Description Usage Arguments Value Author(s) References Examples

`fisher_evaluation`

is used to evaluate the Fisher information matrix for both continuous and discrete data in nonlinear mixed effect models using Markov Chains Monte Carlo.

1 2 3 | ```
fisher_evaluation(t, y_ini=1, model, model2, model3, params, dim_b,
set_seed=TRUE, seed=42, n_samp, n_rep=1, n_iter, n_burn, CV=FALSE,
plot_graph=0, L_boot=1000, nb_patients=1)
``` |

`t` |
Vector of sampling times (or doses). |

`y_ini` |
A possible value for the response y to initialize the MCMC process. The default value is set at 1 (which works for many types of outcomes: continuous, binary, ...). |

`model` |
Compiled STAN model describing the response model to sample in the conditionnal distribution of b given y. |

`model2` |
Compiled STAN model describing the response model for calculating the derivative of the log-likelihood with respoect to each parameter. |

`model3` |
Compiled STAN model describing the response model to sample in the marginal distribution of the response y. |

`params` |
Vector of parameters given as follows: fixed effetcs, variances of the random effets, standard deviations of the residual errors (if continuous data). |

`dim_b` |
Number of random effects. |

`set_seed` |
Boolean indicating if the seed shoud be fixed. The default value is set at TRUE. |

`seed` |
Integer for the fixed seed. Used only if |

`n_samp` |
Integer representing the number of Monte Carlo (MC) samples, (i.e. number of samples for the outcome y). |

`n_rep` |
Integer representing the number of repeated measures at the same time (or dose) for each patient. The default value is set at 1 (for continuous data). |

`n_iter` |
Integer representing the number of Markov Chains Monte Carlo (MCMC) samples. |

`n_burn` |
Integer representing the number of burn-in samples for MCMC. |

`CV` |
Boolean indicating if some convergence information (variance of the determinant, mean of b, mean log-likelihood, ...) should be returned. The default value is set at FALSE. |

`plot_graph` |
An integer with value 0 (no graph should be plotted), 1 (graph of the determinant of the FIM), 2 (graph of the determinant of the FIM with confidence intervals assuming normal distribution), 3 (graph of the determinant of the FIM with bootstrap confidence intervals) or 4 (graph of the determinant of the FIM with both bootstrap confidence intervals and confidence intervals assuming normal distribution). The default value is set at 0. |

`L_boot` |
Number of samples for bootstrap estimation of the confidence intervals of the normalized determinant of the FIM. This argument is used/required only if plot_graph = 3 or 4. The default value is set at 1000. |

`nb_patients` |
Number of patients with the same elementary design for which the FIM is evaluated. The default value is set at 1. |

An list is returned, composed of the following variables:

`FIM` |
Expected Fisher information matrix (FIM). Of note, the FIM is an individual FIM and is calculated for |

`FIM_covar` |
Variance-covariance matrix of the FIM. (Of note, its dimension is of size 4 as the FIM is in dimension 2.) |

`inv_FIM` |
Inverse of the FIM. |

`RSE` |
Relative standard errors (square root of the diagonal elements of the inverse of the FIM). |

`RSE_inf_boot` |
Vector containing the lower bound of the bootstrap confidence interval of the RSEs. |

`RSE_sup_boot` |
Vector containing the upper bound of the bootstrap confidence interval of the RSEs. |

`det_norm_FIM` |
Normalized determinant of the FIM. |

`det_IC_normal` |
Vector containing the lower and upper bound of the confidence interval of the normalized determinant of the FIM assuming normal distribution. |

`det_IC_boot` |
Vector containing the lower and upper bound of the bootstrap confidence interval of the normalized determinant of the FIM. |

If CV=TRUE:

`mean_dloglik1` |
Mean of the partial derivatives of the log-likelihood according to the first MCMC sample and MC sample. Should be equal approximately to 0. |

`mean_dloglik2` |
Mean of the partial derivatives of the log-likelihood according to the second MCMC sample and MC sample. Should be equal approximately to 0. |

`var_dloglik1` |
Variance of the partial derivatives of the log-likelihood according to the first MCMC sample and MC sample. |

`var_dloglik2` |
Variance of the partial derivatives of the log-likelihood according to the second MCMC sample and MC sample. |

`mean_b` |
Mean of the samples in the conditionnal distribution of b given y. Should be equal approximately to 0. |

`mat_A_k1` |
Vector containing for each value sampled of the response y, the estimation of the integral of the partial derivatives of the log-likelihood over the random effects according to the first MCMC sample of the random effects b given y. |

`mat_A_k2` |
Vector containing for each value sampled of the response y, the estimation of the integral of the partial derivatives of the log-likelihood over the random effects according to the second MCMC sample of the random effects b given y. |

In addition, `plot_graph`

enables to plot a graph of the normalized determinant of the FIM with normal and bootstrap confidence intervals in function of the number of MC samples.

Marie-Karelle Riviere-Jourdan eldamjh@gmail.com

Riviere, M-K., Ueckert, S. and Mentre, F,. Evaluation of the Fisher information matrix in nonlinear mixed effect models using Markov Chains Monte Carlo.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
############################
# PLEASE UNCOMMENT EXAMPLE #
############################
#times = c(0.5,1,2,6,24,36,72,120)
#params = c(1,8,0.15,0.6,0.02,0.07,0.1)
# Files cen be found in external data
#model = stan_model("model_b_given_y.stan")
#model2 = stan_model("model_derivatives.stan")
#model3 = stan_model("model_y.stan")
#model_Warfarin = fisher_evaluation(t=times, y_ini=0.5, model=model,
#model2=model2, model3=model3, params=params, dim_b=3, set_seed=TRUE, seed=42,
#n_samp=1000, n_rep=1, n_iter=200, n_burn=500, CV=TRUE, plot_graph=4,
#nb_patients=32)
#model_Warfarin
``` |

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