The need for mixed-effects modeling with population dichotomous data.

Over the past 25 years sophisticated data analytic techniques have been developed which can lead to improved analyses, but at additional computational cost. In particular, this applies to the approach where interindividual random effects are included in a data analytic model for population pharmacokinetic data, which can often lead to substantially improved estimates of fixed-effect parameters. However, there are also commonly occurring situations, notably with some types of pharmacodynamic data, where such improvement is not realized. This study simulates some simple population dichotomous data, and secondarily, some related continuous data. These data are analyzed using both mixed-effect (ME) models that include interindividual random effects and naive (NA) models that do not include interindividual random effects, and it is seen that use of an ME model does not inevitably lead to gains over use of an NA model. In fact, using maximum likelihood estimation with both types of models, the root mean square estimation errors for fixed effect parameters can actually be larger with an ME model than with the corresponding NA model. Using a form of restricted maximum likelihood estimation with the ME model, the two types of models yield root mean square errors which are comparable, but which still do not suggest that there is always marked advantage in using the ME model.

Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check.

The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, "real" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical "sufficiency") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with "statistics" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found.

Ways to fit a PK model with some data below the quantification limit.

Pharmacokinetic data consist of drug concentration measurements, as well as reports of some measured concentrations being below the quantification limit of the assay (BQL). A pharmacokinetic model may befit to these data, and for this purpose, the BQL observations must be either discarded or handled in a special way. In this paper, seven methods for dealing with BQL observations are evaluated. Both single-subject and population data are simulated from a one-compartment model. A moderate amount of data is simulated for each individual. The actual cv of concentration measurements at the quantification limit is assumed to be no greater than 20%, in accord with the FDA Guidance. The results of this paper should be interpreted in this context. The methods include handling BQL observations as fixed-point censored observations, i.e., by using the likelihoods that these observations are in fact BQL. This method is shown to have some overall statistical advantage. However, the gain in using this method over that of simply discarding the BQL observations is not always much, and this is especially so when the frequency of BQL observations is small. Some simple methods entailing (i) replacing one or more BQL observations with the value 0, or (ii) replacing them with the value QL/2, where QL is the quantification limit, are also included. The first of these two approaches should not be used With population data, use of the second approach can result in some noticeably improved estimation of the typical value of a parameter, but then there is also marked degradation in the estimation of the population variance of the parameter.

A population pharmacokinetic-pharmacodynamic analysis of repeated measures time-to-event pharmacodynamic responses: the antiemetic effect of ondansetron.

This paper presents and illustrates methodology for specifying, estimating, and evaluating a predictive model for repeated measures time-to-event responses. The illustrative example specifies a model of the antiemetic effect vs. concentration relationship for the 5-HT3 antagonist ondansetron in the human ipecac model for emesis. A key part of this model is a time-dependent log hazard function for emesis that is increased by ipecac administration and decreased by ondansetron concentration. The model is fit using an approximate maximum likelihood method. The data consist of the time free of emeses and, for those individuals with emetic episodes, the time(s) of the episode(s). Model evaluation is accomplished using residual plots adapted to time-to-event data and a "posterior predictive check" wherein observed data statistics are compared to those obtained from data simulated from the fitted model. The ondansetron concentration required to obtain a 50% reduction in the hazard of emesis is estimated to be 1.4 +/- 0.2 ng/ml, and the rate constant for elimination of ipecac-induced hazard is 1.5 +/- 0.2 hr-1.

Non-steady state population kinetics of intravenous phenytoin.

This observational study explored the effects of demographics, sickness, and polypharmacy on the non-steady state population pharmacokinetics of intravenous phenytoin. One hundred fifteen patients were studied. Models were developed using the NONMEM program with hybrid first-order conditional estimation. A Michaelis-Menten model with delayed induction was preferred over a Michaelis-Menten model without induction, a Michaelis-Menten model with immediate induction, or a linear model with delayed induction. When the data were fit to a Michaelis-Menten model with delayed induction, the volume of distribution (Vd) was found to depend on weight and serum albumin. The Vd was estimated to be 0.95 l/kg, assuming an albumin level of 3 g/dl. The Michaelis-Menten constant (km) was estimated to be 7.9 mg/l. The baseline maximum metabolic rate was 580 mg/day for a 70-kg patient. The average time to onset of induction was 59.5 hours. If a fever developed after induction began, it increased the extent of induction. This model was evaluated retrospectively in 26 additional patients, yielding a mean prediction error of -0.4 mg/l (-3.0-2.2 mg/l) and a mean absolute prediction error of 4.7 mg/l (3.2-6.2 mg/l) based on two-level feedback. Given the large interindividual variances in maximum metabolic rate, phenytoin levels should be measured frequently.

