Parametric and nonparametric population methods: their comparative performance in analysing a clinical dataset and two Monte Carlo simulation studies

BACKGROUND AND OBJECTIVES: This study examined parametric and nonparametric population modelling methods in three different analyses. The first analysis was of a real, although small, clinical dataset from 17 patients receiving intramuscular amikacin. The second analysis was of a Monte Carlo simulation study in which the populations ranged from 25 to 800 subjects, the model parameter distributions were Gaussian and all the simulated parameter values of the subjects were exactly known prior to the analysis. The third analysis was again of a Monte Carlo study in which the exactly known population sample consisted of a unimodal Gaussian distribution for the apparent volume of distribution (V(d)), but a bimodal distribution for the elimination rate constant (k(e)), simulating rapid and slow eliminators of a drug. METHODS: For the clinical dataset, the parametric iterative two-stage Bayesian (IT2B) approach, with the first-order conditional estimation (FOCE) approximation calculation of the conditional likelihoods, was used together with the nonparametric expectation-maximisation (NPEM) and nonparametric adaptive grid (NPAG) approaches, both of which use exact computations of the likelihood. For the first Monte Carlo simulation study, these programs were also used. A one-compartment model with unimodal Gaussian parameters V(d) and k(e) was employed, with a simulated intravenous bolus dose and two simulated serum concentrations per subject. In addition, a newer parametric expectation-maximisation (PEM) program with a Faure low discrepancy computation of the conditional likelihoods, as well as nonlinear mixed-effects modelling software (NONMEM), both the first-order (FO) and the FOCE versions, were used. For the second Monte Carlo study, a one-compartment model with an intravenous bolus dose was again used, with five simulated serum samples obtained from early to late after dosing. A unimodal distribution for V(d) and a bimodal distribution for k(e) were chosen to simulate two subpopulations of 'fast' and 'slow' metabolisers of a drug. NPEM results were compared with that of a unimodal parametric joint density having the true population parameter means and covariance. RESULTS: For the clinical dataset, the interindividual parameter percent coefficients of variation (CV%) were smallest with IT2B, suggesting less diversity in the population parameter distributions. However, the exact likelihood of the results was also smaller with IT2B, and was 14 logs greater with NPEM and NPAG, both of which found a greater and more likely diversity in the population studied.For the first Monte Carlo dataset, NPAG and PEM, both using accurate likelihood computations, showed statistical consistency. Consistency means that the more subjects studied, the closer the estimated parameter values approach the true values. NONMEM FOCE and NONMEM FO, as well as the IT2B FOCE methods, do not have this guarantee. Results obtained by IT2B FOCE, for example, often strayed visibly away from the true values as more subjects were studied. Furthermore, with respect to statistical efficiency (precision of parameter estimates), NPAG and PEM had good efficiency and precise parameter estimates, while precision suffered with NONMEM FOCE and IT2B FOCE, and severely so with NONMEM FO. For the second Monte Carlo dataset, NPEM closely approximated the true bimodal population joint density, while an exact parametric representation of an assumed joint unimodal density having the true population means, standard deviations and correlation gave a totally different picture. CONCLUSIONS: The smaller population interindividual CV% estimates with IT2B on the clinical dataset are probably the result of assuming Gaussian parameter distributions and/or of using the FOCE approximation. NPEM and NPAG, having no constraints on the shape of the population parameter distributions, and which compute the likelihood exactly and estimate parameter values with greater precision, detected the more likely greater diversity in the parameter values in the population studied. In the first Monte Carlo study, NPAG and PEM had more precise parameter estimates than either IT2B FOCE or NONMEM FOCE, as well as much more precise estimates than NONMEM FO. In the second Monte Carlo study, NPEM easily detected the bimodal parameter distribution at this initial step without requiring any further information. Population modelling methods using exact or accurate computations have more precise parameter estimation, better stochastic convergence properties and are, very importantly, statistically consistent. Nonparametric methods are better than parametric methods at analysing populations having unanticipated non-Gaussian or multimodal parameter distributions.     

Outcome prediction by a mathematical model based on noninvasive hemodynamic monitoring

BACKGROUND: The aims are to apply a mathematical search and display model based on noninvasive hemodynamic monitoring, to predict outcome early in a consecutively monitored series of 661 severely injured patients. METHODS: A prospective observational study by a previously designed protocol in a Level I trauma service in a university-run inner city public hospital was conducted. The survival probabilities were calculated at the initial resuscitation on admission and at subsequent intervals during their hospitalization beginning shortly after admission to the emergency department. Cardiac function was evaluated by cardiac output (CI), heart rate (HR), and mean arterial blood pressure (MAP), pulmonary function by pulse oximetry (SapO2), and tissue perfusion function by transcutaneous oxygen indexed to FiO2, (PtcO2/FiO2), and carbon dioxide (PtcCO2) tension. RESULTS: The survival probability (SP) averaged 89 +/- 0.4% for survivors and 75.7 +/- 1.6% (p < 0.001) for nonsurvivors in the first 24-hour period of resuscitation. The CI, MAP, SapO2, PtcO2, and PtcO2/FiO2 were significantly higher in survivors than in nonsurvivors in initial resuscitation, whereas HR and PtcCO2 were higher in nonsurvivors. CONCLUSIONS: During the initial resuscitation period, misclassifications were 102 of 661 or 15%. The SP provided early objective criteria to evaluate hospital outcome and to track changes throughout the hospital course based on a large database of patients with similar clinical-hemodynamic states.     

The pathological findings following laparotomy in Hodgkin's disease

The pathological findings in 50 patients with Hodgkin''s disease following laparotomy for diagnostic purposes are described. Forty-four patients had laparotomy before treatment and within a few months of the original diagnosis, while 6 patients had delayed laparotomies. The Rye histological classification was applied to the original lymph node biopsy, the abdominal lymph node and Hodgkin''s tissue in the spleen. The variation in appearance both of these tissues and of the liver biopsies is discussed.