Evaluates the two-sided asymptotic p-value for the Miettinen-Nurminen
restricted-maximum-likelihood score test of \(H_0: p_T - p_C = \delta\) in
two independent binomial samples (see
InferenceIncidMiettinenNurminenRiskDiff
for the class that consumes this function). Internally: mn_z_statistic_cpp
computes the score \(z\) statistic using the constrained MLEs
\(\tilde p_C, \tilde p_T = \tilde p_C + \delta\)
(mn_constrained_mle_pc_cpp, found by bisecting the constrained
score equation to zero) in place of the unconstrained sample proportions in
the variance formula, with a small-sample correction factor \((n_T+n_C)/(n_T+n_C-1)\)
applied to the naive binomial variance; this function then returns
\(2\,\Phi(-|z|)\), the two-sided normal-tail p-value. Returns NA if
either arm is empty, \(\delta\) is outside \((-1, 1)\), or the resulting
\(z\) is not finite (e.g. the constrained variance estimate is
non-positive).