Three new residual error models for population PK/PD analyses.

Residual error models, traditionally used in population pharmacokinetic analyses, have been developed as if all sources of error have properties similar to those of assay error. Since assay error often is only a minor part of the difference between predicted and observed concentrations, other sources, with potentially other properties, should be considered. We have simulated three complex error structures. The first model acknowledges two separate sources of residual error, replication error plus pure residual (assay) error. Simulation results for this case suggest that ignoring these separate sources of error does not adversely affect parameter estimates. The second model allows serially correlated errors, as may occur with structural model misspecification. Ignoring this error structure leads to biased random-effect parameter estimates. A simple autocorrelation model, where the correlation between two errors is assumed to decrease exponentially with the time between them, provides more accurate estimates of the variability parameters in this case. The third model allows time-dependent error magnitude. This may be caused, for example, by inaccurate sample timing. A time-constant error model fit to time-varying error data can lead to bias in all population parameter estimates. A simple two-step time-dependent error model is sufficient to improve parameter estimates, even when the true time dependence is more complex. Using a real data set, we also illustrate the use of the different error models to facilitate the model building process, to provide information about error sources, and to provide more accurate parameter estimates.

Comparison of the Akaike Information Criterion, the Schwarz criterion and the F test as guides to model selection.

In pharmacokinetic data analysis, it is frequently necessary to select the number of exponential terms in a polyexponential expression used to describe the concentration-time relationship. The performance characteristics of several selection criteria, the Akaike Information Criterion (AIC), and the Schwarz Criterion (SC), and the F test (alpha = 0.05), were examined using Monte Carlo simulations. In particular, the ability of these criteria to select the correct model, to select a model allowing estimation of pharmacokinetic parameters with small bias and good precision, and to select a model allowing precise predictions of concentration was evaluated. To some extent interrelationships among these procedures is explainable. Results indicate that the F test tends to choose the simpler model more often than does either the AIC or SC, even when the more complex model is correct. Also, the F test is more sensitive to deficient sampling designs. Clearance estimates are generally very robust to the choice of the wrong model. Other pharmacokinetic parameters are more sensitive to model choice, particularly the apparent elimination rate constant. Prediction of concentrations is generally more precise when the correct model is chosen. The tendency for the F test (alpha = 0.05) to choose the simpler model must be considered relative to the objectives of the study.

Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis.

The influence of the choice of pharmacokinetic model on subsequent determination of covariate relationships in population pharmacokinetic analysis was studied using both simulated and real data sets. Simulations and data analysis were both performed with the program NONMEM. Data were simulated using a two-compartment model, but at late sample times, so that preferential selection of the two-compartment model should have been impossible. A simple categorical covariate acting on clearance was included. Initially, on the basis of a difference in the objective function values, the two-compartment model was selected over the one-compartment model. Only when the complexity of the one-compartment model was increased in terms of the covariate and statistical models was the difference in objective function values of the two structural models negligible. For two real data sets, with which the two-compartment model was not selected preferentially, more complex covariate relationships were supported with the one-compartment model than with the two-compartment model. Thus, the choice of structural model can be affected as much by the covariate model as can the choice of covariate model be affected by the structural model; the two choices are interestingly intertwined. A suggestion on how to proceed when building population pharmacokinetic models is given.

Maxillofacial trauma: a potentially fatal injury.

Trauma remains one of the fastest growing causes of death in the United States, especially within the young adult population. Injuries to both the soft tissue and bony skeleton of the face constitute a high percentage of all traumatic admissions that pass through many emergency rooms. Because maxillofacial injuries are often dramatic, they can easily divert attention away from other medical priorities. In spite of numerous significant advances, the management of maxillofacial trauma remains a challenging problem for all reconstructive surgeons. From reading the literature, it can be assumed that maxillofacial trauma is rarely life threatening or an immediate cause of death, unless associated with airway compromise. We present our experience with 6 illustrative patients who either succumbed to complications or had life-threatening exsanguination secondary to isolated facial trauma.

Mean time parameters for generalized physiological flow models (semihomogeneous linear systems).

