Preterm birth is a leading cause of under-5 mortality, with the greatest burden in lower-resource settings. Strategies to improve preterm survival have been tested, but strategy costs are less understood. We estimate costs of a highly effective Preterm Birth Initiative (PTBi) intrapartum intervention package  and active control .In our analysis, we estimated costs incremental to current cost of intrapartum care (in 2020 $US) for the PTBi intervention package and active control in Kenya and Uganda. We costed the intervention package and control in two scenarios: 1) non-research implementation costs as observed in the PTBi study , and 2) hypothetical costs for a model of implementation into Ministry of Health programming . Using a healthcare system perspective, we employed micro-costing of personnel, supplies, physical space, and travel, including 3 sequential phases: program planning/adaptation (9 months); high-intensity implementation (15 months); lower-intensity maintenance . One-way sensitivity analyses explored the effects of uncertainty in Scenario 2.Scenario 1 PTBi package total costs were $1.11M in Kenya ($48.13/birth) and $0.74M in Uganda ($17.19/birtth). Scenario 2 total costs were $0.86M in Kenya ($23.91/birth) and $0.28M in Uganda ($5.47/birth); annual maintenance phase costs per birth were $16.36 in Kenya and $3.47 in Uganda. In each scenario and country, personnel made up at least 72% of total PTBi package costs. Total Scenario 2 costs in Uganda were consistently one-third those of Kenya, largely driven by differences in facility delivery volume and personnel salaries.If taken up and implemented, the PTBi package has the potential to save preterm lives, with potential steady-state (maintenance) costs that would be roughly 5–15% of total per-birth healthcare costs in Uganda and Kenya. Each year, about 15 million babies are born prematurely around the world . In addiInterventions to prevent stillbirths and improve preterm survival have been developed and tested in high- and low-resource settings alike , 8, 9, wThe PTBi package of interventions  has been evaluated for effectiveness; however, data on the cost of quality improvement programs are limited , 13. UndData regarding costs of maternity care are limited and estimates vary substantially by country, health facility type/delivery volume, and source/reference . For exaThe goals of our study were 1) to calculate the implementation-level  costs associated with the PTBi program in Kenya and Uganda, as observed in the PTBi study, and 2) to estimate costs associated with public-sector planning, implementation, and maintenance of the package in a non-study, hypothetical, Ministry of Health (MOH) model. Modeled costs in a non-study/MOH setting may be more relevant to decision-makers to inform resource allocation; as such, our analysis focuses primarily on estimates for the cost of public sector implementation. To our knowledge, this is among the first studies to assess the costs of a complex, multicomponent intrapartum quality improvement package in sub-Saharan Africa.Through the PTBi study in Kenya and Uganda, we estimated the per-birth  costs associated with the PTBi package of interventions compared to a more minimal active control. Using a healthcare system perspective, we analyzed incremental costs–costs that could be added to the current cost of obstetric care–associated with the PTBi package and the active control using an activity-based micro-costing approach. Our analysis includes incremental costs for all deliveries with an estimated gestational age of 28 weeks or higher, regardless of delivery outcome . We calculated costs for both the package of interventions and active control through two scenarios: Implementation as observed in the PTBi study (excluding purely research costs) and a hypothetical model led by the Kenyan and Ugandan Ministries of Health.The PTBi study was a cluster-randomized controlled trial implemented in 17 health facilities in Migori County, Kenya and 6 health facilities in Busoga Region, Uganda . This coIn the PTBi study, the comprehensive PTBi package of interventions was demonstrated to reduce the odds of stillbirth and early neonatal death among premature infants by 34% by improving intrapartum and immediate newborn care . ThorougThe PTBi package of interventions included 4 components: data strengthening, a modified WHO Safe Childbirth Checklist (mSCC), PRONTO simulation and team training , 21, andFrom a clinical care perspective, this PTBi package was designed to reinforce evidence-based practices for maternal and newborn care around the time of birth, including provision of antenatal corticosteroids; immediate skin-to-skin contact and kangaroo mother care (KMC); newborn resuscitation; and appropriate feeding , 18. It The active control was also selected through the above-mentioned process. Data strengthening and the WHO mSCC have been outlined by WHO and other local and national organizations as important interventions to better track and compare health outcomes, help improve care during childbirth, and promote the use of evidence-based practices , 23, 24.In the PTBi study, this package of four interventions was compared to a more minimal active control that included data strengthening and mSCC . ActivitAs described above, the selection, design, and implementation of the PTBi package of interventions and control was a collaborative effort by researchers and clinicians in Kenya, Uganda, and the US, and was based on specific in-country needs . IndividIn our analysis, we costed implementation of the PTBi package and control under two scenarios: 1) implementation-level costs (non-research) as observed in the PTBi study (Scenario 1) and 2) costs for a hypothetical model of implementation by local Ministries of Health (Scenario 2). In Scenario 1, we took care to identify and exclude activities that were exclusively associated with research activities, such as data collection that would only be undertaken in a study setting. However, even after excluding activities and costs associated with research, clinical studies typically reflect prices and intensity levels that are not representative of costs associated with program implementation in the public sector. Because of this, we developed our second scenario to model hypothetical implementation (“ownership”) and management by local MOHs in a non-research setting, using mostly public-sector inputs.In both Scenarios, we calculated costs incremental to the cost of providing intrapartum maternal and newborn care; as such, our findings represent the additional costs necessary to implement the PTBi package or control within the current level of care provided in our analysis setting. Further, costs in this analysis focus on those related to the direct planning, implementation, and maintenance of the PTBi package of interventions; costs do not include indirect or downstream changes in medical care. For example, we included costs for resources  and health worker time completing the mSCC for each delivery, but we did not include the costs associated with changes in the usage of medications or devices following PTBi package implementation.To understand the costs for both scenarios, we created an “implementation framework” that documented the phases, activities, and key personnel involved in each PTBi package component for both scenarios. Within this framework, we also outlined activities that are shared between intervention components or are not easily distinguishable . Descriptions of both scenarios are outlined in In our framework, we outlined three critical and distinct implementation phases associated with both scenarios: 1) program design and planning (6–9 months), 2) high-intensity initial implementation (12–18 months) and 3) annual maintenance. Phases and timing of activities are depicted in For both scenarios, we used empirical bottom-up activity-based micro-costing to estimate incremental costs associated with activities within each phase of the PTBi package and control. Key activities included stakeholder meetings to discuss and adapt intervention components; component-specific training  for program-based and facility-based staff and clinicians; program management by MOH MNCH staff; and time spent by program and facility staff “using” the interventions . Activities are further described in Our main cost input categories included costs associated with personnel, consumable goods, capital equipment, travel, and program office/conference space. Input categories are outlined in We tabulated total costs per country, phase, intervention component, health/birth facility, and birth  and report in $US 2020 . When prices and costs were derived from PTBi study invoices and ledgers , in-country prices and costs were converted from Kenyan Shillings and Ugandan dollars into $US using the exchange rate for the month of the invoice/ledger. Where prices and costs were derived from annual statements or estimates , costs were converted using the average exchange rate for the year of the estimate. All prices and costs were then converted to 2020 $US to account for inflation using annual within-country inflation rates.Costs for each phase were tabulated for all activities within each phase; costs per facility were tabulated by dividing total country costs by the number of facilities in each country. Costs per birth were tabulated by