Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Impact of model misspecification on model-based tests in PK studies with parallel design: real case and simulation studies.

This article evaluates the performance of pharmacokinetic (PK) equivalence testing between two formulations of a drug through the Two-One Sided Tests (TOST) by a model-based approach (MB-TOST), as an alternative to the classical non-compartmental approach (NCA-TOST), for a sparse design with a few time points per subject. We focused on the impact of model misspecification and the relevance of model selection for the reference data. We first analysed PK data from phase I studies of gantenerumab, a monoclonal antibody for the treatment of Alzheimer's disease. Using the original rich sample data, we compared MB-TOST to NCA-TOST for validation. Then, the analysis was repeated on a sparse subset of the original data with MB-TOST. This analysis inspired a simulation study with rich and sparse designs. With rich designs, we compared NCA-TOST and MB-TOST in terms of type I error and study power. With both designs, we explored the impact of misspecifying the model on the performance of MB-TOST and adding a model selection step. Using the observed data, the results of both approaches were in general concordance. MB-TOST results were robust with sparse designs when the underlying PK structural model was correctly specified. Using the simulated data with a rich design, the type I error of NCA-TOST was close to the nominal level. When using the simulated model, the type I error of MB-TOST was controlled on rich and sparse designs, but using a misspecified model led to inflated type I errors. Adding a model selection step on the reference data reduced the inflation. MB-TOST appears as a robust alternative to NCA-TOST, provided that the PK model is correctly specified and the test drug has the same PK structural model as the reference drug.

Efficiency of fine scale and spatial regression in modelling associations between healthcare service spatial accessibility and their utilization.

BACKGROUND: Healthcare accessibility, a key public health issue, includes potential (spatial accessibility) and realized access (healthcare utilization) dimensions. Moreover, the assessment of healthcare service potential access and utilization should take into account the care provided by primary and secondary services. Previous studies on the relationship between healthcare spatial accessibility and utilization often used conventional statistical methods without addressing the scale effect and spatial processes. This study investigated the impact of spatial accessibility to primary and secondary healthcare services on length of hospital stay (LOS), and the efficiency of using a geospatial approach to model this relationship. METHODS: This study focused on the ≥ 75-year-old population of the Nord administrative region of France. Inpatient hospital spatial accessibility was computed with the E2SFCA method, and then the LOS was calculated from the French national hospital activity and patient discharge database. Ordinary least squares (OLS), spatial autoregressive (SAR), and geographically weighted regression (GWR) were used to analyse the relationship between LOS and spatial accessibility to inpatient hospital care and to three primary care service types (general practitioners, physiotherapists, and home-visiting nurses). Each model performance was assessed with measures of goodness of fit. Spatial statistical methods to reduce or eliminate spatial autocorrelation in the residuals were also explored. RESULTS: GWR performed best (highest R2 and lowest Akaike information criterion). Depending on global model (OLS and SAR), LOS was negatively associated with spatial accessibility to general practitioners and physiotherapists. GWR highlighted local patterns of spatial variation in LOS estimates. The distribution of areas in which LOS was positively or negatively associated with spatial accessibility varied when considering accessibility to general practitioners and physiotherapists. CONCLUSIONS: Our findings suggest that spatial regressions could be useful for analysing the relationship between healthcare spatial accessibility and utilization. In our case study, hospitalization of elderly people was shorter in areas with better accessibility to general practitioners and physiotherapists. This may be related to the presence of effective community healthcare services. GWR performed better than LOS and SAR. The identification by GWR of how these relationships vary spatially could bring important information for public healthcare policies, hospital decision-making, and healthcare resource allocation.