Do current maternal health staffing and bed occupancy benchmarks work in practice? Results from a simulation model

Model description

We use a stochastic, individual-based model to simulate all women entering and leaving delivery rooms and maternity wards over a period of 1 year (see online supplemental appendix 1 figure S1 for schematic diagram). The number of women modelled depends on the scenario (for the WHO benchmark scenario, it is the WHO estimate of numbers of births in a year in a ‘typical district’; for the Zanzibar scenario, it is informed by the data). Each delivery is modelled individually as a stochastic event. Multiple births are counted as one delivery event. The date and time of presentation of each woman delivering at a facility are assigned at random. The woman stays in the delivery room of the facility for an assigned duration before moving to the maternity ward after delivering her baby. After a second assigned duration, each woman leaves the maternity ward and is discharged from the facility. We assume that all women deliver in facilities and that there is no provision for referral between facilities which is representative for many resource-poor settings where referral between facilities can be difficult.

Online supplemental appendix S1 summarises all model inputs; 15% of deliveries are defined as complicated,2 7 assigned at random. Length of stay (LOS) in the delivery room is determined by complication status. Only limited data on the LOS in delivery rooms in resource-poor settings in sub-Saharan Africa are available. We fitted a gamma distribution to data on LOS in delivery rooms from Nigeria8 (see online supplemental appendix 1 for details), then censored to be a minimum of 2 hours. LOS in the maternity ward is also determined by complication status, and the distribution of LOS in the maternity ward has been found to be highly skewed.9 The LOS in the maternity ward for each woman is drawn randomly from a gamma distribution fitted to DHS data from sub-Saharan Africa9 (WHO benchmark analysis) or The United Republic of Tanzania (hereafter referred to as Tanzania) (Zanzibar case study).10 As women are not discharged from maternity wards at night, all discharge times falling between 8 pm and 8 am are delayed until 8 am the following morning.

The model outputs the number of women in delivery rooms and maternity wards of each facility at set time points. For each scenario and each facility, the number of women in the delivery rooms of the facility at 4 am, 12 pm and 6 pm each day is determined from the time when each woman enters the delivery room and her assigned LOS. The 4 am, 12 pm and 6 pm snapshots represent points in time mid-shift for SBAs in the EmOC facilities (shifts in Zanzibar start at 6 am, 2 pm and 8/9 pm), including one snapshot during the long, overnight shift. After delivery, each woman is transferred to the maternity ward for recovery. Maternity ward occupancy is assimilated in the same way as delivery room occupancy, with number of women in the maternity ward of each facility calculated each day at 4 am, 12 pm and 6 pm. We generated hourly snapshots of delivery room occupancy by comparing occupancy levels (number of women in delivery and maternity wards) with the number of beds available, to calculate the per cent of time when the capacity of each ward in each facility is exceeded. Similarly, we calculated the per cent of time when there are more women than SBAs in the delivery room so that one-to-one care, as recommended in many high-income countries,11 12 is not possible. We also calculated the per cent of time when delivery rooms in each facility are empty and the number of births per SBA per year in each facility. In order to assess the impact of stochasticity, we repeated each of the analyses described above 1000 times.

The model was implemented and simulations were run in R V.4.0.3.13 Model and analysis code are available at: https://github.com/kl3mn9/maternity-model.git.

WHO benchmark analysis

The model represents the assumptions made by the WHO benchmarks2 for a typical sub-Saharan African district with around 120 000 inhabitants; assuming a birth rate of 30 per 1000 inhabitants, there are 3600 mothers giving birth per year (box 1). Each of the 3600 pregnant women in the model is assigned a health facility for delivery.

We consider the following two scenarios for size and distribution of maternity facilities in such a district:

Scenario A: one CEmOC facility staffed by 10 SBAs and two BemOC facilities each staffed by five SBAs.

Scenario B: one CEmOC facility staffed by 10 SBAs and five BEmOC facilities staffed by two SBAs each.