dividing total country costs by the total number of births that occurred in facilities over the duration of implementation .We estimated Scenario 1 program-based personnel costs as observed in the PTBi study. Data sources included salary records, budget and expenditure records, timelines, and other project records for the PTBi study; such costs are representative of the private sector. For Scenario 1 facility-based personnel and all non-consultant Scenario 2 personnel, salary data were extracted from published pay scales for program-based, specialist, and facility-based workers that would be involved in the planning and implementation of the interventions in the public sector , 26. We We quantified personnel effort for each facility-based cadre and program-based staff in both scenarios using study records and interviews with program experts. We estimated the amount of time spent on each intervention component and activity, taking care to exclude activities specifically associated with clinical research. Personnel time included time spent by study coordinators and program managers to lead, implement, and monitor intervention activities; clinical specialists and supervisors providing oversight and expertise on specific topics; PRONTO training specialists and Quality Improvement experts ; data specialists and health records clerks receiving training and tracking indicators; and health workers receiving training in facilities and participating in intervention activities. We estimated that, on average, between 8 and 15 health workers would receive at least some level of training or exposure to the PTBi intervention and control per facility .In the PTBi study, new clinical providers were not added to the health facilities within the study; as such, we assumed that new clinical providers would not be hired specifically for the PTBi intervention or control in our cost analysis, and thus did not include costs associated with new clinical providers in either Scenario 1 or 2. We did, however, account for the need for additional training regarding PTBi intervention and control components for health workers who are hired to replace other staff as part of the natural hiring process .In Scenario 1, PTBi study staff undertook all program management activities; via interviews, we estimated the percentage of personnel time spent on general program activities and for each PTBi package component. In Scenario 2, we assumed that program management would be undertaken by local MOH personnel working on existing MNCH platforms/programs. However, we also estimated that two new roles would need to be created to implement PTBi activities: 1) a data specialist role that would be responsible for overseeing DS and mSCC activities, and a 2) QI specialist role that would be responsible for overseeing PRONTO and QI activities. We used MOH organograms to understand reporting, hierarchies, and appropriate pay scales, and supervision for these roles. We included onboarding and supervisory time in our personnel cost estimates for these roles, and we assumed that one specialist within each role would be needed for every 5–8 facilities, depending on facility delivery volume .PRONTO Nurse Mentors are experts in maternity and neonatal care and are essential to the successful implementation of PRONTO activities , 31, 32.In the PTBi study, the PRONTO and QI activities required the intensive involvement of private-sector experts and specialists for the design and implementation of simulation/team training and QI activities . ScenariConsumable goods in our scenarios included office and simulation supplies used for the package of interventions and control. Office supplies included printed training materials, checklists (mSCC), and goods used for QI activities . Simulation supplies included syringes, gauze, dipsticks, and other clinical goods used for PRONTO training activities. Unit prices and quantities for all consumable goods for Scenario 1 were extracted from PTBi study budget and expenditure records; Scenario 2 unit prices were extracted from published price lists and order forms , 34, andTM simulation training kit and neonatal resuscitation mannequins for PRONTO activities. We assumed replacement laptops, projectors, and PRONTOPacksTM every 3–5 years. Because Scenario 2 assumes integration of the PTBi package into existing MNCH programming, we assumed that laptops and office furniture would only be purchased for the new roles described in the personnel section. The value of capital office goods for existing MNCH program staff was prorated based on the percent effort used to incorporate the package of interventions into the local MNCH platform. We also assumed that all PRONTOPackTM components in Scenario 2 would be purchased in-country. Unit prices and quantities in Scenario 1 were extracted from study budget and expenditure files; unit prices for Scenario 2 capital goods were extracted from MOH price lists for most items, with PTBi study prices for specialized goods that were not available in MOH price lists.We identified the capital goods (including quantities and replacement frequencies) required to implement and maintain interventions through a review of study records and interviews with study staff. Capital goods in both scenarios included laptops and office furniture for program coordinators/managers, projectors for training and ongoing QICs, and the PRONTOPackWhile the PTBi package of interventions does not include the use of clinical supplies or capital goods that are not already part of essential maternity and newborn care in-country, facility assessments in the PTBi study found that some facilities did not have all the necessary goods required to provide care per guidelines . As suchWe estimated costs for transportation in each scenario, including vehicle costs for travel to and from facilities for regular intervention activities. We also estimated consultant travel costs, which included limited regional and international airfare, ground transportation, and lodging for multi-day activities, such as training of PRONTO mentors. Travel costs were calculated in Scenario 1 were using on observed prices and quantities in study documents and invoices. Scenario 2 costs were calculated using local price estimates collected in-country by local health economists in March 2020; travel units were based on our analysis of program activities that would require travel for consultants, program staff, and limited travel for select in-facility workers.We estimated costs associated with program office space based on study office rent in the PTBi study  and hotel conference rooms rented for major meetings and training sessions, including food and beverages provided during offsite meetings. In Scenario 2, we estimated the value of program office space that would be used within existing MOH program offices for program-based staff and limited use of conference rooms for annual, offsite MNCH planning meetings, prorated for the percentage of the meeting that would be used to discuss PTBi activities. Scenario 2 assumes that all training activities, PRONTO sessions, and QICs would take place within existing space in health facilities; therefore we did not include health facility space costs for these activities.For Scenario 1 (costs observed in the PTBi study), we calculated total incremental costs associated with package implementation in 9 health facilities in Kenya and 4 in Uganda; we also calculated total costs for 8 control facilities in Kenya and 2 control facilities in Uganda. In our hypothetical MOH model (Scenario 2), we calculated total incremental costs associated with the package of interventions and active control in all 17 facilities in Kenya and all 6 facilities in Uganda. For both scenarios, we calculated total program costs, cost per facility, and cost per birth for each the package of interventions and control. We also tabulated the percent contributions of by input category and intervention component for the PTBi package.Costs per facility were based on the number of facilities in each country. Cost per birth was based on number of facilities, birth volumes per month per facility, and duration of implementation. Kenyan facilities had volumes of 30–360 deliveries per month, with most facilities having fewer than 100 deliveries per month. Ugandan facilities had volumes of 90–585 deliveries per month, with most facilities having more than 150 deliveries per month. Total costs included 27 months of in-facility activities across phases 2 and 3.For Scenario 2, we relied on several key assumptions, which were identified through interviews with in-country stakeholders. For example, we assumed that all intervention and control activities would be fully integrated within existing MOH MNCH activities. As such, we also assumed that majority of activities for each phase would be managed and implemented by MOH MNCH program leadership and staff within each geographic area. Other key assumptions and rationale are described in We conducted sensitivity analyses to understand the impact of uncertainty in Scenario 2, including higher intensity of program planning activities and intervention adaptation; higher intensity of QI and PRONTO activities, including more frequent refresher training; hiring/use of “centralized” nurse mentors instead of facility-based nurse mentors; and differences in facility size and worker