Protocol for a stepped wedge randomized controlled trial to optimize antibiotics prescription in Nepal

Abstract

Background

Antimicrobial resistance (AMR) is one of the top ten threats to global health. Over-prescription of antibiotics, a key driver of AMR, has been documented in many low- and middle-income countries. Low-cost interventions that do not add substantially to the physician workload, are consistent with good physician practices and WHO guidelines, and serve as a reminder on the risks of overprescribing antibiotics are critically needed. This protocol describes a study that aims to test the effect of two such interventions among junior physicians in Nepal. The first intervention requires physicians to specify the diagnosis in their prescription note—thus reminding them of the risks of over-prescription at the time of care. The second intervention provides individualized feedback on their actual prescription behavior.

Methods

The study is a stepped-wedge randomized controlled trial among an anticipated 60 physicians in 5 hospitals in Nepal, with data collected from approximately 3600 patients over a 6-month period. Physicians in the hospitals will receive the first intervention (the mandate), sequentially, beginning at the end of the first month after a refresher training on AMR. They will receive the second intervention (the feedback), again sequentially, beginning at the end of the third month. The primary outcome is the antibiotics prescription rate, which will be assessed—for both interventions—using multilevel, mixed-effect regressions (random intercepts for physicians and fixed effects for hospitals) accounting for potential confounders.

Conclusion

The study will contribute to current global efforts to combat AMR by utilizing low-cost, context-informed interventions to reduce inappropriate antibiotic prescribing in resource-limited settings.

1. Introduction

Antimicrobial resistance (AMR) is one of the top ten threats to global health, with an estimated 4.71 million deaths associated with bacterial AMR in 2021 [1]. In low- and middle-income countries (LMICs), antibiotic use in human health, a key driver of AMR, has increased exponentially over the last decade [2,3]. Although much of the antibiotic use in these countries takes place in community settings, inappropriate prescribing persists, including broad-spectrum agents given without documented diagnoses and for likely viral illnesses, thereby accelerating resistance [4].

AMR is rising in Nepal, the site of this study. Recent studies indicate high and increasing levels of resistance among key bacterial pathogens. For example, in a 2016-2017 surveillance in Kathmandu, 71 patients were hospitalized with multidrug-resistant (MDR) infections, with resistance observed against critical antibiotic classes including extended-spectrum beta-lactamase (ESBL), carbapenem, and colistin [5]. Another study found that among community-associated isolates in hospitalized patients, 78% were MDR, with notable production of ESBL, metallo-beta-lactamase (MBL), and AmpC enzymes [6]. At a tertiary care center, 97% of Acinetobacter calcoaceticus-baumannii complex (ACBC) isolates were carbapenem-resistant [7]. A 2021 study showed that 29% of E. coli cases were MDR, with 88% resistant to third-generation cephalosporins and 31% to carbapenems, while 18% of Klebsiella spp. were MDR, with resistance rates of 95% and 47-63% to third-generation cephalosporins and carbapenems, respectively [8]. These data underscore the alarming rise in resistance to what are essentially the last-resort antibiotics in Nepal, especially because most of the newer antibiotics active against bacteria with the currently prevalent MDR mutations are not available in the country.

Over-prescription of antibiotics by physicians has been recognized as a key driver of AMR in low-income countries like Nepal [[9], [10], [11], [12]]. Limited evidence from Nepal suggests that physicians tend to “err on the side of caution” by prescribing antibiotics even for viral infections, a practice similar to that observed in other LMICs [12]. They prescribe at least one antibiotic in 44.7% of the visits, twice the WHO-recommended level of 20-27% [12]. This over-prescription is driven by multiple factors, including the large number of patients physicians see within a short time and the attendant need to make treatment decisions quickly, as well as the inherent uncertainty involved in treating medical conditions. To illustrate one factor, on average, physicians spend only 6 min per patient in Nepal [13].

Low-cost interventions that do not add substantially to the physician workload, are consistent with good physician practices and WHO guidelines [14], and serve as a reminder of the risks of overprescribing antibiotics are critically needed. Our years of research in Nepal and interaction with physicians, hospital administrators, and government officials suggest that requiring physicians to specify the diagnosis in their prescription notes and providing them with individualized feedback on their prescription behavior are potential interventions.