These scenarios broadly represent recommendations in the WHO 2005 report (see box 1).2 Data from sub-Saharan Africa suggest that women prefer to give birth in CEmOC facilities and that in resource-poor settings, it can be difficult to predict complications during birth.14 Therefore, we assume that the probability of births happening in CEmOCs is 50% regardless of complication status. The remaining births happen in BEmOCs with equal probabilities for each BEmoC facility.

For scenario B, where each BEmOC is only staffed by two SBAs (ie, only two shifts per day can be covered), we calculated how many women on average present at night when the delivery room is unstaffed. We assume that delivery rooms are staffed 06.00–14.00 (first 8 hour shift) and 14.00–22.00 (second 8 hour shift).

In this analysis, we chose to focus on delivery room occupancy rather than maternity ward occupancy because of the acute needs of women while in the delivery room, where understaffing and overoccupancy are likely to have the most important consequences.

WHO benchmark analysis with seasonality

To investigate the potential impact of birth seasonality on utilisation and risk of exceeding capacity of EmOC facilities, we repeated the WHO benchmark analysis for a hypothetical setting with marked birth seasonality. We weighted the probability of a birth happening in a given month. Weights were derived from data on birth seasonality in Sierra Leone, the country with the greatest amplitude of birth seasonality presented in a study by Dorélien.3 We extracted data on the average monthly amplitude in births for Sierra Leone from figure 4B in online supplemental appendix B of Dorélien3 using Datathief.15 We estimated the probability of giving birth during each month of the year by dividing each monthly birth rate from the data by the total annual birth rate. The date and time of presentation of each woman delivering at a facility were assigned at random, weighted by the probability of giving birth in a given month. We calculated the percentage of time during which the delivery room is empty for the busiest month (January in the Sierra Leone data) and the least busy month (November in the Sierra Leone data).

Zanzibar analysis

We used data on births and Caesarean sections per facility, number of beds and staffing levels at am and pm times from 37 EmOC facilities in Zanzibar for a representative month in 2014 (data have been collected by the Pemba Public Health Laboratory and can be made available on request). Staffing levels included information on SBAs only, not on medical doctors or nurses. Data on facilities were collected during an assessment across maternity units in Zanzibar, commissioned by the MoH in 2013 to inform a quality improvement process for maternity wards (further details on methodology and findings are reported elsewhere13). Seven of the facilities carried out Caesarean sections in 2014. We assumed that these facilities were CEmOCs, while all other facilities were BEmOCs. Two of the 37 facilities did not report any births in 2014 and were excluded from the analysis. Births requiring a Caesarean section were classified as complicated, while all other births were assumed to be uncomplicated. In total, 2943 births were recorded in EmOC facilities in Zanzibar over this average month. In 2013, the year of the facility survey, 48 763 births were reported in Zanzibar.16

Similar to the WHO benchmark analysis, we assigned each woman a time for presentation in a maternity facility and a complicated or uncomplicated birth at random. The proportion of births ending in Caesarean sections reported in the Zanzibar data set was 11.9% which is close to the 15% complicated births assumed in the World Health Report.2 To account for complicated births other than Caesarean sections, we assume a probability of 15% for a birth to be complicated. We assume that the number of births reported for each facility in the data set over a month are representative. Consequently, the probability of a woman presenting at each facility depends on the monthly births reported for this facility. However, we assumed that women with complicated births only give birth at one of the facilities identified as CEmOCs, because complicated births were not reported in other facilities.

