Modeling patient access to therapeutic oxytocin in Zanzibar, Tanzania

Zanzibar is an East African archipelago composed of two major islands - Unguja and Pemba. Zanzibar’s health system presents a unique opportunity for development of this model due to its relatively small size, availability of data on the drug delivery system, Geographic Information System (GIS) data, and well-understood gaps in access to quality maternal health care [17‐20]. Data for our study was collected from site visits in 2015 and 2016, and documented reports from the Zanzibar Central Medical Store (CMS) regarding oxytocin procurement, and delivery [12, 13, 17, 19, 20]. From this data, temperature logs were incorporated into a decay function to predict natural oxytocin decay. CMS procurement records were used to model the frequency and cost of drug delivery, and to understand stock-outs and patterns in distribution. A systematic literature review was conducted to examine the supply chain structure of similar healthcare systems, and identify factors affecting access to care in sub-Saharan Africa [14, 16, 21‐29].

The collected data was used to develop a conceptual framework (Fig. 1), which was converted into a computational model and analyzed using MATLAB (Mathworks, Inc., Needham, MA). The model incorporates both the supply and demand pathways in oxytocin access: the availability of quality oxytocin, and patient access to it (Fig. 1). Availability describes oxytocin’s journey through the supply chain, from arrival in Zanzibar to distribution to health facilities. Access represents the likelihood a woman will choose to deliver at a health facility. A weekly access ratio is determined. The ‘weekly access ratio’ is defined as the number of oxytocin doses available each week compared to the demand for oxytocin that it must serve for all remaining weeks until the next shipment arrives. User inputs to the model include number of annual births, temperature of oxytocin storage, annual oxytocin supply, and frequency of oxytocin delivery. Annual births and oxytocin supply can be input at a national level, or for a desired catchment area around an Emergency Obstetric and Newborn Care facility (EmONC).

Patient access depends on factors that determine the likelihood a pregnant woman will deliver at birthing facility. Variable selection is based on factors found in the literature that have the most influence on patient access [15].

Tsawe et al. estimate that variables that seem to have a greatest impact on a woman’s access to a birthing facility are distance to the nearest facility, literacy status of the woman, and socioeconomic status of the woman and her family [15]. To quantitatively represent the relationships between these variables, a weighted probability was derived from odds ratios (ORs) of factors influencing maternal health outcomes in Sub-Saharan Africa. The richest wealth quintile was associated with an OR of 2.55, literacy with an OR of 1.99, and rural residence with an OR of 0.82 [15].

The input number of annual births is used to approximate the number of weekly births at the national or facility level. This in turn is used as a measure of the number of women in need of oxytocin each week within a defined region of interest. The model then estimates the proportion of these women that would seek delivery at a health facility. The total national or facility level demand for oxytocin is determined by assuming that each woman receives one dose of prophylactic oxytocin, and that 2% of all women will develop postpartum hemorrhage, requiring four additional doses, as per the standard practice in Zanzibar.

The total weekly demand is used to track oxytocin consumption upon arrival at the health care facility each week. The model assumes there are no delays in arrival of oxytocin shipments to Zanzibar from the manufacturer, nor are there breaks in cold chain storage during shipment to CMS. This assumption is consistent with the records at the Central Medical Stores in Zanzibar, though the limitations of this assumption are discussed in a later section. The model also assumes that demand for oxytocin remains the same each week. It then determines the total number of remaining oxytocin doses each week based on the total supply, frequency of supply, the total weekly demand for oxytocin, and the rate of oxytocin decay.

The model accounts for multiple shipments of a total annual supply of oxytocin. It also accounts for the depreciation of oxytocin quality over the supply chain cycle due to variations in storage temperature, which significantly impacts oxytocin decay rates [30, 31].

The decay of a given shipment of oxytocin is tracked weekly and with a rate constant described by a first-order decay for oxytocin at pH 4.5 -- pH at which the drug is most stable (Eq. 1) [27, 28]. The rate constant k_oxytocin was calculated from the Arrhenius constant A, the activation energy E_a of oxytocin at pH of 4.5, and the ideal gas constant R, each of which was determined by kinetic studies of Hawe et al. [29] The rate constant is multiplied by the concentration of oxytocin in one dose to determine the rate of decay in mg/mL/day. The rate of decay is integrated over a specified interval of time to determine the concentration of oxytocin that has decayed. The decayed concentration is subtracted from the original dose concentration to determine the concentration of viable oxytocin remaining. The viable dose strength is then calculated as percent of viable oxytocin remaining after decay over the given time interval relative to the original concentration of oxytocin in the dose.

To track the quality of available oxytocin, the model inputs temperature and length of time in storage into eq. 1 to determine the amount of viable oxytocin remaining after decay. The viable dose strength for each week is multiplied by the number of total doses in inventory to obtain the number of effective doses. For dose strengths between 50 and 85% of a full strength dose, twice as many doses per patient will be required, halving the number of viable doses remaining. Similarly, for dose strengths between 33 and 54%, three times as many total doses per patient will be required, reducing the number of viable doses by 2/3. A dose strength below 33% assumes zero effective doses meaning the remaining dose stock is not viable.

The weekly access ratio illustrates the number of effective doses available in a given week compared to the demand for oxytocin available until the next shipment arrives. A weekly access ratio of 1.0 indicates oxytocin supply is exactly meeting weekly demand. The average access ratio is the average of the weekly access ratios over 52 weeks.

