  We consider a non-proportional hazards model where the regression coefficient
is not constant but piecewise constant. Following Andersen and Gill (1982), we
know that a knowledge of the changepoint leads to a relatively straightforward
estimation of the regression coefficients on either side of the changepoint.
Between adjacent changepoints, we place ourselves under the proportional
hazards model. We can then maximize the partial likelihood to obtain a
consistent estimation of the regression coefficients. Difficulties occur when
we want to estimate these changepoints. We obtain a confidence region for the
changepoint, under a two-step regression model (Anderson and Senthilselvan,
1982), based on the work of Davies (1977). Then we introduce a new estimation
method using the standardized score process (Chauvel and O'Quigley, 2014),
under a model with multiple changepoints. In this context, rather than make use
of the partial likelihood, we base inference on minimization of quadratic
residuals. Simulations and an example are provided.

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