composition within facilities.For Scenario 1, we calculated costs associated with package implementation in 9 health facilities in Kenya and 4 in Uganda, and 8 control facilities in Kenya and 2 control facilities in Uganda, as observed in the PTBi study. Scenario 1 total program costs by country, input type, intervention, facility, and birth are in In the hypothetical MOH model (Scenario 2), we calculated costs associated with package intervention and control in all 17 facilities in Kenya and all 6 facilities in Uganda. Scenario 2 total program costs by country, input type, intervention, facility, and birth are in Scenario 2 costs per birth were 50% lower in Kenya and 68% lower in Uganda compared to Scenario 1. In both scenarios, personnel time made up the majority of total program costs. In Scenario 2, 88% and 72% of costs were for personnel in Kenya and Uganda, respectively. Cost by input type, intervention component, and phase for Scenario 2 are in Among implementation phases in Scenario 2, Phase 1, 2, and 3 activities comprised 26%, 44%, and 30% of total costs in Kenya, respectively; in Uganda this was 38%, 37%, and 25%, respectively . Among iSensitivity analyses focused on areas of uncertainty in Scenario 2, identified through discussions with PTBi study team members and experts in the local healthcare systems in Kenya and Uganda. Key sensitivity analyses included differences in the intensity of program activities, including a higher level of program adaptation during Phase 1, more frequent in-facility trainings in Phase 2, and a different “model” for PRONTO Nurse Mentors . We also analyzed the effect of differences in health facility volumes between Kenya and Uganda to understand the impact of PTBi study facility type/volume between the two countries. Finally, we estimated total costs when excluding costs associated with facility-based workers.Results from our sensitivity analyses are outlined in Using a combination of quantitative and qualitative methods, we estimated costs associated with the implementation of the PTBi package of interventions in two distinct scenarios: one that represents non-research costs observed in a study setting and one that represents hypothetical costs of an MOH-led model. We found that package costs were $48.13 per birth in Kenya in the PTBi Study and $17.19 per birth in Uganda . In Scenario 2, costs per birth were $23.19 in Kenya and $5.47 in Uganda ; steady-state costs for phase 3 alone were $16.36 per birth in Kenya and $3.47 in Uganda.Our study adds to the limited evidence on the costs associated with interventions to improve preterm survival in lower-resource settings, where the burden of preterm birth is highest . It is bDue to limited data regarding the costs of interventions for preterm birth in lower-resource settings, differences in interventions, and differences in setting and results reporting, comparisons in costs between our analysis and other cost analysis in MNCH are limited. However, our input categories and unit costs are consistent with those in other cost analyses in similar settings for intrapartum care interventions , 36, 37,Scenario 2 costs were substantially lower than Scenario 1 in both countries. This reflects differences in personnel pay, intensity of activities, and number of facilities in the two scenarios: Scenario 1 program-based staff were paid private-sector salaries/benefits; Scenario 1 includes time spent on full program and intervention development (higher intensity); and Scenario 2 includes more facilities (greater efficiency per facility and birth). The difference in Scenario 2 total costs and cost per birth are also due to differences in birth volumes in PTBi study facilities in Kenya and Uganda, which we used for estimating facility-level costs in both scenarios: In Kenya, most study facilities were smaller, lower-volume with a higher health-worker-to-birth ratio; in Uganda, most study facilities were larger, with higher birth volumes and a lower health-worker-to-birth ratios. As we found in sensitivity analyses, implementation in larger, high-volume facilities (vs lower volume) results in greater efficiencies and lower cost per birth. This may be helpful for resource allocation, as more complicated deliveries often are referred to larger facilities when possible. However, that does not warrant the exclusion of smaller facilities from intervention activities. Maximizing impact and efficiency is relevant for resource allocation, but decision-making should also be based on burden and other needs.In Scenario 2, total costs in Uganda were 33% of those in Kenya. This reflects the differences in the Kenyan and Ugandan economies and health care systems—Kenya has transitioned to being a lower-middle income country , while Uganda remains a low-income country (GDP per capita in 2020: $817 USD) . As we oIn our study, personnel were the single largest cost input, which reflects the fact that the PTBi package uses training and monitoring to improve health worker skills, including the identification and management of preterm birth. The package does not require the purchasing or maintenance of new high-tech goods or the implementation of new clinical interventions, which helps account for the relatively low estimated costs for consumable and capital goods. Our analyses included time spent by consultants who provide specialized guidance and training in clinical care and quality improvement. In Scenario 2, the total cost for specialist consultants was relatively comparable between Kenya and Uganda; this is due to anticipated similar pay for specialist consultants between the two countries.Because we aimed for a robust economic evaluation, we included in-facility health worker time spent in training and QI activities in our analysis. While this allows us to understand the total value of the PTBi package of interventions and the opportunity costs of implementing health interventions, it is important to note that findings from our cost analysis is neither a budget estimate nor a financial analysis and should not be used as such. Removing costs associated with health professional time, given they are salaried employees already working in facilities, resulted in 20–50% lower total costs. Because our analysis includes time spent by existing health workers—the total “new” costs incurred by the PTBi package of interventions is potentially lower than estimated in our analysis.PRONTO had the single largest cost among intervention components. This is in part due to the limited local experience with highly realistic simulation and team training offered by PRONTO, including training of trainers, which is led by US-based experts in simulation and team-based training. While the costs associated with PRONTO are substantial compared to that of the mSCC, for example, they represent the intensive, skills-based, capacity-building nature of the PRONTO intervention. PRONTO has been demonstrated in several studies to significantly improve maternal and neonatal care , 40, 41 Our analysis has important limitations. First, since Scenario 2 is hypothetical, we did not directly observe costs for this scenario, and we relied on several assumptions, including heavy use of public sector personnel and minimal adaptation of package interventions. Actual in-country costs may differ, as outlined in our sensitivity analyses, and the effectiveness of the PTBi package of interventions and active control in Scenario 2 may differ from the PTBi study. We relied on publicly available information from in-country governments regarding public-sector health worker pay, especially in Scenario 2; any differences between publicly available salary information and actual health worker pay may affect our estimates. However, our assumptions were based on information from in-country researchers, health workers, and healthcare system experts. Changes in key model assumptions resulted increases in cost per birth of 3–22% in sensitivity analyses.Second, our costs represent implementation in a county-specific context in Kenya and a region-specific context in Uganda over the course of 3 years. Our two scenarios and their associated costs are also based on information from the specific facilities included in the PTBi study. Scaling at a national level may result in modest efficiencies, though costs and resources required to plan, implement, and maintain the PTBi package may differ in other facilities. Third, the PRONTO implementation model in our study is focused on preterm birth and select obstetric emergencies. Broader PRONTO models covering more clinical situations would cost more.Strengths of our study include its high level of detail, robust data collection, and in-depth analysis of costs by activity, input type, phase, and intervention component. Our modeling of scenarios provides insights into both private-sector and public-sector costs, and our analysis approach can be applied to other settings. While costs in our study are specific to local contexts in Kenya and Uganda, our methods may be of use for understanding costs in other geographic settings. Additionally, the analysis approach and our use of national data for health worker composition and costs may be applied to other clinical situations related to obstetric and neonatal care, using the same intervention components . Indeed, we found that costs for PTBi intervention maintenance were