Markov-Switching Regime Dynamics of Maternal Mortality in Kenya: A State-Dependent Analysis of Health System Transitions with Bootstrap Uncertainty Quantification (2000-2023

Abstract Background: Maternal mortality is still a significant issue affecting public health in Kenya today. Typically, traditional statistical methods make the assumption of constancy across thedata, and this assumption could mask some critical events in the health outcome. Methods: Annual maternal mortality rate (MMR) from 2000 to 2023 in Kenya was used to conduct this study, fitting the two-state Markov switching model. In this method, the MMR does not predefine which state it belongs to and instead uses an optimal criterion that identifies high and low maternal mortality rates based on the data. In each state, there are regime-specific mean MMR and variance with regimes switching based on the hidden Markov processes. The estimates of the model are obtained using the maximum likelihood estimation with Hamiltonfilter and EM algorithm. To deal with the small sample size (T = 24), a parametric bootstrap method was employed, resampling 500 times. Results: Two regimes are detected with this method. High regime (mean = 488.7, 95% CI [431.6,497.5]) dominated between 2007 and 2014, and low regime (mean = 428.2, 95% CI [410.1, 468.3])occurred before 2007 and after 2015. Both regimes have a very high persistence rate, with a 87.5% probability for the high regime and 93.3% probability for the low regime, resulting in expected duration of 8 years and 15 years, respectively. Bootstrap results also confirm accurate mean estimates in each regime, while there is considerable uncertainty regarding transition probability(95% CI [0.300, 0.950]). Note that there is a relatively small number of transitions between regimes (only two). On the other hand, since 2015, Kenya keeps more than 95% probability forlow regime, even through the COVID-19 period. Conclusion: Maternal mortality in Kenya has been an unpredictable path rather than a continuous straight line, as its movements between high and low regimes seem to reflect structural changes within the health care system. The insights generated by the application of the Markov switching model are crucial for understanding regime shifts, their lengths, and their certainty, which is not possible using traditional approaches.