description of the PCA-results would increase understanding.

Answer: We have added supportive text in lines 201-202, and think this would be helpful here as well as later for understanding Figure 6.

Discretionary Revisions

Materials and methods; last paragraph: “Multivariate” could be omitted.

Answer: We have deleted the word multivariate as suggested . (line 170).

Reviewer 3 (Ryan Lennon)

5

GENERAL

The authors have gathered data to study the treatment and development of caries in an adult population. The data may be useful but the study methods need more explanation and consideration.

MAJOR COMPULSORY

1. Study population

How many of the 42,276 with an exam in 2005 also had a recall visit in

2011?

Answer: This information has been added (line 125).

2. Study population

"Selection was stratified for sex, ten-year age groups, coast (more urban) areas, and inland

(more rural) areas. An equally sized, matched control group with no/low caries risk was randomly selected." I appreciate the detail here, but more is needed. Was the stratified selection used so that the resulting sample had the same strata frequencies as the 196998 adult inhabitants of Västerbotten County? Or the same frequencies as the 76320? Or the

42276? Presumably, the matched control group was not matched in a 1:1 style, but merely be selecting from strata at the same frequency?

Answer: The two groups were selected to have a balanced number according to the criteria described above, and not stratified according to proportions in the target population. Please, also see previous comment that the sample collection for the no/low group was not a true case-referent matching, but a randomized sample selection at the same frequencies. The text has been edited to clarify this (lines 131, 133).

3. Study population

"To ensure an 80% power of detecting difference..." The sample size statement is unclear.

What parameter(s) are being tested and what is the null hypothesis? What test statistic is the sample size calculation based on?

Answer: Sample size calculation was based on information on means and measures of variation for caries prevalence (DMFS used in the present study) and incidence for adults with different caries risk scores in the entire target population. Such data were available when the study was designed as population statistics are continuously evaluated by the

County Council of Västerbotten. The power estimation was done with the null hypothesis there would be no difference between a high and low caries risk group.

4. Data handling and statistical analysis, para 2

"Measures for caries prevalence and incidence were averaged among participants using general linear regression modeling (glm), including sex, age group, and clinic as covariates."

Models don't produce averages, they produce parameter estimates, so the term "averaged" is unclear here. What link function was used for the model? Additionally, if the control group represents a matched sample, why bother with covariate adjustment?

Answer: Sorry, this was badly phrased. GLM was used to calculated estimated marginal means when adjusting for described covariates, before testing the difference between adjusted means. The text was corrected (lines 155-157). Please, see also previous comment on matching vs sample selection.

5. Data handling and statistical analysis, para 2

"Differences between means were tested using analysis of variance and a post hoc test with

Bonferroni correction." It is not clear to me to which p-values the Bonferroni correction was implied or why.

Answer: We ha ve edited the text to describe that Student´s t -test was used for comparisons of means in two groups and ANOVA when more groups. ANOVA was only used to compare data among clinics and no post hoc test was performed (lines 157-159).

6

6. Data handling and statistical analysis, para 2

"Correlations between variables were calculated as Spearman or Fischer correlations depending on the numbers in each cell." What have cells got do with it?

Answer:

The word cell has been deleted and the text reads “number of observations” (line

160).

7. Data handling and statistical analysis, para 3

There are several issues regarding the logistic regression for improvement/maintenance of caries risk. a) There are a lot of correlated independent variables, which would result in unstable estimates. For example, the number of visits to a dental office appears to be the sum of the number of visits to a dentist and a dental hygienist. Why include all 3?

Answer: We have rerun the regression analyses. First we (i) repeated the previous model

(but excluded visits to dentist and visits to hygienist) with sex, age group and total number of visits to clinic and the various counselling treatments (these results are presented in Table

4). Then variables were run in separate models, i.e. (ii) total number of visits, (iii) number of visits to a dentist or a dental hygienist (these two models had sex and age group as covariates), and (iv) basic information, (v) oral hygiene counselling, (vi) diet counselling, and

(vii) fluoride counselling (models (iv) to (vii) included sex, age group and total number of visits to clinic as covariates). The results from the first model was stable also in the reduced models. We decided to take out diet counselling in the A section of Table 4 since this was neither statistically significant in model (i) nor in model (vi). We kept the information on counselling on oral hygiene in section B, table 4 since it was borderline significant in model

(i) and statistically significant in model (v, p=0.031). Information was added in footnote 1 and

2. We also realized that the word “not” was missing in footnote 1. (table 4, footnotes 1 and 2).

b) Clarify if age group and living region means those values at 2005 or at 2011.

Answer: This information has been added to footnote 1. (table 4, footnotes 1 and 2). c) It appears from Table 4 that some form of variable selection was used, but no details are given here. This is especially problematic considering the issues with multicollinearity already noted.

