  Several demographic and health indicators, including the total fertility rate
(TFR) and modern contraceptive use rate (mCPR), evolve similarly over time,
characterized by a transition between stable states. Existing approaches for
estimation or projection of transitions in multiple populations have
successfully used parametric functions to capture the relation between the rate
of change of an indicator and its level. However, incorrect parametric forms
may result in bias or incorrect coverage in long-term projections. We propose a
new class of models to capture demographic transitions in multiple populations.
Our proposal, the B-spline Transition Model (BTM), models the relationship
between the rate of change of an indicator and its level using B-splines,
allowing for data-adaptive estimation of transition functions. Bayesian
hierarchical models are used to share information on the transition function
between populations. We apply the BTM to estimate and project country-level TFR
and mCPR and compare the results against those from extant parametric models.
For TFR, BTM projections have generally lower error than the comparison model.
For mCPR, while results are comparable between BTM and a parametric approach,
the B-spline model generally improves out-of-sample predictions. The case
studies suggest that the BTM may be considered for demographic applications
