code: def correct_approx_firth(
      x: NDArray[(Any,), Float],
      y: NDArray[(Any,), Float],
      firth_offset: NDArray[(Any,), Float],
      mask: NDArray[(Any,), bool],
  ) -> Optional[FirthStatistics]:
      """
      Calculate LRT statistics for a SNP using the approximate Firth method.
  
      Args:
          x : Genotypes for SNP
          y : Dependent variable (phenotype)
          offset : Phenotype offset including covariate effects from the null model fit
          mask : Missingness array; false if the sample is missing a phenotype value, true otherwise
  
      Returns:
          None if the Firth fit did not converge.
          Otherwise, likelihood-ratio test statistics.
      """
  
      beta_init = np.zeros(1)
      masked_y = y[mask]
      masked_X = x[mask, None]
      masked_offset = firth_offset[mask]
      firth_fit = _fit_firth(
          beta_init, masked_X, masked_y, masked_offset
      )
      if firth_fit is None:
          return None
  
      effect = firth_fit.beta.item()
      # Likelihood-ratio test
      null_model = Model(masked_X, masked_y, masked_offset)
      null_deviance = _calculate_log_likelihood(
          beta_init, null_model
      ).deviance
      chisq = null_deviance - firth_fit.log_likelihood.deviance
      pvalue = stats.chi2.sf(chisq, 1)
      # Based on the Hessian of the unpenalized log-likelihood
      stderror = np.sqrt(
          np.linalg.pinv(firth_fit.log_likelihood.I).diagonal()[-1]
      )
      return FirthStatistics(
          effect=effect, stderror=stderror, chisq=chisq, pvalue=pvalue
      )
  
file_path: glow/python/glow/gwas/approx_firth.py
imports: from typing import Any, Optional
  import numpy
  from dataclasses import dataclass
  import scipy
  from typeguard import typechecked
  from nptyping import Float, NDArray
  from scipy import stats
label_desc: Use image node_id 4 for calling a global function with example usage: correct_approx_firth(x, y, firth_offset, mask) and returns: FirthStatistics, None