The model factors in oxytocin supply shipments, population growth, temperature-dependent oxytocin degradation, and the impact of socioeconomic factors on a woman’s decision to deliver at an EmONC. These variables are used to generate an access ratio of supply (available oxytocin at facility) and demand (women delivering at health facility), allowing the comparison of various scenarios on women’s accessibility to oxytocin at facilities. The variables are shown in Table 1.

Figure 2 describes the impact of different sizes of annual oxytocin supply to Zanzibar. As per CMS records, 100,000 doses is the actual supply of oxytocin ordered each year. However, the model predicts that 26,500 doses are required for an average access ratio of 1, while 25,500 doses are required for an average access ratio of 0.85. The ratio of 0.85 is used as a benchmark to reflect the larger demand for oxytocin than supply. A peak occurs at Week 25 due to the restocking of the oxytocin inventory at the CMS every 6 months. Just prior to a shipment being received, the amount of oxytocin in stock relative to the number of patients that will need oxytocin before the next shipment is very low -- resulting in a drop in weekly access ratio.

The model estimates the number of doses reaching patients and the number that are unaccounted for can thus be translated to the cost of losing 73.5% of annual national oxytocin supply. Based on the socioeconomic factors previously described, our model predicts that, based on current wealth distribution, literacy rates, and EmONC facility distribution, approximately 50% of Zanzibari women will deliver at a facility. This corroborates with current data that shows the proportion of the female population delivering at facilities is approximately 50% [32]. With 50% of the pregnant population accessing facilities, Zanzibar would require 26,500 oxytocin doses in order to meet the demand and obtain an average access ratio of 1.0. This supply is significantly below the 100,000 doses that is currently ordered by the Ministry of Health through CMS, and still results in shortages of oxytocin at facilities in Zanzibar. Even with 100% of the pregnant population in Zanzibar accessing facilities for delivery, only 53,000 doses would be required to obtain an average access ratio of 1.0. Our model points to bottlenecks and can help to identify inefficiencies in the system that ultimately impede access to oxytocin.

Population growth in Zanzibar occurs at 3% per year, requiring an increasing annual supply of oxytocin to meet patient needs. Our model predicts oxytocin supply would have to double over a period of 30 years in order to obtain an average access ratio of 1 amid current population growth (Fig. 3a). Figure 3b shows the percentage decrease in access ration if the birth rate remains unchanged.

While high temperature contributes to quality decay, our model shows that ambient temperature appears to have a negligible effect on oxytocin dose strength until 30 °C, after which it decays rapidly at higher temperatures. Dose strength degrades to below 90% at 30 °C after one quarter, reaching 80% at 35 °C, 60% at 40 °C, and 20% at 45 °C. Figure 4 shows the impact of temperature-affected oxytocin dose strength on the access ratio, confirming that the critical temperature is approximately 30 °C, after which the access ratio decreases dramatically through reduction in dose strength. Improper storage at higher temperatures (50 °C, 45 °C, 40 °C, 30 °C) leads to quicker degradation of dose strength [30, 31], requiring more oxytocin to achieve the same therapeutic effect. Therefore, the demand for oxytocin outweighs the supply in the latter weeks of a shipment cycle before the next shipment of the drug arrives (Fig. 4). The model’s results corroborate with the WHO’s survey on the stability of oxytocin, which illustrates a negligible degradation until approximately 30 °C, after which the rate of degradation increases significantly with increased temperature [33].

Literacy is one of the most successful predictors in determining whether women will deliver at a birthing facility. The predicted proportion of women visiting a health facility to deliver increased from 41% in the case of a completely illiterate population, to 53% in the case of a completely literate population. Zanzibar’s current literacy rate is 67% which corresponds to approximately 50% of women accessing a birthing facility [9]. Figure 5 demonstrates the effects of implementing initiatives to increase literacy, family planning, or both by tracking the annual supply required if literacy increased by 2% per year or the annual birth rate decreased by 0.5% per year or both literacy increased by 2% and birth rate decreased by 0.5%. The annual oxytocin supply to accommodate increased demand due to higher literacy is demonstrated in Fig. 5, with approximately 2000 more doses per year required by 2042 as compared to no intervention.

While the model is able to capture a number of essential features of the Zanzibari health system and provide new insights into access to quality oxytocin, it has a number of limitations, and conclusions drawn are subject to model validation. When assessing oxytocin quality, the model does not account for improper packaging or storage that would expose oxytocin to light and accelerate decay and assumes that there is no loss of drug quality during the manufacturing process. Furthermore, there is no standard to measure actual dose strength of oxytocin in hospitals, so administered dosage by health workers in practice may fluctuate per patient. The model assumes the therapeutic dose of oxytocin is 10 IU. Although studies have shown comparable clinical effectiveness between doses of 5 and 10 IU, the current model assumes loss of clinical effectiveness with loss of potency [34]. When assessing the socioeconomic determinants of women seeking to deliver at a health facility, the model uses a fixed hierarchy of wealth, literacy, and travel time, and does not account for any factor increasing or decreasing in predictive value over time. Further, we have not examined how cultural beliefs play a role in a woman’s decision to deliver at a health facility. The model only considers government funded supply of oxytocin, and excludes oxytocin supplied by private donors. We assume that oxytocin from the Central Medical Store is delivered only to the six EmONC facilities in Zanzibar based on demand from each facility, and these are the only facilities included in our model as they are the only ones required to have oxytocin at all times [35]. The model assumes an equal number of doses per shipment to the CMS or EmONC within a given year, as well as equal timing between shipments in that year, and does not examine the effects of transit time of oxytocin shipments between the CMS and EmONC [3]. Because of the lack of facility-level data, this model is currently most applicable to oxytocin access at a national level.