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

Technical Summary: Markov-Switching Regime Dynamics of Maternal Mortality in Kenya (2000-2023)

Problem Statement
Maternal mortality remains a critical public health challenge in Kenya, with traditional statistical analyses often failing to capture the non-linear and structural shifts inherent in health system performance. Conventional methods, such as linear or joinpoint regressions, typically assume parameter stability within identified segments or treat change-points as deterministic events. These approaches may obscure critical dynamics, such as hidden "crisis" or "recovery" states, and fail to account for the probabilistic nature of transitions between different health system regimes. Furthermore, existing literature often assumes constant variance, ignoring the heightened volatility that may characterize periods of systemic crisis. The study addresses the gap in understanding whether Kenya's maternal mortality trajectory (MMR) exhibits distinct, persistent regimes and how these regimes transition over time, particularly in the context of political and policy shifts between 2000 and 2023.

Methodology
The study employs a two-state Markov-switching model to analyze annual MMR data for Kenya from 2000 to 2023 ($T=24$). The data, sourced from WHO/UNICEF/UNFPA/World Bank and UNPD (MMEIG) estimates, is treated as a time series where the underlying state (regime) is latent and unobserved.

• Model Specification: The authors specify a regime-switching mean model where $y_t = \mu_{s_t} + \epsilon_t$, with $\epsilon_t \sim N(0, \sigma^2_{s_t})$. The hidden state $s_t$ follows a first-order Markov chain with time-invariant transition probabilities. The model allows for regime-specific means ($\mu_j$) and variances ($\sigma^2_j$).
• Estimation: Parameters are estimated using Maximum Likelihood Estimation (MLE) via the Expectation-Maximization (EM) algorithm, incorporating the Hamilton filter to compute smoothed probabilities of regime occupancy.
• Small Sample Handling: Given the limited sample size ($T=24$), a parametric bootstrap method with 500 replications is utilized to quantify uncertainty in parameter estimates, specifically addressing the variability of transition probabilities and expected regime durations.
• Model Selection: The optimal number of regimes ($K$) is determined using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), alongside likelihood ratio tests.
• Validation: Stationarity is assessed via Augmented Dickey-Fuller (ADF) and KPSS tests, and structural breaks are examined using Chow tests. Robustness checks include residual analysis for normality, serial correlation, and heteroskedasticity.

Key Results

1. Regime Detection: The two-regime model is selected as optimal (AIC = 224.37, BIC = 231.44), significantly outperforming one- and three-regime specifications. Two distinct regimes are identified:
   • High Mortality Regime (Regime 1): Mean MMR = 488.7 (95% CI [431.6, 497.5]), Standard Deviation = 10.6. This regime dominated from 2007 to 2014.
   • Low Mortality Regime (Regime 2): Mean MMR = 428.2 (95% CI [410.1, 468.3]), Standard Deviation = 19.9. This regime prevailed from 2000–2006 and 2015–2023.
2. Regime Persistence and Transitions: The system exhibits high persistence. The probability of remaining in the high regime is 87.5%, and in the low regime is 93.3%. Consequently, the expected duration of the high regime is 8 years, while the low regime is expected to last 15 years.
   • Only two regime transitions were detected over the 24-year period: a shift from low to high in 2006–2007 and a return from high to low in 2014–2015.
   • Bootstrap results indicate high precision in estimating regime means but considerable uncertainty regarding transition probabilities (95% CI [0.300, 0.950]), attributed to the small number of observed transitions.
3. Temporal Dynamics:
   • 2000–2006: Stable low-mortality period.
   • 2007–2014: Crisis period coinciding with post-election violence and health system devolution implementation.
   • 2015–2023: Recovery period. Notably, the system maintained the low-mortality regime with >95% probability even during the COVID-19 pandemic (2020–2021), demonstrating system resilience.
4. Comparison with Traditional Models: The Markov-switching model outperforms a standard ARIMA(0,1,0) model in terms of AIC and BIC, confirming that the non-linear, state-dependent nature of the data is better captured by regime-switching dynamics.

Significance and Claims
The paper claims that maternal mortality in Kenya follows an unpredictable path characterized by structural regime shifts rather than a continuous, linear decline. The application of the Markov-switching model provides crucial insights that traditional approaches cannot offer:

• Identification of Hidden States: The model successfully distinguishes between "crisis" and "recovery" states, revealing that the health system operates under two distinct statistical realities with different means and variances.
• Policy Correlation: The identified regime transitions align temporally with major national events. The shift to the high-mortality regime coincides with the 2007–2008 post-election violence, while the transition back to the low-mortality regime aligns with the implementation of the 2010 Constitution (devolution) and the 2013 free maternity policy.
• Resilience and Sustainability: The high persistence of the low-mortality regime (expected duration of 15 years) suggests that policy interventions, once successful, can yield long-lasting stability. The system's ability to remain in the low-mortality state during the pandemic underscores its resilience.
• SDG 3.1 Implications: Despite the successful transition to a low-mortality regime, the current rate of decline within this regime is insufficient to meet the Sustainable Development Goal 3.1 target (<70 deaths per 100,000 live births) by 2030. The authors note that at the current pace, the target may not be reached until 2060, necessitating accelerated interventions.

The study concludes that while the Markov-switching approach reveals the structural breaks and persistence of Kenya's maternal mortality trends, the wide confidence intervals in transition probabilities (due to the small sample size) warrant cautious interpretation. The findings underscore the need for sustained policy efforts to maintain the low-mortality regime and accelerate progress toward global health targets.