Symptom-based documentation by physicians, as opposed to diagnosis-specific documentation, may be associated with higher rates of antibiotic prescribing in outpatient settings. Symptom-based documentation may obscure the underlying etiology of illness, contributing to the inappropriate use of antibiotics for conditions that do not warrant such treatment. Studies from both high- and low-income countries have shown that up to 30–50% of antibiotics are prescribed for conditions where they are not clinically indicated [15], and that requiring diagnostic justification can help curb unnecessary prescribing [16].

Various studies have also proven that the audit and feedback interventions decrease the prescribing rate of antibiotics by physicians. For example, an intervention that provided pediatricians in 18 pediatric primary care practices in the US with education and feedback on prescribing patterns for themselves, their practice, and their network reduced broad-spectrum prescribing for ARI by 12.5% [17]. In another study, general practitioners in the UK were sent letters signed by England's Chief Medical Officer informing them of their antibiotic prescription rate and with recommendations to help reduce the rate [18]. The intervention significantly lowered prescribing rates in the intervention group relative to the control group [18]. Similar interventions are largely lacking in LMICs.

Drawing on this evidence, in this study, we will test the effect of two interventions targeted to junior physicians on their antibiotics prescription rate. The interventions are: 1) a hospital management-endorsed diagnosis mandate and 2) individualized feedback based on actual prescribing behavior. Based on our interactions with physicians and policymakers in Nepal, these types of interventions would cater to multiple drivers of over-prescription mentioned above. The diagnosis mandate standardizes documentation according to best prescription practices at the point of care, and the feedback offers concise, non-punitive performance summaries to prompt reflection and improvement.

1.1. Significance of the study

Pragmatic, low-cost approaches to optimize antibiotic prescribing are urgently needed in LMICs. The proposed study includes a number of innovations. First, we move beyond the de facto hospital-based stewardship programs, which have so far shown mixed results, both in Nepal and in LMICs generally [19,20]. In fact, in the absence of a regulatory body to enforce stewardship programs, only a limited number of hospitals have initiated stewardship programs in Nepal. In most cases, hospitals lack human and physical resources, such as infectious disease specialists and laboratory facilities, to run stewardship programs [[21], [22], [23]].

Second, a simple requirement to record a working diagnosis at the point of prescribing serves as a real-time nudge, making clinical indication explicit and discouraging “just-in-case” antibiotic use when not warranted.

Third, to our knowledge, this is the first rigorously evaluated, physician-targeted intervention outside Kathmandu and centered on outpatient care. Prior efforts in Kathmandu - ranging from post-prescription review to ASP toolkits and formal programs - reported improvements (e.g., better justification within 72 h, perceived utility of toolkits, and reduced aminoglycoside and IV use) but also highlighted barriers such as limited prescriber buy-in and diagnostic capacity [[24], [25], [26], [27]]. These studies reflect best-case urban infrastructure and seldom prioritize outpatient settings. By testing scalable, behaviorally informed interventions in mixed public–private hospitals in Chitwan, our study enhances generalizability and policy relevance for Nepal's broader health system.

2. Research design and methods

Target Population. Junior physicians working in outpatient clinics across five hospitals in Chitwan District, Nepal, and the patients they serve. Chitwan is a major health hub in central Nepal with a diverse patient catchment, making it an appropriate setting for this study. To protect institutional confidentiality, hospital names are not disclosed. The sample spans academic and non-academic facilities and both public and private sectors. Public hospitals include those managed by all three tiers of government (federal, provincial, and municipal).

Recruitment. At each hospital, we will obtain rosters of clinicians providing outpatient care in internal medicine and its subspecialties. Eligible physicians are ≥18 years old and actively seeing outpatients during the study period. We will invite all junior clinicians - defined as junior consultants with <10 years since medical school graduation, postgraduate (MD) residents, super-specialty (DM) residents, and medical officers (MBBS) - with the goal of near-complete enrollment of residents and other junior outpatient physicians. Patients will be randomly selected from those seen by participating physicians and approached for enrollment as they leave hospital premises after a checkup (details below).