This note gives expressions for recirculation mean time parameters of the disposition kinetics of particles in a semihomogeneous stationary linear system. In such a system each compartment may have an arbitrary single-pass disposition function, rather than a known parametric (usually monoexponential) one. Such systems provide a generalization of physiological flow models. Given observations of arterial blood concentrations and tissue amounts, and making the additional assumptions that (i) the fraction of total blood flow exiting each tissue that goes to each other tissue is constant and known, and (ii) the fraction of drug entering each tissue that is eliminated to the outside is constant and known, the input to each tissue can be known, and therefore both its total blood flow and its single-pass disposition function can be estimated. Recirculation mean time parameters can be computed from these estimates. Application to real thiopental data is presented as an example.

A simulation study comparing designs for dose ranging.

Only with knowledge of the (prior) distribution of dose-response parameters in a population, can one determine both the initial dose of a drug for chronic administration to an individual (such as the dose producing a fixed degree of response in a fixed proportion of the population) and an appropriate subsequent (adjusted) dose (such as the dose yielding a desirable response according to the posterior parameter distribution, given an observed response to an initial dose). The currently FDA-sanctioned design for a dose-ranging study, the parallel-dose design, assigns just one of several doses to each patient. It does not provide good information on the distribution of individual dose-response parameters. A cross-over design assigns several dose levels to each patient. It therefore can provide better information, but does not resemble clinical practice. Consequently, study participants must be restricted to patients who can tolerate such non-therapeutic drug exposure, posing problems in extrapolation of study results to other types of patients. A titration or dose-escalation design begins all patients on placebo and, except for those patients assigned to a placebo-only group, escalates the dose for a patient at preset intervals only when clinical response at lower doses is inadequate. It both exposes patients to several dose levels and resembles good clinical practice, allowing study of a representative patient sample. We report here the simulation results of parameter estimation for the three designs when the data arise from complex and realistic dose-response models and/or with certain complications in study execution. The dose-escalation design clearly performs better overall than the parallel-dose design for the models considered here, and generally, just a little worse than the cross-over design. These results support the conclusion that for dose ranging, depending on the demands of the clinical situation, one should use either the cross-over or the dose-escalation design.

Fatal hepatic hemorrhage: an unresolved problem in the management of complex liver injuries.

The operative records of 683 patients who required an exploratory laparotomy for trauma with the findings of a liver injury were reviewed. Of the 683 patients 18% (121) sustained severe liver injuries with difficult to control hemorrhage, and 82% of the deaths, in this group of severe liver injuries, were due to exsanguination. A critical analysis of the specific surgical techniques used for hemostasis was undertaken. Hepatotomy with subsequent direct vascular and/or biliary duct repair or ligation was used in 44% of the cases and was successful 87% of the time. Hepatic resection was employed in 10% of the cases with a 50% mortality. Liver packs were used in 29% of the cases which included 14 hepatic vein and six retrohepatic vena caval injuries and five extensive bilobar parenchymal disruptions. The survival rate for this group of patients was 86%. Vascular isolation of the liver was used 8.3% of the cases and was successful 40% of the time. An algorithm for the successful surgical control of hemorrhage from severe liver injuries including indications and contra-indications of specific surgical techniques is presented.

Successful atrial caval shunting in the management of retrohepatic venous injuries.

Over a 3-year period, 519 patients underwent laparotomy for liver injuries. Nine (2 percent) required insertion of an atrial caval catheter to control hemorrhage from perihepatic venous injuries. In three cases, the shunt arrested the hemorrhage, allowing successful surgical repair of the venous injuries. From a careful analysis of our experience, we have identified common errors made in shunt placement, developed a modified atrial caval catheter, and have simplified the surgical technique for insertion.

Traumatic hemipelvectomy: a catastrophic injury.

Traumatic hemipelvectomy is a catastrophic injury resulting from violent blunt shearing forces which cause massive skin, bone, and soft-tissue destruction. The initial extent of the injury as well as the complexity of the consequent problems is staggering. As such it constitutes one of the major challenges seen by trauma surgeons. Patients surviving traumatic hemipelvectomy are rare. We found a total of 36 cases reported in this century. The University of California at Davis General Surgery Trauma Service admitted 9,369 major trauma victims from June 1985 to May 1988. During this 3-year period eight patients sustained a traumatic hemipelvectomy, of whom three survived. Given the complexity, yet rarity, of this injury, a review of the world literature was undertaken to compile collective experiences to aid surgeons in the management of this injury.

Sample size determination for confidence intervals on the population mean and on the difference between two population means.