lower than for previous phases, which indicates that PTBi may be a suitable platform for the efficient inclusion additional training and curricula in other areas of emergency obstetric, intrapartum, and neonatal care. This is another important area that should be explored in future economic evaluations.We found that the PTBi package may be implemented and maintained by the public sectors in Kenya and Uganda at a relatively low cost per birth. While our study is limited by its assumptions and specific setting and context, our findings add to the limited data regarding the total economic costs associated with interventions to improve preterm survival in lower-resource settings. Such findings may help inform future policy and implementation of this critical, life-saving package of interventions.S1 FigS1 Fig provides detailed timing, phasing, and activities for each of the PTBi package intervention components through all phases of program planning, initial high-intensity implementation, and maintenance. All activities are based on activities for and findings from the PTBi study. All activities and durations were used for the Scenario 2 cost analysis. Control costs included only activities for data strengthening and the WHO modified safe childbirth checklist, along with general program activities that pertained to these two components. Intervention package costs included all activities for data strengthening, mSCC, PRONTO, Quality Improvement, and general program activities.(XLSX)Click here for additional data file.S2 FigDetailed model assumptions for PTBi costing Scenario 2.(XLSX)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S1 Checklist(DOCX)Click here for additional data file. 2 Jun 2022 <div> PONE-D-22-11311 </div>  <div> Estimated costs for an intrapartum quality improvement package for improving preterm survival and reinforcing best practices in Kenya and Uganda </div>  <div> PLOS ONEDear Dr. Smith Hughes,Thank you for submitting your manuscript to PLOS ONE. 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Review Comments to the Author </font> Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: Thank you for the opportunity to review this manuscript. I liked the paper a lot and feel that the methodology and approach will be really useful for other researchers to use as it sets out a very clear and logical approach.There are some points of clarification needed – especially in the Abstract which I felt did not well reflect the paper. Recognizing that the Abstract is all that many people read, I feel it could be clearer.The abstract talks about an intervention and an active control. I think it would be more useful to say that one was the non-research costs associated with a study and one was implementation by the Ministry of Health. That feels clearer than an active control which suggests a trial.The Preterm Birth Initiative East Africa needs to be mentioned in the Introduction to the Abstract. At the moment the intro is about the Safe Childbirth check and then the next sentence is about the PTBi. There is no clear connection and this could be stronger and better linked.It is really helpful to have the costs for each scenario but what was missing for me was the effectiveness. Was it the same in each? Did the lesser cost result in less effectiveness? I know this is probably another study but it feels like a significant gap.The authors say that the PTBi costs are relatively low cost to implement but relative to what? For many countries, a cost of $23 per birth for an education and support program would be more than is spent on the woman’s care overall? I would like some more about how these costs compare relative to the overall costs.Reviewer #2: For the sensitivity analysis using scenario2, please call it hypothetical model and avoid using the term implementation. Overall the paper is good and may add to the body of knowledge on costing studies of PTBi interventions.Reviewer #3: This manuscript gives a detailed account about the costs of a complex intervention package aiming to improve preterm bird outcomes (PTBi) in Kenya and Uganda. From actual costs of a cluster-randomised trial, costs of real-world implementation were projected. A full and a minimum implementation scenario was compared.Overall, the manuscript is well written, reporting is detailed, methods and assumptions are well justified. Nevertheless, some important questions need clarification and the below suggestions may help the authors to improve the manuscript.a) Please clarify the decision situation and implications on real-life care: it was not clear, if the program implementation changes the costs of actual practice (e.g. if more resources are used after implementing the mSCC tool) and whether it is taken into account in cost calculations.b) I suggest the authors briefly introduce the essential content and clinical evidence concerning the interventions of the package. External references were provided, 1-2 more sentences would help the reader to understand the programc) Please briefly justify that the PTBi study hospitals reflected the national average and extensions to national costs can be made.e) I suggest that in addition to main unit costs, the authors provide details of resource use by each study component, and link assumptions / scenarios to actual resource use figures. The paper provides lengthy explanations about various assumptions, but it remains unclear, how they were operationalised in the analysis.f) It was not entirely clear, why minimal implementation was chosen as control. In my opinion, incremental costs vs current practice would be more relevant. The authors should briefly describe current practice in the index countries, and if any elements of the PTBi package are being spontaneously implemented across the countriesg) In the results tables and figures it was difficult to follow if total costs or incremental costs vs control were provided or where the incremental costs vs control are detailed.h) When calculating costs per birth, did the authors project costs to live births or per delivery (resulting in live births and still births)? Were the expected effects of the program on live births taken into consideration when projecting costs per birth? While the paper is not a full economic analysis, the authors may consider projecting costs per natural outcome such as cost per prevented stillbirth or cost per baby surviving one year etc...i) the authors should comment about the uncertainty of their estimates********** <font color="black"> 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. </font> Reviewer #1: NoYes: Roopali GoyankaReviewer #2: Yes: Zsombor Zrubka, MD, MBA, PhDReviewer #3: **********https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. 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We confirm that we have revised to manuscript to ensure that all relevant components from the CHEERS checklist have been included in our manuscript. I look forward to receiving your resubmission.[Note: HTML markup is below. Please do not edit.] Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: YesReviewer #2: YesReviewer #3: Yes• Thank you for reviewing; based on this we did not make specific edits.2. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: YesReviewer #2: YesReviewer #3: Yes• Thank you for reviewing; based on this we did not make specific edits.3. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #1: YesReviewer #2: YesReviewer #3: Yes• Thank you for reviewing; based on this we did not make specific edits.4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: YesReviewer #3: Yes• Thank you for reviewing; based on this we did not make specific edits.5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics.  Reviewer #1: Thank you for the opportunity to review this manuscript. I liked the paper a lot and feel that the methodology and approach will be really useful for other researchers to use as it sets out a very clear and logical approach.• Thank you for your thorough review and extremely helpful comments. We made revisions as appropriate to the manuscript, as detailed below. There are some points of clarification needed – especially in the Abstract which I felt did not well reflect the paper. Recognizing that the Abstract is all that many people read, I feel it could be clearer.• We have revised the abstract based on your helpful comments and requests for clarification, and to ensure it better reflects the paper. Further details on specific changes are listed in the specific comments below.The abstract talks about an intervention and an active control. I think it would be more useful to say that one was the non-research costs associated with a study and one was implementation by the Ministry of Health. That feels clearer than an active control which suggests a trial.