Predicting resource-dependent maternal health outcomes at a referral hospital in Zanzibar using patient trajectories and mathematical modeling

Abstract

Poor intra-facility maternity care is a major contributor to maternal mortality in low- and middle-income countries. Close to 830 women die each day due to preventable maternal complications, partly due to the increasing number of women giving birth in health facilities that are not adequately resourced to manage growing patient populations. Barriers to adequate care during the 'last mile' of healthcare delivery are attributable to deficiencies at multiple levels: education, staff, medication, facilities, and delays in receiving care. Moreover, the scope and multi-scale interdependence of these factors make individual contributions of each challenging to analyze, particularly in settings where basic data registration is often lacking. To address this need, we have designed and implemented a novel systems-level and dynamic mathematical model that simulates the impact of hospital resource allocations on maternal mortality rates at Mnazi Mmoja Hospital (MMH), a referral hospital in Zanzibar, Tanzania. The purpose of this model is to provide a rigorous and flexible tool that enables hospital administrators and public health officials to quantitatively analyze the impact of resource constraints on patient outcomes within the maternity ward, and prioritize key areas for further human or capital investment. Currently, no such tool exists to assist administrators and policy makers with effective resource allocation and planning. This paper describes the structure and construct of the model, provides validation of the assumptions made with anonymized patient data and discusses the predictive capacity of our model. Application of the model to specific resource allocations, maternal treatment plans, and hospital loads at MMH indicates through quantitative results that medicine stocking schedules and staff allocations are key areas that can be addressed to reduce mortality by up to 5-fold. With data-driven evidence provided by the model, hospital staff, administration, and the local ministries of health can enact policy changes and implement targeted interventions to improve maternal health outcomes at MMH. While our model is able to determine specific gaps in resources and health care delivery specifically at MMH, the model should be viewed as an additional tool that may be used by other facilities seeking to analyze and improve maternal health outcomes in resource constrained environments.

Fig 1. Schematic of the first step in the algorithm—the creation and admission of a new patient (blue) to the simulated ward with a high probability of mortality (red), a moderate probability of mortality (orange and yellow), or low probability of mortality (green).

Fig 2. Schematic of the second step of the algorithm—allocation of resources to patients as prescribed by their respective treatment plans, starting with the patients with the highest probability of mortality (red) and ending with patients with the lowest probability of mortality (green).

Fig 3. Schematic of the third step in the algorithm—the probabilities of mortality for patients who were treated will decrease as per the efficacy of their assigned treatment plans, while the probabilities of mortality for patients that did not get treated due to insufficient resources will increase based on the deterioration rates of their respective complications (if any).

Fig 4. Schematic of the fourth and final step in the algorithm, before the four steps are repeated for the next fifteen minute cycle—medications are restocked if necessary, and any doctors or nurses that were treating patients in the current cycle but are not required for treatment in the next cycle are returned to the staff pool to be re-allocated in the following cycle.

Fig 5. Comparison of case fatality rates for each complication outputted by the calibrated model and case fatality rates recorded by Herklots et al for the five complications incorporated in the model.

Box plots represent distribution of data over n = 50 identical simulations. Outliers have been omitted from the box plots for clarity. Predicted case fatality rate is depicted as the mean of each data set, inclusive of outliers.

Fig 6. Comparison of complication incidence rates outputted by the calibrated model and complication incidence rates recorded by Herklots et al for the five complications incorporated in the model.

Box plots represent distribution of data over n = 50 identical simulations. Outliers have been omitted from the box plots for clarity. Predicted case fatality rate is depicted as the mean of each data set, inclusive of outliers.

Fig 7. Impact of oxytocin inventory and supply frequency on maternal deaths over a 3 month period.

Box plots exclude outliers and whiskers reflect local maxima and minima among n = 50 runs for each data point. Line plots reflect mean values for each data point, including outliers.

Fig 8. Impact of hydralazine inventory and supply frequency on maternal deaths over a 3-month period.

Box plots exclude outliers and whiskers reflect local maxima and minima among n = 50 runs for each data point. Line plots reflect mean values for each data point, including outliers.

Fig 9. Predicted effect of staffing combinations for nurses and doctors when staffed consistently across morning, evening, and night shifts.

Data depicts mean maternal deaths for each staff combination over n = 50 identical simulations of over a simulated timeframe of 3 months with 20,000 IU of oxytocin and 2200 mg/mL of hydralazine being supplied each month.

Fig 10. Effect of different staffing distributions during the morning, evening, and night on maternal mortality.

Inset depicts zoomed version of shift patterns excluding the 1 fewer doctor and nurse condition. All data sets were found to be statistically significant from one another, except for the current staff distribution compared to the 5 nurses for all shifts, with p < 0.05 using a two-tailed test.

Fig 11. Predicted effect of patient influx rate on mortality rates for patients with complications.