The LOS in the delivery room for each woman is drawn from the same gamma distribution as for the WHO benchmark scenario. The LOS in the maternity ward for each woman is drawn from a gamma distribution fitted to data from the DHS for Zanzibar.10

Zanzibar analysis with seasonality

We extracted data on the number of births by month in Zanzibar from the 2015–2016 District Health Survey for Tanzania. We obtained probability weights for giving birth in a specified month by dividing the number of births reported in each month by the total annual number of births. In the simulation, we randomly assigned a date and time of presentation of each pregnant woman at a facility weighted by the probability of giving birth in each month. We calculated the percentage of time during which the delivery room is empty for the busiest month (June in Zanzibar) and the least busy month (January in Zanzibar). We also calculated the percentage of time during which the capacity of each facility is exceeded in terms of beds and staffing. We assumed that each SBA should look after only one woman in labour at once, as recommended in the UK,17 Australia18 and New Zealand,19 and under discussion in Germany.20 21

Patient and public involvement

Patients and the general public were not involved in data collection or analysis of this study.

WHO benchmark analysis

Figure 1A,B show the number of women in the delivery room in each facility in a single model run of the stochastic simulation for both scenarios of the WHO benchmark analysis. This model run has been selected at random and highlights the stochastic variation in chance events. SBAs working in the small BEmOC facilities in scenario B only see a few complicated births over a month. If women can feasibly travel to a CEmOC rather than a BEmOC (as may be the case in more densely populated areas where facilities are close to one another), then midwives in the BEmOC facilities may well see very few complicated cases and start to lose their skills to recognise signs for high-risk conditions. Online supplemental appendix 2 figures S3A,B show the number of women in postpartum beds over a month, for the same scenarios. Note that the proportion of women who have experienced complicated births is larger in postpartum beds because their expected LOS is longer.

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Figure 2A,B show the summary results from running the stochastic simulation 1000 times to understand the general behaviour of the model. The simulation samples reflected our model inputs well. Across the 1000 simulations generated, the mean and median proportion of deliveries that were complicated were both 15.0% and for duration in the delivery room, the mean of the means for 3600 births across 1000 iterations was 4.48 hours and the median of the medians of 3600 births across 1000 iterations was 3.92 hours, in close agreement with our inputs for these parameters, shown in online supplemental appendix 1 table S1.

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Figure 2A,B show the percentage of time over a year in which delivery rooms in different facilities are empty for the two WHO benchmark scenarios. For both scenarios, CEmOCs are busier than BEmOCs; they are empty a mean 40.1% of the time (median 40.1%, 95% credible interval (95% CrI) 38.5%–41.6% for scenario A, 38.4%–41.7% for scenario B), while BEmOCs are empty a mean 63.3% of the time (median 63.3%, 95%CrI 61.5%–65.1%) for scenario A (two BEmOCs), and 83.3% of the time (median 83.8%, 95%CrI 81.8%–84.9%) for scenario B (four BEmOCs). Maintaining a larger number of smaller BEmOCs (scenario B) therefore increases the percentage of time in which delivery rooms in BEmOCs are empty relative to a scenario with fewer and larger BEmOCs. Although smaller BEmOCs are empty more frequently in the simulated scenarios, individual SBAs in these BEmOCs see the same number of deliveries per year as SBAs in larger CEmOCs because the staffing ratio in smaller facilities is lower (online supplemental appendix 2 figures S4A,B). This is because we assume that the probability for a pregnant woman to give birth at a CEmOC or in any of the BEmOC facilities is 50%. Under the simulated conditions, SBAs in both CEmOCs and BEmOCs see approximately 175 deliveries per year, the number recommended by WHO.2

On average, 1176 pregnant women enter labour at night (SD 28.65) for a ‘typical’ district over 1 year. This is roughly a third of total births which is intuitive if time of day of birth is random and there are three daily shifts. Out of these 1176 births on average 112 (SD 10.58) can be expected to be complicated. In scenario B, BEmOCs would not be staffed at night. Therefore, women entering labour at night would have to attend the CEmOC facility which would increase delivery room occupancy at night and in the early morning.

WHO benchmark analysis with seasonality

Over a year, the average results for the WHO benchmark analysis with seasonality do not differ from the analysis in which seasonality is ignored (online supplemental appendix 2 figures S4C,D and S5). However, there are noticeable differences between the busiest (January) and least busy month (November) (figure 2C–F). In November, delivery rooms are empty most of the time. Small BEmOCs in scenario B are empty 95% of the time (figure 2F). In contrast, in January delivery rooms in scenario A are busy most of the time (figure 2C). In scenario B, with more smaller BEmOC facilities, delivery rooms are still empty at least 50% of the time (figure 2D,F).