Answer: Please, se answer above. No other variables than those listed were included and hence not excluded. d) I may misunderstand Table 1, but it seems some patients are not capable of moving down a risk group. For example, if a patient is in the high risk group due to several root canal treatments, then that patient will always have that history and never be able to move down to a lower risk group, correct? In which case, it does't make sense to model their probability of moving down to the low risk group, since the probability is zero.

Answer: Table 1 describes the different types of risk scores that are determined for each patient, i.e.

there are separate scores for the general, caries, periodontal and technical risk.

Here we focused on the caries risk score based on disease activity and that may change and hence the score.

8. Results, Caries prevalence and incidence (and Figures 3 and 4) It is unclear why estimate are reported at 2 year intervals, instead of, say, 1 year intervals. It is also unclear how patients who did not visit during such a year were handled. For example, if a subject visited in late 2006 and early 2008, how do they contribute to the 2007 estimate?

Furthermore, the legend states the plot shows mean (SE). What represents the standard error? The whole whisker? Half a whisker? Why not just show 95% confidence intervals instead?

Answer: The reason for not selecting annual evaluations was that virtually all low risk patients did not attend the clinic every year leading to low numbers. This was circumvented by selecting every second, which is the period most people are scheduled for a revisit. Since

7

the symptoms of dental caries develop slowly, 2-3 years is a suitable time period to evaluate progression. Figures 3 and 4 now show 95% CI as suggested and Figure legends have been changed accordingly (Figures 3 and 4).

9. Results, Caries risk assessment

"The proportions of subjects who remained.... (p=0.057)."

What are the two p-values reported in these sentences testing? 90% vs

24% and 89% vs 18%? Or are they overall p-values testing for any difference between clinics?

Answer: Yes they are overall p-values testing for any difference between clinics. The text has been edited to clarify this. (lines 234 and 237).

10. Results, Preventive and non-operative treatment measures, para 2

"whereas the total number of visits to the clinic, was strongly correlated with the number of visits to a dentist" Aren't most of these the same visits? Doesn't a visit to the dentist typically mean a visit to the clinic? It may be coincidence, but the means on Table 1 imply that a visit to the clinic was classified as either a visit to a dentist or a visit to a hygienist. In which case, correlation is not the proper analysis.

Answer: A visit to the clinic is either a visit to a dentist or a dental hygienist, i.e.

they are independent measures. A visit to the dentist is typically an examination or operative treatment and a visit to the hygienist an examination or some kind of non-operative treatment for caries or periodontal disease.

11. Table 1

Clearly, no subject will have all of the criteria for Risk group 2. So how does one end up in the high risk group? Do they only need 1 of the criteria? What about the moderate risk group? Any criteria and none from the high risk group?

Answer: It is true that fulfilling one of the two criteria for caries risk 2 allocates the patient to that level, and one cannot fulfil any criterion for the high risk level and be scored as a medium risk.

12. Table 2

Was the gender forced to be 50% in both groups according to stratified selection? If so, there is no p-value to calculate.

Answer: Yes. Thanks, the p-value is deleted.

13. Table 3

It would be interesting to know what proportion of patients received each counselling service at least once during the 7-year period.

Answer: The figures for never (in the 7-year period) having basic information is 12.3%, never been recommended to use fluoride besides toothpaste 43%, never been counselled on dietary habits 90.5%, never been counselled on oral hygiene 44.5%. This information was added (lines 243-247).

14. Table 4

How do the authors explain that counselling on tooth cleaning and diet intake reduce the odds of improved caries risk score? Might the practitioners be saving these measures for the very highest risk individuals? If so, can you really evaluate its effectiveness in this data set?

Answer: This seemingly paradox result most likely reflects that the treatment is given to the most diseased patients, which parallels a common finding for e.g. fluoride treatment in other studies. We show the association but do not claim a causal associations for which one would need an intervention study. For dietary counselling the data was deleted as described above.

MINOR ESSENTIAL

15. Results, Study group characteristics at baseline

8

"However, randomization in a ten-year age stratum..."

This study contained no randomization. Consider "sample selection" instead.

Answer: This has been changed as suggested (line 188).

16. Results, Caries risk assessment

"In comparison, 32% the no/low caries risk subjects..."

Insert "of" after "32%".

Answer: The text has been changed as suggested (line 227).

17. Discussion, para 2

"Furthermore, means...from the different clinics after randomization."

Again, "sample selection" is more appropriate than "randomization".

Answer: The text has been changed as suggested (line 315).

DISCRETIONARY

18. Methods section

It may be helpful to include a "Definitions" section, or at least put all definitions in the

Methods section. For example, in the "Number of visits and costs" section of the Results, the authors define "recall period", which ideally would be defined earlier.

