Multivariable flexible modelling for estimating complete, smoothed life tables for sub-national populations

Background: The methods currently available to estimate age-and sex-specific mortality rates for sub-populations are subject to a number of important limitations. We propose two alternative multivariable approaches: a relational model and a Poisson model both using restricted cubic splines. Methods: We evaluated a flexible Poisson and flexible relational model against the Elandt-Johnson approach in a simulation study using 100 random samples of population and death counts, with different sampling proportions and data arrangements. Estimated rates were compared to the original mortality rates using goodness-of-fit measures and life expectancy. We further investigated an approach for determining optimal knot locations in the Poisson model. Results: The flexible Poisson model outperformed the flexible relational and Elandt-Johnson methods with the smallest sample of data (1%). With the largest sample of data (20%), the flexible Poisson and flexible relational models performed comparably, though the flexible Poisson model displayed a slight advantage. Both approaches tended to underestimate infant mortality and thereby overestimate life expectancy at birth. The flexible Poisson model performed much better at young ages when knots were fixed a priori. For ages 30 and above, results were similar to the model with no fixed knots. Conclusions: The flexible Poisson model is recommended because it derives robust and unbiased estimates for sub-populations without making strong assumptions about age-specific mortality profiles. Fixing knots a priori in the final model greatly improves fit at the young ages.