• Thank you for the opportunity to clarify and your comments. In the PTBi effectiveness study, the PTBi package of interventions was compared to the more minimal active control. In this cost analysis, we calculated costs associated with the PTBi package of interventions and the active control in two scenarios: o Our first scenario reflects the observed non-research costs within the PTBi study (for the PTBi package of interventions and active control), which includes many private-sector costs that would not be incurred if the program was implemented in the public sector.o Our second scenario estimates the hypothetical costs for non-study public-sector implementation  of the PTBi package of interventions compared to the active control.o We have worked to make this clearer in the abstract and throughout the full manuscript as well. • We have provided more detail about the process used in the PTBi study to develop the package of interventions and active control, and our rationale for the inclusion of the active control in the cost analysis . We have also worked to make this more clear in the abstract. The Preterm Birth Initiative East Africa needs to be mentioned in the Introduction to the Abstract. At the moment the intro is about the Safe Childbirth check and then the next sentence is about the PTBi. There is no clear connection and this could be stronger and better linked.• Thank you for this comment; we have revised the abstract accordingly to more clearly describe the PTBi intervention and active control (and components within them) in the introduction to the abstract.It is really helpful to have the costs for each scenario but what was missing for me was the effectiveness. Was it the same in each? • The effectiveness of the intervention and control in Scenario 1 are known and are mentioned in the second paragraph of the “Study Setting” section . • The effectiveness of the PTBi package of interventions versus active control in Scenario 2 – hypothetical MOH model – was not observed and is not known. We have clarified this caveat in the limitations in the discussion on PDF page 92, lines 702-712. However, the frequency of activities and types of activities associated with each of the intervention components is assumed be similar, and, as we note in the manuscript, our assumptions for Scenario 2 were developed in collaboration with in-country experts in program implementation and costs.• We have revised the full text manuscript to include some additional details regarding the process by which the PTBi package of interventions was developed, and its effectiveness and feasibility on PDF page 67-68, lines 151-158.Did the lesser cost result in less effectiveness? I know this is probably another study but it feels like a significant gap.• Because the focus of this analysis is on costs, the effectiveness details have been published elsewhere and are referenced in full text, and given the limited space in the abstract, we have not included a detailed description of the effectiveness in the abstract or main text. • As you’ve noted, the effectiveness of the PTBi package is an extremely important consideration. We plan to assess the cost-effectiveness of the PTBi package vs active control (for both Scenarios) – including under potentially lower effectiveness in Scenario 2 due to differences in implementation model – in a forthcoming cost-effectiveness analysis that will integrate the health effects/health outcomes of the PTBi package of interventions vs active control in both scenarios. The authors say that the PTBi costs are relatively low cost to implement but relative to what? For many countries, a cost of $23 per birth for an education and support program would be more than is spent on the woman’s care overall? I would like some more about how these costs compare relative to the overall costs.• We really appreciate this point, and we have removed the mention of “low” in the abstract and discussion. We had intended to mean “low” compared to the cost of delivery, but we appreciate that such a statement is subjective and requires more information. • In addition to removing the word “low” from the abstract and discussion: We have revised the Introduction in the manuscript to include the estimated costs of maternity care in sub-Saharan African countries to provide some context and information by which to compare the costs of the PTBi intervention to overall costs of current practice . We also provide details on the current cost per delivery for maternity care in each country in the discussion on PDF page 90, lines 635-637. We hope this sufficiently answers the question regarding how the costs compare to overall costs of maternity care in the region. Reviewer #2: For the sensitivity analysis using scenario2, please call it hypothetical model and avoid using the term implementation. Overall the paper is good and may add to the body of knowledge on costing studies of PTBi interventions.• Thank you for this opportunity to clarify. We have revised the wording/labelling accordingly throughout the paper, using “hypothetical MOH model” in most instances where we refer to Scenario 2, especially in tables and visuals (Tables 2-5).  Reviewer #3: This manuscript gives a detailed account about the costs of a complex intervention package aiming to improve preterm bird outcomes (PTBi) in Kenya and Uganda. From actual costs of a cluster-randomised trial, costs of real-world implementation were projected. A full and a minimum implementation scenario was compared.Overall, the manuscript is well written, reporting is detailed, methods and assumptions are well justified. Nevertheless, some important questions need clarification and the below suggestions may help the authors to improve the manuscript.• Thank you for your comments and questions. We feel they helped us greatly in improving the study and manuscript. Our responses to each of your comments are below. a) Please clarify the decision situation and implications on real-life care: it was not clear, if the program implementation changes the costs of actual practice (e.g. if more resources are used after implementing the mSCC tool) and whether it is taken into account in cost calculations.• Thank you for this question. Our analysis focuses on the costs of implementing the activities outlined within the PTBi package of interventions, which includes health worker training, data strengthening, and other activities that reinforce the use of evidence-based practices and care per guidelines. However, because the PTBi intervention does not include the use of new medical interventions that are not part of the current standard of care, we did not include costs associated with most changes to direct patient care in our study. For example, we did include the additional time it would take for health workers to fill out the mSCC while providing care, but we did not include costs associated with downstream changes in care. • To help clarify, we have provided additional details on the focus of our cost analysis in the Abstract; the details of the PTBi package of interventions and control on PDF page 67, lines 132-140; PDF page 68, lines 161-176; PDF pages 71-72, lines 235-243; and page 78, lines 356-362. • We will be taking into account the changes in the costs of actual practices in a forthcoming cost-effectiveness analysis. While we do assume that implementation of the PTBi intervention and active control would have an impact on the costs of actual practices, the affect may increase some costs and may decrease others. For example, the package promotes the use of antenatal corticosteroids  for lung maturation in preterm infants, so implementation of the package would result in greater use—and associated costs—of ACS. However, when used appropriately, ACS can also avert costs associated with the need for ventilation and use of more intensive care among some infants. Our planned cost-effectiveness analysis takes these changes in clinical care and associated costs and health outcomes, including longer-term costs and outcomes, into account. b) I suggest the authors briefly introduce the essential content and clinical evidence concerning the interventions of the package. External references were provided, 1-2 more sentences would help the reader to understand the program• We have revised the manuscript to include further details regarding the package of interventions – including information on clinical evidence for each intervention component and their inclusion in the package of interventions and control – in the track-changes portion of the manuscript , including the process behind and rationale for their selection. c) Please briefly justify that the PTBi study hospitals reflected the national average and extensions to national costs can be made.• In a peer-reviewed publication regarding the design and implementation of the PTBi study, the selection of study facilities is described. The paper notes that “Given that facilities were not selected from a target population of hospitals, the intervention effects should be interpreted as impact evaluation of the intervention package implemented at the said facilities.” This is also true of results from our cost analysis, as we note in the revised limitations of our track-changes manuscript on PDF page 93, lines 714-718. • However, the PTBi study included facilities that were operated through the local public sector MNCH programming offices, which are under the purview of the national MOH. We reviewed organizational charts, staffing guidelines, and reporting structures to ensure our estimates for the composition of health workers in the study facilities – health worker costs made up the largest proportion of costs in our study – were representative of those outlined in national recommendations. • Further, we would like to note that, in Scenario 2, we used national data for all in-country programmatic and facility-based health worker salaries, and, where possible, national data from public-sector tenders, WHO pricelists, and UNICEF pricelists for resources used. To the best of our knowledge, these costs represent national costs. Study co-authors collaboratively collected and validated data to ensure their representativeness and to ensure they were appropriate for use in our study.e) I suggest that in addition to main unit costs, the authors provide details of resource use by each study component, and link assumptions / scenarios to actual resource use figures. The paper provides lengthy explanations about various assumptions, but it remains unclear, how they were operationalised in the analysis.