Answer: Here we mean that terms and expressions that are defined are basic terms in odontology and would unlikely need further definitions for the reader of this journal. We would also like to point to that recall period is defined in lines 104-105.

19. Data handling and statistical analysis, para 4

The principal component analysis is not really warranted. It is clear enough from Table 2 that the 2 groups represent truly different populations. Furthermore, it would be possible for 2 groups to be significantly different between 2 sets of characteristics, yet look similar by the

PCA analysis, depending on the magnitude of the variables' coefficients for the first 2 principal components. The authors may choose to keep it in if they like.

Answer: We appreciate the comment, but prefer to keep the PCA figures.

20. Results, Preventive and non-operative treatment measures, para 2

"...whereas increasing age was associated with..."

Consider "whereas older age at baseline was associated with". Everyone's age is always increasing.

Answer: The text has been edited as suggested (line 257 ).

21. Discussion, para 2

"It has previously been found that behaviours and attitudes towards oral disease prevention differ between clinics..."

Between patients at the clinics, or staff?

Answer: Statistics on dental status and treatment success vary between clinics as seen in both the present study and County Council statistics. It has not been evaluated if this is due to attitudes among personal or patients, but a qualified guess is that also the reasons differ between clinics. This is a sensitive question that needs to be under-pinned firmly, and we have avoided to speculate on this in the paper.

22. Discussion, para 4

"It cannot be evaluated whether the present results reveal an over-treatment in low risk subjects, but the lack of difference in treatment intensity in the two groups opens the question." How? The authors seem to conclude that the high-risk group was under-treated. If the low-risk group is treated similarly, how can we label it "over-treatment"? The low-risk group still saw positive incidence of lesions/caries over time. How low must such incidence measures be to suggest over treatment?

9

Answer: It is correct that we conclude that the high risk group is under-treated, but this does not, in our opinion, contradict that the no/low group may be over-treated. It was quite surprising that the latter group got the same level of attention as the high risk group. The reason for this is not known, but it may be speculated that personal are stuck in a rut, it is more convenient to advice easy-treated patients, there is more money in operative treatments, patients expect operative treatments, and personal feel a shortness of time. The answer would be interesting and potentially could save time and money for those who need care, but this is outside the scoop of the present paper.

23. Conclusions

"(ii) preventive measures..." should really be "(ii) some preventive measures..."

Answer: The text is changed as suggested (line 388).

24. Conclusions

"Future research should evaluate obstacles that prevent dental caregivers from providing effective guidelines for patients who tend to be non-compliant". This sentence reads like a string of buzz words. I'm not sure what it really means. Isn't non-compliance the real obstacle? Aren't the current guidelines effective when complied with? What obstacle could prevent a caregiver from providing guidelines to a patient?

Answer: The present study shows that dental personal do not provide preventive treatment and counselling as recommended by the National Board of Health and Welfare and at least for use of fluoride is scientifically evidence based. There may be various, as of yet unknown, reasons for this. The text has been edited to clarify this. It now reads “Future research should evaluate what aspects influences dental caregivers to provide and succeed in caries preventive treatments also in patients at high risk to develop disease” (line 392-394).

25. Conclusions

"In addition, future studies should examine how to improve implementation of preventive treatments as well as aim at separating these preventive treatments from lack of patient compliance." Do you mean separating the estimation of the effectiveness of such treatments from the effects of compliance?

Answer: The text has been edited to clarify that we mean “ separating the estimation of the effectiveness of such treatments from the effects of compliance ” (line 396-397).

26. Table 2

It would be helpful to show the percentages in each of the 10-year age groups that were used for stratified selection.

Answer: The proportion of participants in 10-year age groups (25.0-24.9, 35.0-44.9, 45.0-

54.9 and 55.0-65.0 years) were 24.8, 23.5, 26.3 25.5%, respectively, with similar proportions men and women in each age group. This information was not added to the Table since the information on group sampling in the Methods section was edited to clarify that equal portions were sampled from the 10-year age groups.

27. Table 2

The "Preventive/non-operative measures" summarized here indicate such usage at baseline.

It might be interesting/informative to also report whether such measures were taken at any point in the last, say, 3 years. However, I understand such data may not be available.

Answer: We interpret this comment as the reviewer is asking about preventive measures after 2011, i.e.

2012-2014, and that information is not available. Presently a motivation/ further education program is planned for the dental personal and effects will be evaluated later.

28. Figure 5

Consider using "Low" "Mod" "High" instead of 0, 1, 2.

10

Answer: We appreciate this improvement, but keep 0,1,2 for space reasons. The interpretation is found in the figure legend.

11

Download