Inclusion criteria. Physicians are eligible if they are clinicians (as defined above), are providing outpatient care in internal medicine or its subspecialties, are ≥18 years at recruitment, and provide informed consent. Patients are eligible if they are ≥18 years, have just consulted a participating physician, and provide informed consent at the end of the visit.

The intervention. There are three main components in the intervention.

• (1)Refresher Training on AMR: A practicing infectious disease specialist will provide a 2-h refresher training (in groups of ∼10 physicians/day to accommodate their schedules). Key topics in the training will include: 1) introduction to antibiotics, 2) common mistakes physicians make when prescribing antibiotics, 3) AMR and its current drivers in Nepal, 4) microbiomes, how antibiotics affect them, 5) the importance of One Health approach in addressing AMR, and 6) the standards for appropriate documentation of diagnosis in the prescription note. Recognizing that many physicians already have the knowledge on these areas (i.e., the “know” part in the “know-do” gap), and the limitations of lecture-based training on how learners absorb, retain, and use the information provided, we will develop several case studies. The case studies will involve reflecting on real-world scenarios, role playing, and collective problem solving centered on conditions endemic in Nepal, such as diarrhea and URTI.
• (2)Diagnosis Mandate: At the end of the training, the highest authority of the hospital (either the CEO, the Medical Director or the Medical Superintendent will announce in person (at the venue of the training) that physicians will henceforth be required to specify the diagnosis each time an antibiotic is prescribed to a patient and that the hospital authorities will occasionally assess individual physician's compliance with the requirement by checking the prescription notes from the patients. The physicians will also be given a written letter from the hospital management to this effect (see template in Fig. 3).
• (3)Individualized Feedback: Approximately six weeks after the refresher training and the Diagnosis Mandate, each participating physician will receive a confidential, individualized feedback memo (see template in Fig. 4) summarizing their antibiotic prescribing rate and diagnosis documentation practices. The memo draws on prescription audit and patient exit interviews to report the share of prescriptions with a recorded diagnosis, antibiotic use among acute presentations, and the distribution of agents across WHO AWaRe categories. It presents simple pre/post summaries around the knowledge-sharing workshop and documentation request, avoids cross-physician or cross-hospital comparisons, and is explicitly framed as a non-punitive prompt for reflection and quality improvement. Thus, this memo will serve both as a reminder of the mandate and of the physician's “performance” in the first two months.

2.1. Study Design

We will conduct this study as a stepped-wedge randomized controlled trial, as shown in Fig. 1. We will randomly select the hospitals to receive the intervention at a given time using a random number generator in R version 4.4.3. Given the small number of physicians in Hospitals 4 and 5, we will conduct the intervention in these two hospitals at the same time.

Fig. 1.

Study design.

2.2. Data collection

We will conduct a baseline survey among participating physicians during the training to collect demographic and occupational information (e.g., age, gender, years of experience, knowledge of AMR, and appropriate prescription practices). Data on the outcomes will be collected from patients’ outpatient booklets as they exit the hospital premises. Trained nurses from the Institute for Social and Environmental Research-Nepal (ISER-N) will obtain consent from each patient, collect patient-level demographic information using REDCap^Ⓡ, click the pictures from the prescription, and upload them. We will use those prescription notes to extract the necessary information into a pre-designed template. We will verify a subset of the records collected by nurses using uploaded pictures of the prescription notes.

The assignment of nurses will be done randomly using R version 4.4.3. The study is divided into 12 phases, with each phase consisting of 12 working days: 10 planned and 2 reserve days. The reserve days will be used to collect the missing information and to conduct the targeted intervention for that phase at the hospital. All recruited physicians are scheduled for visits three times per week, and each nurse is assigned to physicians from one hospital per day and 8 patients per day. Visits will be randomized at all levels: nurse, physician, and physician–patient according to the above-mentioned considerations. The nurses on the field will obtain consent and collect the basic demographic information, and take pictures of the prescription notes from the patient as they exit the hospital premises.

The information from the prescriptions will be extracted the following day. A pre-designed questionnaire is filled out on the REDCap^Ⓡ app based on the information from the prescription note. We will ensure that the information from the in-field interview and prescription extraction information is properly sequenced for each patient by using instruments from the REDCap^Ⓡ. The prescription extraction form focuses on identifying medicines prescribed, diagnostic tests ordered and diagnosis- and symptom-writing practices of the recruited physicians.