• Thank you for this comment. We agree that the units for resource use are important. We have added units for major inputs into Table 3 for key resources. Full details on units per input and by each component are in our full data set, available through the linked data repository and available upon reasonable request. f) It was not entirely clear, why minimal implementation was chosen as control. In my opinion, incremental costs vs current practice would be more relevant. The authors should briefly describe current practice in the index countries, and if any elements of the PTBi package are being spontaneously implemented across the countries• Thank you for this question/note. Regarding the question about why minimal implementation was the control: We costed the active control as a comparator because it was the comparator in the effectiveness portion of the PTBi study. For reference, this active control will also be used to assess cost-effectiveness, which is also a reason why we costed the control in our analysis. • To make this clearer in the manuscript – this is an important clarification that you’ve raised – we’ve added the rationale for the use of the active control in the effectiveness study and the cost analysis to the paper on PDF page 69, lines 187-192; and page 70, lines 208-212. • Regarding the comment about the current practice: In conjunction with changes outlined above, we have noted that prior to the PTBi study, none of the PTBi package or control components were being consistently implemented . • Full details on the current clinical practices in obstetric care have been added to the manuscript as well, which helps provide rationale for the PTBi package and the active control . We included some contextual information regarding costs of current practice from other studies on PDF page 66, lines 108-115.g) In the results tables and figures it was difficult to follow if total costs or incremental costs vs control were provided or where the incremental costs vs control are detailed.• All costs reported (for each the intervention package and active control) are incremental to the current practice; in our study, the current practice was not costed, but was assumed to be the current costs of providing intrapartum care for mothers during labor, delivery, and the immediate postpartum period and care for newborns during the delivery admission. • We have clarified in the Abstract, Introduction, and Methods that the goal of our study is to calculate incremental costs; these changes are specifically detailed in the track-changes file on PDF page 63, lines 52-53; page 67, lines 132-137; pages 71-72, lines 235-243; page 81-82, lines 450-459. h) When calculating costs per birth, did the authors project costs to live births or per delivery (resulting in live births and still births)? • We calculated the costs per delivery/birth (inclusive of both live births and stillbirths), regardless of neonatal outcome. We have made this clearer in the manuscript, for example on PDF pages 67, lines 130-131. we have also replaced the mentions of “infants” and “babies” where relevant in the manuscript and used “births” or “deliveries”. Were the expected effects of the program on live births taken into consideration when projecting costs per birth? While the paper is not a full economic analysis, the authors may consider projecting costs per natural outcome such as cost per prevented stillbirth or cost per baby surviving one year etc...• We did not take into account the expected effects of the program on live births vs stillbirth, since we will be evaluating cost per health outcome (cost per stillbirth averted and cost per DALY averted for intervention package versus active control) in a forthcoming cost-effectiveness analysis that will be a follow-up to this study.i) the authors should comment about the uncertainty of their estimates• We have updated our discussion section to further describe our uncertainties in the limitations section of our discussion on PDF pages 92-93 in lines 702-720 – including more details regarding our uncertainties in Scenario 2. Our sensitivity analyses explore the effects of uncertainty in many inputs, as described on PDF pages 87-88 in the manuscript and Table 7.AttachmentResponse to Reviewers.docxSubmitted filename: Click here for additional data file. 4 Jun 2023Cost analysis of an intrapartum quality improvement package for improving preterm survival and reinforcing best practices in Kenya and UgandaPONE-D-22-11311R1Dear Dr. Carolyn Smith HughesWe’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. 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Subsequent analysis focuses on the denoised fBm classifier ensemble from each mucus sample and bead diameter. Every ensemble fails a homogeneity test, compelling clustering methods to assess levels of heterogeneity. The first binary level detects beads within vs. outside flakes. A second binary level detects within-flake bead signals that can vs. cannot be disentangled from the experimental noise floor. We show all denoised ensembles, within- and outside-flakes, fail a homogeneity test, compelling additional clustering; next, all clusters with sufficient data fail a homogeneity test. These levels of heterogeneity are consistent with outcomes from a stochastic phase-separation process, and dictate applying the generalized Stokes-Einstein relation to each bead per cluster per sample, then frequency-domain averaging to assess rheological heterogeneity. Flakes exhibit a spectrum of gel-like and sol-like domains, outside-flake solutions a spectrum of sol-like domains, painting a rheological signature of the phase-separation process underlying flake-burdened mucus.The mucus lining of the human airway epithelium contains two gel-forming mucins, MUC5B and MUC5AC. During progression of cystic fibrosis (CF), mucus hyper-concentrates as its mucin ratio changes, coinciding with formation of insoluble, dense mucus flakes. We explore rheological heterogeneity of this pathology with reconstituted mucus matching three stages of CF progression and particle-tracking of 200 nm and 1 micron diameter beads. We introduce statistical data analysis methods specific to low signal-to-noise data within flakes. Each bead time series is decomposed into: (i) a fractional Brownian motion (fBm)  We enforce uniformity of We first briefly recall the experimental and data-analysis protocols of Passive Particle-Tracking Microrheology (PPTM) , 2, 3. Mked bead ,24,25, MPure medium-induced increments and MSD statistics, free from experimental noise and tracking error, are inserted into the Generalized Stokes-Einstein Relation (GSER), mapping from increments at lag times ensemble-averaged MSD, is the standard formula employed for presumed homogeneous materials, wheredenotes the ensemble average over all tracked beads. PPTM has been indispensable for soft complex fluids with extremely low yield thresholds and low volume availability, such as human bronchial epithelial (HBE) mucus , 22Pure flakes. In advanced stages of CF, up to 50% of the gel-forming mucins (MUC5B and MUC5AC) in airway mucus is sequestered within flakes that do not swell nor dissolve in airway surface salt-water solvent. Advanced CF mucus can therefore be represented, at a coarse scale, as a two-phase mixture: a dense phase of mucin-rich flakes, and a more dilute phase consisting of the remaining mucins. Additional scales of spatial heterogeneity potentially exist within the two coarse phases for any given sample [In addition to previously documented increases in mucus concentration ,12, cystn sample : the dilHeterogeneity and insufficient random sampling of flake-burdened mucus samples impose hard constraints on the form of the Generalized Stokes-Einstein Relation (GSER) one should use. The inherently low bead numbers within flakes further limit inference of rheology. Ensemble averaging of bead MSDs in the GSER is justified by an ergodicity assumption for homogeneous materials: ensemble averaging of bead MSDs in the time domain is equivalent to frequency-domain averaging of the Fourier-transformed MSDs, further assuming a random sampling of the material. These assumptions are strongly violated for flake-prevalent mucus ,22.To overcome these limitations, we proceed in the following steps:Experimental: Reconstitute bulk samples of HBE mucus to match the MUC5B:MUC5AC ratio during three progressive stages of CF [es of CF . DispersFiltering of the data. Apply a proximity filter to ensure beads are isolated and not within 5 diameters of another bead to avoid bead-bead interactions and cross-correlations, cf. [ons, cf. ,17,18. Fuse the sophisticated denoising procedure of [to analyze low mobility data from beads in flakes. Explore several classifier metrics of individual bead time series and seek the optimal metric for the experimental data.Given that within-flake beads often have mobilities on the order of the noise floor, edure of , generaledure of  and hereUse synthetic simulated data to replicate features of the experimental data, in particular, heterogeneous tracked particle time series, extremely low mobility and signal-to-noise (SNR) time series, and then to identify an optimal classifier metric (described in detail below).With the optimal classifier metric, hierarchically cluster the experimental datasets. 