Zanzibar analysis

Figure 3 shows the number of women in delivery rooms in 35 EmOC facilities in Zanzibar in 8 hour snapshots over 1 month, estimated using our model, calibrated using empirical data on number of deliveries over a representative month in all facilities on the island. The same stochasticity is observed in this real-world scenario as in the generic WHO benchmark analysis. However, the differences in the numbers of women attending different facilities are more striking. The majority of facilities are small and rarely see more than one woman in the delivery room at a time, whereas in the largest facility (facility 1) at times, there are more than 10 women in the delivery room at once. A similar pattern can be observed for postpartum bed occupancy (online supplemental appendix 2 figure S6). However, in CEmOCs women who have experienced complicated births are over-represented, occupying more than half of postpartum beds, because their average LOS is longer.

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Delivery room capacity in terms of beds is rarely exceeded and if so, then only in smaller CEmOCs and BEmOCs (figure 4A, online supplemental appendix 2 figure S7A). However, these rare events are important because they can lead to a deterioration of quality of care for affected women. Figure 4B shows that BEmOCs are empty most of the time. Smaller BEmOCs are empty more than 80% of the time (online supplemental appendix 2 figure S7B). The larger a CEmOC facility is (ie, the larger the mean number of women attending a facility within a month), the less likely it is that the delivery room is unoccupied. The largest CEmOC facility is almost never empty (facility 1, online supplemental appendix 2 figure S7B). The ratio of women in labour to SBAs is exceeded on average 25% of the time in CEmOCs (figure 4C), ranging from 5% to 56% of the time in individual facilities (online supplemental appendix 2 figure S7C). Staff capacity in BEmOCs is exceeded less than 5% of the time on average, but can be exceeded up to 20% of the time in some BEmOCs (online supplemental appendix 2 figure S7C).

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As figure 4D shows, SBAs working in busy CEmOCs on average attend more than the 175 births per year in Zanzibar, in some facilities three times that number (online supplemental appendix 2 figure S8). This means that the overall workload on SBAs in these facilities may be excessive. Conversely, SBAs in small BEmOCs on average attend considerably fewer than 175 births per year. This means that in the least frequented facilities SBAs may not see enough births per year to maintain adequate training.

Zanzibar analysis with seasonality

Similar to the WHO benchmark analysis, the average results over a year do not change significantly if birth seasonality is considered in the Zanzibar analysis (online supplemental appendix 2 figure S9). However, there are important differences in delivery room occupancy between the busiest month (June) and the least busy month (January) (figure 5, online supplemental appendix 2 figures S10,11). While delivery room capacity in terms of beds is rarely exceeded in either January or June, the risk of staff capacity being exceeded in June is double the risk in January. In particular, CEmOC facilities 1 and 7 have on average a greater than 50% risk of exceeding staff capacity in June (online supplemental appendix 2 figure S11C), and CEmOC facility 2 has an average risk of 10% of exceeding bed capacity in June (online supplemental appendix 2 figure S11A). A few BEmoCs (facilities 21, 24, 27) have a greater than 5% risk of exceeding staff capacity in both January and June despite being empty most of the time (online supplemental appendix 2 figures S10B,C and S11B,C).

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Conclusion

Our simulation analysis shows that considering maternal health benchmarks based on average estimates of women presenting at obstetric care facilities may be insufficient to provide adequate standard of care during peak times, when crowding in the delivery room occurs. Crowding or lumping is an intrinsic feature of systems with random events (births) and waiting times (time in the delivery room). Stochastic individual-based models capture important features of these systems and, combined with additional contextual information, can be used to optimise obstetric care provisions, for example, to support decisions on maintaining/closing or upgrading individual facilities, required resourcing and staffing.