ISER-N will recruit and train the nurses required for the data collection. The training will include three days on general interview techniques, three days on study-specific training, and 5 days on simulations and field practice done at other local-level health institutions. A practicing pharmacist and a trained physician (outside the study) will be recruited to extract the information from the prescription and fill out encounter-level data. Local pharmacists and a practicing doctor will guide and assist the pharmacist throughout the study, with the study team verifying the information on a randomly selected subset.

2.3. Sample size and statistical power

We aim to collect the data from 60 physicians and 3600 patients. This sample size was calculated using the -steppedwedge- command in Stata version 17 [28]. The command allows us to incorporate various design factors specific to stepped-wedge randomized trials. We discuss the various assumptions and design characteristics included in the power calculation next.

In the absence of prior data on the effectiveness of mandate and feedback interventions, we assume that a 10-percentage point reduction would be meaningful from a policy standpoint. A 10-percentage point reduction from the current rate of approximately 45% does not bring down the prescribing rates to the WHO-recommended range of 20-27% [29]. However, reaching the WHO target with light-touch, short-term behavioral interventions like the ones in the current study is likely not a realistic expectation given the many structural drivers of overprescribing in Nepal—including short consultation times, diagnostic uncertainty, and pressure from patients to receive antibiotics. The current study is designed to provide evidence for scalable first-step interventions; the long-term goal of reaching WHO-recommended levels likely requires sustained, multi-component programmatic efforts. Finally, note that the study's goal is to optimize antibiotic prescription without discouraging physicians from prescribing an antibiotic in clinically appropriate cases.

In our design, there are 4 steps, with an average of 15 physicians receiving treatment in each step. We plan to collect data on 60 patients per physicians (total 3600 patient visits). We assumed a conservative intra-cluster correlation of 0.2. Many previous studies on antibiotics prescribing report smaller ICCs with one study reporting an ICC of 0.2 [30]. In a parrel cluster RCT, a larger ICC yields lower power for a given sample size. For a stepped-wedge RCT like the current study, the impact of ICC on power is not as straightforward, as the variance structure is different than in a parrel cluster RCT. Therefore, we also calculate power for ICCs between 0.05 and 0.25 (see Table 1). Under these assumptions, with 3600 patients, we have >95% power to detect the 10-percentage point effect at the 5% significance level.

Table 1.

This table shows statistical power under various assumptions about the number of physicians and patients in the analytic sample and about intra-class correlation in the key outcome.

ICC	Power – full sample (N = 60 physicians, 3600 patients)	Power – sample with 20% attrition (N = 48 physicians, 2880 patients)
0.05	95.8%	90.2%
0.10	95.5%	89.7%
0.15	95.9%	90.4%
0.20	96.6%	91.6%
0.25	97.3%	92.6%

Based on our prior experience, attrition in this setting will be in the vicinity of 10%. Even with a 20% attrition rate (thus, ending up with a sample of 48 physicians and 2880 patient visits), we will still have power in the vicinity of 90% across the ICC range from 0.05 to 0.25 (see Table 1, final column).

2.4. Measures

We will collect data from patients of each physician in three different phases, shown in Fig. 1 (before Individual Mandate, after Mandate but before Feedback, and after Feedback). This will enable us to compare the effectiveness of each intervention. Key information that will be collected is shown in Table 2.

Table 2.

Measures.

Measures	Timing and rationale of data collection
Antibiotics Prescribed (Yes/No)	We will collect this throughout the 6-month period, for a total of 60 patients per physician (12 per month). Data will be used to assess the primary and secondary outcome.
Name of the antibiotics prescribed	We will collect this throughout the 6-month period, for a total of 60 patients per physician (12 per month). Data will be used to document common antibiotics prescribed.
Demographic information for each physician	This will be collected at baseline, before the training. Information will be used to conduct subgroup analysis in the effect of the intervention by physician characteristics.
Demographic information for each patient	This will be collected during the data collection period by nurses. The information will be used to assess heterogeneity in effect of the intervention across gender and caste groups.

2.5. Key general hypotheses

We will use the data to test the following general hypotheses.

