Analyzing maternal mortality rate in rural China by Grey-Markov model.

Maternal mortality rate (MMR) in China has reduced during a decade but still higher than many countries around the world. Rural China is the key region which affects over all maternal death. This study aims to develop a suitable model in forecasting rural MMR and offer some suggestions for rural MMR intervention. Data in this study were collected through the Health Statistical Yearbook (2017) which included the overall MMR in China and urban and rural mortality rate. A basic grey model (GM(1,1)), 3 metabolic grey models (MGM), and a hybrid GM(1,1)-Markov model were presented to estimate rural MMR tendency. Average relative error (ARE), the post-test ratio (C), and small error probability (P) were adopted to evaluate models' fitting performance while forecasting effectiveness was compared by relative error.The MMR in rural China reduced obviously from 63.0 per 100,000 live births in 2005 to 21.1 per 100,000 live births in 2017. One basic GM(1,1) model was built to fit the rural MMR and the expression was X^((1)) (k + 1) = 553.80e^0.0947k - 550.00 (C = 0.0456, P > .99). Three MGM models expressions were X^((1)) (k + 1)  = 548.67e^0.0923k - 503.17 (C = 0.0540, P > .99), X^((1)) (k + 1) = 449.39e^0.0887k - 408.09 (C = 0.0560, P > .99), X^((1)) (k + 1) = 461.33e^0.0893k - 425.23(C = 0.0660, P > .99). Hybrid GM(1,1)-Markov model showed the best fitting performance (C = 0.0804, P > .99). The relative errors of basic GM(1,1) model and hybrid model in fitting part were 2.42% and 2.03%, respectively, while 5.35% and 2.08%, respectively, in forecasting part. The average relative errors of MGM were 2.07% in fitting part and 17.37% in forecasting part.Data update was crucial in maintain model's effectiveness. The hybrid GM(1,1)-Markov model was better than basic GM(1,1) model in rural MMR prediction. It could be considered as a decision-making tool in rural MMR intervention.