Sample size determination is usually based on the premise that a hypothesis test is to be used. A confidence interval can sometimes serve better than a hypothesis test. In this paper a method is presented for sample size determination based on the premise that a confidence interval for a simple mean, or for the difference between two means, with normally distributed data is to be used. For this purpose, a concept of power relevant to confidence intervals is given. Some useful tables giving required sample size using this method are also presented.

Study designs for dose-ranging.

Premarketing dose-ranging studies of a drug are done to establish a reasonable initial dose. According to the current procedure sanctioned by the Food and Drug Administration, each patient is given one of several possible doses, including placebo, after an initial placebo run-in period. Data analysis is based on a model in which the mean response at each dose is independent of the magnitude of the dose. The initial dose is the lowest dose tested that has a response that is statistically significantly greater than the response after placebo administration. We suggest that the present conceptual approach to, and standard study design and analysis for, dose-ranging studies be changed. We believe one must begin with a parametric model for patient-specific dose-response curves. Knowledge of the distribution of these curves in a population provides a basis for choice of an initial dose (e.g., the dose that achieves a given response in a given fraction of patients) and, after observation of response to an initial dose, for choice of an incremental dose for a specific patient (by use of Bayes rule). The current parallel-dose design can provide only poor information about the distribution of dose-response curves, biased estimates of the typical curve, and little information on interpatient variability. Crossover studies provide better information. In studies in which a parametric patient-specific dose-response model is used, a dose-escalation design provides no less information than a crossover design, and it has ethical advantages that allow a more representative patient group and clinical setting to be studied.

Rapid venous access using saphenous vein cutdown at the ankle.

Injured adults can usually be treated adequately with peripheral intravenous lines. However, in hypotensive patients, alternative techniques such as venous cutdown may be necessary. There are no adult studies that document the success rate or time required to complete this procedure in the emergent situation. During a 1-year period, 73 cutdowns were attempted on 56 patients. Sixty-two of these attempts resulted in venous cannulation with a free flow of fluid (84.9%). The average time required for placement was 4.9 minutes. First-year residents had a significantly lower success rate (70%) than emergency department staff (89%) or second- through fifth-year surgical residents (94%). One patient who lived developed a local cellulitis. There were no other complications. In the hands of an experienced operator, saphenous vein cutdown at the ankle is a reliable method of rapidly gaining venous access in the adult patient. There are few immediate or late complications if the catheter is removed within 24 hours.

Semiparametric approach to pharmacokinetic-pharmacodynamic data.

A semiparametric model for analysis of pharmacokinetic (PK) and pharmacodynamic (PD) data arising from non-steady-state experiments is presented. The model describes time lag between drug concentration in a sampling compartment, e.g., venous blood (Cv), and drug effect (E). If drug concentration at the effect site (Ce) equilibrates with arterial blood concentration (Ca) slower than with Cv, a non-steady-state experiment yields E vs. Cv data describing a counterclockwise hysteresis loop. If Ce equilibrates with Ca faster than with Cv, clockwise hysteresis is observed. To model hysteresis, a parametric model is proposed linking (unobserved) Ca to Cv with elimination rate constant kappa ov and also linking Ca to Ce with elimination rate constant kappa oe. When kappa oe is greater than (or less than) kappa ov clockwise (or counterclockwise) hysteresis occurs. Given kappa oe and kappa ov, numerical (constrained) deconvolution is used to obtain the disposition function of the arterial compartment (Ha), and convolution is used to calculate Ce given Ha. The values of kappa oe and kappa ov are chosen to collapse the hysteresis loops to single curves representing the Ce-E (steady-state) concentration-response curve. Simulations, and an application to real data, are reported.

Esophageal perforation following external blunt trauma.

Esophageal perforation from external blunt trauma is an exceedingly rare injury. Since 1900, including our five cases, we found 96 reported cases. The most common cause was violent vehicular trauma. The cervical and upper thoracic esophagus was the site of perforation in 82%. In 78% of the cases, there were findings consistent with esophageal injury, but there was a delay in diagnosis in two thirds of these. The diagnostic difficulty was due to lack of a specific symptom complex for esophageal perforation. Often esophageal perforation was not suspected and the symptoms were attributed to the more common injuries, or the diagnostic workup was incomplete. There were 24 (38%) infectious complications directly related to the esophageal perforation. In 21 of these, there was a delay in diagnosis. There were five (9.4%) deaths due to sepsis from the esophageal perforation.