Hypothesis 1 (Primary): Antibiotic prescription rate will be lower after the mandate than before.

Hypothesis 2 (Secondary). Antibiotic prescription rate will be lower after the feedback compared to the rate before the mandate.

Hypothesis 3 (Secondary). Antibiotic prescription rates will decrease further after receiving feedback, compared to the rate observed after the mandate.

2.6. Analysis plan

We will begin by assessing the dataset for missing values and outliers and generating descriptive statistics to summarize the characteristics of patients, physicians, and hospitals. We will use Student's t-test or χ² analysis to compare means and proportions across groups and cross phases (before the individual mandate, after the individual mandate but before feedback, and after feedback), as appropriate.

Our analysis will be intent-to-treat—all enrolled physicians will be analyzed according to their assigned hospital sequence regardless of compliance. As a sensitivity tests, (1) we will drop physicians who move across hospitals during the study period, (2) we will conduct analysis on those who receive the interventions (as documented by the research team). The main analyses will be conducted on the sample of physicians for whom we have complete data on outcomes and covariates. We will also report the proportion of missing data by phase and hospital and assess the randomness of the missing information—for example, if ‘missingness’ in the post mandate or feedback period is systematically correlated with physician characteristics measured at baseline—and comment on the potential direction of the bias in our estimates.

To examine the effect of the two interventions, following previous studies using a similar experimental setup [[31], [32], [33], [34], [35], [36]], we will fit a multilevel, hierarchical, mixed-effects regression model to account for the clustered data structure (patients within physicians, nested within hospitals) [37]. The model will include random intercepts for physicians (within hospitals) and hospital fixed effects. Patient covariates (age, sex, comorbidity, etc.) will be included to adjust for case mix. Standard errors will be clustered at the physician–phase level, thus allowing arbitrary correlation in the outcome for patients seen by a physician in a given phase. We will use a logistic link (mixed-effects logistic regression) to model the two primary and one secondary outcome that are binary [38]. From the fitted models, we will estimate the change in each outcome rate after each intervention relative to baseline.

The regressions will take the following form:

$$Y_{ijkt}={\beta }_0+{\beta }_1.{Mandate}_{kt}+{{\beta }_2.Feedback}_{kt}+{\beta }_3.{Time}_t+{\delta }_k.{Hospital}_k+{\lambda }_{1-4}.{\mathit{X}}_{ijkt}+u_{jk}+{ϵ}_{ijkt}$$

In the equation above, ​ $Y_{ijkt}$ is the outcome for patient i, under physician j, in hospital k, at time t. Mandate_kt​ and Feedback_kt are binary indicators for the two interventions, which occur at different times for each hospital. Time_t​ represents fixed effects for the 12 two-weeks data collection phases (included as categorical values) and captures underlying trends in the outcome common to all hospitals, including seasonal effects. Hospital fixed effects control for time-invariant hospital-level confounders that would otherwise bias our estimates. X captures the vector of patient characteristics meant to capture changes in patient case-mix over time, even for the same physician. These include patient age (continuous), patient sex (binary), presence of at least one comorbidity (binary, self-reported), and whether the visit was a new versus follow-up visit (binary). u_jk are physician random fixed effects, and ϵ_ijkt is the error term. In the main analysis, we will report model-based standard errors from the mixed-effects model.

Given our research questions, ${\beta }_1$ and ${\beta }_2$ are the key coefficients of interest and represent, respectively, the effect of the mandate and the feedback on the outcomes relative to the pre-mandate period. A formal test of ${\beta }_1$ = ${\beta }_2$ reveals if the effects of the two interventions are different from each other. Interpretation of β₁​ and β₂​ as causal effects relies on (i) no unmeasured, time-varying confounding within hospitals beyond covariates included in the model, and (ii) hospitals following common secular trends absent the interventions. To probe these assumptions, we will include measured time-varying covariates (patient and case mix) and day-of-week fixed effects; estimate event-study models with leads and lags around the mandate and feedback interventions to check for anticipatory effects and differential pre-trends (pre-period leads should be statistically equal to zero); add hospital-specific linear time trends as a sensitivity analysis; and re-estimate the coefficients by excluding transition periods (e.g., first week after each intervention) to address short-run adjustment. As a sensitivity test on the variance structure, we will also report robust standard errors clustered at the facility level as well as wild bootstrapped standard errors.