1st, distinguish beads outside and within flakes.  beads correctly identified.) 2nd, distinguish whether tracked beads within flakes can be confidently disentangled from the noise floor. 3rd, test whether the ensembles of denoised within-flake and outside-flake beads, per reconstituted sample, are statistically homogeneous. (N.B. All fail the homogeneity test.) 4th, given that within-flake and outside-flake ensembles are non-homogeneous, apply a clustering algorithm to the within-flake and outside-flake datasets for the three bulk samples for each bead diameter. 5th, test homogeneity of all individual clusters containing at least 4 beads. (N.B. All clusters fail the homogeneity test.)apply the GSER to single beads in each cluster and then cluster average in frequency space to infer the dynamic moduli of all denoised data clusters within and outside of flakes, for 200 nm and 1 μm diameter beads. Assess the resulting rheological heterogeneity between clusters within and outside of flakes, for each probe size.Given non-homogeneity of each cluster, Assess probe length-scale dependence in the dynamic moduli from the 200 nm and 1 μm bead diameter results for all three mucin-ratio samples. Make preliminary inferences of pore-size distributions of flakes for the three CF-like mucin-ratio samples and summarize future steps to make inferences of pore-size distributions rigorous.Next, we explain the predictor-corrector method, then the experimental data collection, and finally we analyze data from flake-prevalent mucus samples and discuss the results.Recall over experimental timescales, each individual tracked bead approximately exhibits a sub-diffusive MSD power law,for sub-diffusive fractional Brownian motion, the classifier is two-dimensional, 2 and therefore can be readily compared across multiple beads, and used for averaging or cluster analysis. Alternatively, one can also use the GSER per bead and compare the dynamic moduli −1, or perform other statistical analyses. The potential problem with any of these single lag time or frequency projections onto a scalar quantity arises when the bead time series data has not been denoised first, and the potential for error is exaggerated for the highly sub-diffusive time series of beads inside flakes. We illustrate this point below in Soft biological materials like mucus are both viscous and elastic, with different responses at different frequencies of forcing. In viscoelastic materials, the MSD of passive beads is sub-linear over the timescales for which the medium exhibits memory due to elastic recoil of the polymeric network. For 200 nm to 1 μm diameter passive beads in respiratory mucus, and for our microscope system, the memory timescales encompass the camera shutter timescale (1/60 sec) and the total bead observation time (30 sec). Furthermore, al, α,Dα . The powthe MSD classifieris a denoised projection onto fractional Brownian motion (fBm). This classifier further provides an analytical formula for the dynamic moduli surrounding each tracked bead by virtue of the exact Fourier transform of any power-law MSD:the denoised classifierper individual bead yields an exact analytical formula, thereby avoiding numerical error:three-stage analysis. The first stage is binary: one cluster of all tracked beads with a water-like, weakly sub-diffusive, signal consistent with tracking of beads in a relatively dilute mucin solution with the experimental instrumentation (thus likely outside flakes); a second cluster of tracked beads with a clear sub-diffusive signal bounded away from water-like signals (thus likely within flakes). The second stage is also binary, applied to the within-flake cluster. Bead increment time series are divided into those that are, or are not, distinguishable from the noise floor of the experimental instrumentation. The signature of the noise floor is achieved by tracking stationary beads glued to a glass plate with the experimental instrumentation, thereby identifying the classifier range where the signal is indistinguishable from the noise floor. The third stage involves two steps: a finer clustering of the successfully denoised outside- and within-flake clusters using a standard clustering algorithm ; follow mclust , 29), th, ththe Mequivalence of using forms (2) and (3) of the GSER for homogeneous clusters. The left panel data mimics water-like signals in dilute HBE mucus and the middle panel mimics flake-like signals, both drawn from a normally distributed mean MSD classifier guaranteed to give power-law scaling. For the heterogeneous mixture in the right panel, methods (1) and (2) produce a non-power law scaling of fractional autoregressive moving average (fARMA) denoising model developed in [Our strategy is to extract the pure stochastic fluctuation signal using an extension of the loped in . From [3loped in , Figure The standard method for estimating the dimensional MSD classifier parameters relation logMSDXSince the empirical MSD is contaminated by noise at both the smallest (static and dynamic camera error)  and largfractional-diffusion MSD classifier, From here on, we use the LS (predictor) -- fARMAs (corrector) procedure to estimate the diffusion parameters. The resulting mclust [mclust estimates the posterior membership probabilitymclust chooses mclust estimates the posterior membership probabilities Let e mclust  using fible 3 of ). This iNow suppose that in addition to The so-called Cochran’s Q statistic ,29Q=∑i2 for all beads, and thus admits inter-bead comparisons. A downside of this classifier is that the choice of MSD lag-time we define a power lawspatial dimensionand bead radius-dependent rescaling ofmclust clustering algorithm with unconstrained variances.A natural choice for the classifier of sub-diffusive particle trajectories is and the material is sol-like , whereas when and the material is gel-like .For viscoelastic media, a fundamental property is that, instead of a scalar metric  the viscous and elastic moduli are functions of frequency. In this respect, a standard viscoelasticity metric is the loss tangent:For pure power-law viscoelastic materials, collapses to a scalar function of the MSD power law exponentindependent of both frequencyand the MSD pre-factorgel-like phases correspond tosol-like phases correspond to. positive values ofare sol-like and negative values gel-like. All water-like data is sol-like, all noise-floor data is gel-like, and all flake-like data lies between these extremes. We are interested especially in the percentage of sol-like and gel-like signals in flake-like data as a coarse scalar metric of heterogeneity.1 μm and 200 nm beads are embedded in a mixture of purified mucins  derived from either HBE (predominantly MUC5B) or the human airway epithelial Calu3 cell line (MUC5AC). We chose to study the effect of the changed ratio of muc5b to muc5ac during the progression of CF . Three dfollowed by injecting that mixture into a calcium chloride solution. Imaging revealed both within-flake and outside-flake beads. There are two reasons that some beads are not found in flakes at the time of tracking: 1) the process doesn’t have 100% encapsulation, and 2) beads formerly inside may diffuse out.The flakes were made by mixing beads into the mucin solution Before diffusion parameters are estimated using fARMAs, first all beads are passed through a series of filters; the most notable of which is the proximity filter which ensures that the only forces acting on the bead are from the medium itself and not from other beads in proximity. A full analysis of the data and details on the pre-filtering is provided in the All datasets are visually divided into three clusters: water-like or outside flakes, within flakes but entangled in the noise floor, and flake-like with recoverable signal. The designation of tracked beads are indistinguishable from the “noise floor” is based on a stuck bead analysis provided in the loor. In , this clWe draw further consequences from the comparison of 1 μm and 200 nm diameter probes in all three samples.The results support several flake structure properties: (i) flake encounters of 200 nm beads almost always lead to entry, implying a high percentage of pores at the boundary of flakes is above 200 nm; (ii) flake encounters of 1 μm diameter beads have a high (~74%) failure rate of entry, even though each freely diffusing bead likely has many flake encounters. Assuming purely steric interactions, this data suggests a maximum 26% of boundary pores of flakes are above 1 μm, and a minimum 74% of boundary pores of flakes are below 1 μm, with a very low % of boundary pores below 200 nm. A series of steps is required to do better than these crude estimates of pore-size distributions. If: (i) the interactions of beads with mucus are purely steric; (ii) the volume % of flakes versus dilute solution is known; (iii) the relative sub-diffusive bead mobilities within flakes and dilute solution can be transformed to flake encounter frequencies; and (iv) the pore-size distributions at the boundary of flakes is known; then it would be possible to estimate the quasi-stationary percentages of 200 nm and 1 μm diameter beads in flakes and solvent. An interesting open challenge is: given the experimental data on percentages of 200 nm, 500 nm, 1 μm diameter beads in flakes and solvent, infer the pore-size distributions across the entire sample. This inverse problem is solvable for normally diffusive probes, cf. [~ 74% of 1 μm diameter beads exhibit water-like signals versus ~ 5% of 200 nm diameter beads (0/23 in the 60 and 90 samples and 2/21 in the 80 sample). These statistics of entry into flakes far outweigh, based on normal diffusion, the 5:1 expected flake encounter frequency of 200 nm vs. 1 μm diameter beads.  