To conduct subgroup analysis by physician characteristics, we will interact the intervention variables with indicator terms reflecting the specific physician characteristics in the regressions, and generate figures showing marginal effects of the intervention by the characteristics. We will conduct these analyses along the following three dimensions: 1) physician experience (<5 vs. ≥5 years since graduation), as less experienced physicians may be more responsive to normative interventions such as the ones in the current study; (2) physician designation (MBBS vs. resident vs. junior consultant), as prescribing autonomy and accountability may differ across these groups; and (3) hospital type (public vs. private), as resource constraints in public hospitals may moderate how physicians respond to the interventions. All subgroup analyses will be exploratory/hypothesis-generating. Therefore, no multiple testing adjustment will be applied.

2.7. Current implementation status

Fig. 2 shows the various steps involved in our study. As of October 28, 2025 (the date of initial submission of this manuscript to the journal), we had completed recruitment of physicians, both interventions in 3 of the 5 hospitals, and collected data from 2731 patients.

Fig. 2.

Study flowchart.

2.8. Limitations of the study

There are several limitations to note in the study. First, due to the lack of publicly available data on physicians’ education and experience in the rest of the country, it is not possible to quantitatively assess the external validity of the findings. To help address this, qualitative analyses will explore the potential for broader scalability. Second, while assessing cost-effectiveness is not the primary goal of this study, available data - including direct training costs and opportunity costs of physician time - will allow for preliminary evaluation. Future research could rigorously assess both the long-term economic value and equity impacts of the intervention.

3. Conclusion

AMR remains a pressing global health threat, with particularly severe consequences in LMICs like Nepal, where antibiotic misuse is driven by systemic challenges such as limited diagnostic tools, overburdened healthcare providers, and the absence of stewardship programs [2,3,39]. In this study, we will test the effect of two interventions on optimizing antibiotic prescription practices among junior physicians in outpatient clinics across five hospitals in Nepal. By combining a refresher training on AMR, a diagnosis mandate, and individualized feedback on prescribing behavior, the intervention is designed to be both context-sensitive and scalable. To our knowledge, this is the first study in Nepal to test such an intervention outside of Kathmandu. The study's findings will contribute to current global efforts to combat AMR by utilizing low-cost, context-informed interventions to reduce inappropriate antibiotic prescribing in resource-limited settings.

Ethical clearance

The study has been approved by the Institutional Review Boards of Nepal Health Research Council (ref: 1925) and the Pennsylvania State University (STUDY00025143). Since we collect individual health data, we have taken caution to ensure that privacy is protected.

Data and safety monitoring

We have formed a Data Safety Monitoring Board (DSMB), which will review and approve the study procedures, as well as procedures for reporting and tracking adverse events, and study progress. The DSMB will receive a progress report on a weekly basis during the survey period. If needed, meetings will be convened to discuss significant concerns. There are no planned interim analyses or stopping rules given the low-risk nature of the interventions.

Registration

This study has been registered in the US Government's Trial Registry (ClinicalTrials.gov ID: NCT06436690).

Funding statement

This study is funded by the Merck Investigator Support Program (MISP #102072) to the Pennsylvania State University.

CRediT authorship contribution statement

Prashant Acharya: Data curation, Formal analysis, Project administration, Writing – original draft, Writing – review & editing. Prajwol Nepal: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Anup Subedee: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Prem Prakash Pandit: Project administration, Resources, Supervision, Writing – original draft, Writing – review & editing. Supriya Joshi: Investigation, Project administration, Resources, Writing – original draft, Writing – review & editing. Achintya Perumal: Data curation, Formal analysis, Investigation, Software, Writing – original draft, Writing – review & editing. Sanjay Kumar Nirala: Data curation, Investigation, Writing – original draft, Writing – review & editing. Nisha Shrestha: Data curation, Investigation, Writing – original draft, Writing – review & editing. Sagun Gurung: Data curation, Project administration, Writing – original draft, Writing – review & editing. Yubraj Acharya: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing.

Declaration of competing interest

All authors declare they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Data availability

No data was used for the research described in the article.