bes, cf. , but not200 nm data across the three different samples suggests a non-monotone pore structure transition from the 60 to 80 to 90 samples: in the 60 sample, 10/14 beads enter flakes and become trapped with SNR buried in the noise floor; in the 80 sample, 0 beads enter a flake and become trapped with SNR in the noise floor; in the 90 sample, all 9 beads enter and become trapped with SNR indistinguishable from the noise floor. The total within-flake data gives further insights into internal flake pore morphology. The bead data for 60, 80 samples are consistent with a broad pore size distribution so that beads randomly sample outside and within flakes, with some within-flake beads in pores larger than 1 μm and others entering and being trapped in pores slightly larger than a micron, the latter reflected by beads in the noise floor. The 1 μm, 90 sample dataset is smaller, yet suggestive that the pore-size distribution is broader with many multi-micron pores, so that beads freely enter and escape flakes. This would be consistent with a less dense flake formation at the smallest, 10%, Calu3 MUC5AC consistent with early CF progression.The 1 μm Use of tan We now proceed to two-parameter clustering and estimates of dynamic moduli, focusing on within-flake beads at 200 nm and 1 μm diameter scales and tracking data distinguishable from the noise floor.clustering results obtained from mclust for beads above the noise floorand with a flake-like signal for each of the two-dimensional classifiers: (i) The top panel of The experiments with mclust has selected a constrained variance matrix, which is typically not invariant to the linear transformation between Overall, the two classifiers, mclust picks more than two clusters for all four experiments. However, the mclust mixture-normal clustering approach struggles with non-elliptical clusters. That is, each of the mclust clusters can be identified with an ellipse, and the data points belonging to it are those for which the “natural” distance to the ellipse centroid -- i.e., along its principal axes and inversely proportional to the length of these axes -- is smaller than for any other cluster’s ellipse. This is why, e.g., the results with mclust separates them between top and bottom, because the small elliptical cluster at the top and large elliptical cluster at the bottom resulted in the smallest within-ellipse natural distance between data points and ellipse centroids.The BIC-based selection of the number of clusters employed by mclust typically selects more than two clusters, i.e., preferring to split highly non-elliptical clusters into several more elliptical ones. That being said, clusters corresponding to perfectly homogeneous particles according to the setup in the The extent to which the visual clusters are not elliptical also explains why Taking all visual and algorithmic clustering results into account, we select a single clustering per experiment from the two panels of It should be noted that while In order to assess within-cluster homogeneity, values are extremely small, so that Cochran’s Q test strongly rejects cluster homogeneity. The lack of homogeneity is expected for flake-like clusters as the data comes from different flakes, each with pore structures arising from the stochastic phase separation process of flake formation. Furthermore, only one water-like / outside-flake cluster passes a homogeneity test, and this is a weak conclusion since it is based on three beads. The outside-flake heterogeneity is also consistent with the stochastic dilution outside of phase-separated flakes, creating dilute phases that vary with relative proximity to flakes and degrees of dilution, with signals ranging from pure water-like to varying mucin concentrations.All but five data-analysis protocol: (1) for each batch sample, separately for sub-samples with 200 nm and 1 μm beads, use coarse clustering on the average the dynamic moduli from all beads within each cluster; (5) assess cluster to cluster heterogeneity at the coarse scale of the within and outside flake ensembles, and then at the finer scale of clusters within flakes and outside flakes. We refer to this data-analysis protocol for heterogeneous clusters as GSER Average. These steps yield the within-flake and outside-flake dynamic moduli as revealed by 200 nm and 1 μm diameter probes, for each of the 3 reconstituted HBE samples, in This determination of heterogeneity, both between and within the coarse within-flake and outside-flake bead signals, strongly supports the following there is a potential for within-flake and outside-flake sol-gel frequency transitions. Due to evidence of heterogeneity in each cluster, we also display the mean ± two standard deviations of The storage and loss moduli for each cluster reported in We find that for the 1μm 60% HBE sample, one within-flake cluster reflects a sol rheology and the other a gel rheology over all frequencies. The 200 nm 60% sample has clusters at the transition between gel-like and sol-like; one “cluster” contains a single bead and thus there are no intervals around the moduli curves. These results comport with the stochastic phase separation process that produces flakes.The 1μm 80% HBE sample shows two clusters with a sol rheology, one with a gel rheology, and once again hovering around the transition. However, unlike the previously discussed sample, the cluster at the gel-sol boundary reflects a slight sol-gel transition as frequency increases. This cluster is the only one to reflect a sol-gel transition. If one averages over the entire within-flake bead ensemble, again averaging in frequency space as the only justifiable average, An important result of the justifiable GSER Average method is evidence of a sol-gel transition from the ensemble of probes within flakes. While one can focus on details revealed in Experiments and statistical methods are developed and applied to analyze particle-tracking data from reconstituted airway mucus samples that replicate changes in the MUC5B/MUC5AC ratio characteristic of CF progression. This task of particle tracking to infer equilibrium rheological properties is challenging in highly heterogenous soft materials in general, and more so with flake-burdened CF mucus where within-flake and outside-flake domains are a result of a poorly understood, stochastic, phase-separation process. In our analysis, three levels of heterogeneity are identified and characterized from the tracked bead data: (1) a coarse scale, binary separation of dense, phase-separated, mucus flakes and dilute solution of remaining mucins; (2) within flakes, a binary separation of dense domains where bead signals can versus cannot be confidently disentangled from the experimental noise floor; and (3) in light of failed tests for sample homogeneity based on tracked beads within and outside of flakes, cluster analysis is applied to the ensembles of 200 nm and 1 μm diameter beads both within and outside flakes.For each tracked bead, we develop a two-parameter classifier metricof the denoised entire experimental time series. This fractional Brownian motion (fBm) classifier of the pure medium-induced signal for each tracked bead has been shown to be a robust statistical metric for passive particle tracking in HBE mucus (cf. [cus (cf. –12,14–16predictor step is based on a least-squares fit to the mean-squared-displacement of fBm, corrector step using the fARMAs method initially developed in [The fBm classifier metric involves two steps, each utilizing the full bead time series. The first loped in  and exteloped in . This prWe next apply cluster analysis to assess heterogeneity in each of the three reconstituted samples of flake-burdened mucus reflected by each bead diameter. While the power law an exact power-law formula for the complex modulus, This results in a non-power law rheology both for each cluster within both flakes and for the remaining dilute solvent. The within-flake data with both 200 nm and 1 μm diameter beads in samples from the same reconstituted batch also reveals probe size-dependent heterogeneity. Finally, we use the relative number of 200 nm vs. 1 μm diameter beads that enter and reside in flakes to roughly estimate flake pore size distributions to reside predominantly between 200 nm and 1 μm, with some percentage of pores above 1 μm. Further experiments and analysis are necessary to more quantitatively estimate pore-size distributions.The fBm classifier 1