Prices and Portfolio Choices in Financial Markets: Theory,Econometrics, Experiments

Many tests of asset‐pricing models address only the pricing predictions, but these pricing predictions rest on portfolio choice predictions that seem obviously wrong. This paper suggests a new approach to asset pricing and portfolio choices based on unobserved heterogeneity. This approach yields the standard pricing conclusions of classical models but is consistent with very different portfolio choices. Novel econometric tests link the price and portfolio predictions and take into account the general equilibrium effects of sample‐size bias. This paper works through the approach in detail for the case of the classical capital asset pricing model (CAPM), producing a model called CAPM+ε. When these econometric tests are applied to data generated by large‐scale laboratory asset markets that reveal both prices and portfolio choices, CAPM+εis not rejected.     

Reassessing Benzene Cancer Risks Using Internal Doses

Human cancer risks from benzene exposure have previously been estimated by regulatory agencies based primarily on epidemiological data, with supporting evidence provided by animal bioassay data. This paper reexamines the animal-based risk assessments for benzene using physiologically-based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. It demonstrates that internal doses (interpreted as total benzene metabolites formed) from oral gavage experiments in mice are well predicted by a PBPK model developed by Travis et al. Both the data and the model outputs can also be accurately described by the simple nonlinear regression model total metabolites = 76.4x/(80.75 + x), where x = administered dose in mg/kg/day. Thus, PBPK modeling validates the use of such nonlinear regression models, previously used by Bailer and Hoel. An important finding is that refitting the linearized multistage (LMS) model family to internal doses and observed responses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to cubic, leading to low-dose risk estimates smaller than in previous risk assessments. This is consistent with the conclusion for mice from the Bailer and Hoel analysis. An innovation in this paper is estimation of internal doses for humans based on a PBPK model (and the regression model approximating it) rather than on interspecies dose conversions. Estimates of human risks at low doses are reduced by the use of internal dose estimates when the estimates are obtained from a PBPK model, in contrast to Bailer and Hoel's findings based on interspecies dose conversion. Sensitivity analyses and comparisons with epidemiological data and risk models suggest that our finding of a nonlinear MLE dose-response curve at low doses is robust to changes in assumptions and more consistent with epidemiological data than earlier risk models.     

Uncertainties in Pharmacokinetic Modeling for Perchloroethylene: II. Comparison of Model Predictions with Data for a Variety of Different Parameters

In this paper we compare expectations derived from 10 different human physiologically based pharmacokinetic models for perchloroethylene with data on absorption via inhalation, and concentrations in alveolar air and venous blood. Our most interesting finding is that essentially all of the models show a time pattern of departures of predictions of air and blood levels relative to experimental data that might be corrected by more sophisticated model structures incorporating either (a) heterogeneity of the fat compartment (with respect to either perfusion or partition coefficients or both) or (b) intertissue diffusion of perchloroethylene between the fat and muscle/VRG groups. Similar types of corrections have recently been proposed to reduce analogous anomalies in the fits of pharmacokinetic models to the data for several volatile anesthetics.^(17-20) A second finding is that models incorporating resting values for alveolar ventilation in the region of 5.4 L/min seemed to be most compatible with the most reliable set of perchloroethylene uptake data.     

A Simple Toxicokinetic Model Exhibiting Complex Dynamics and Nonlinear Exposure Response

Uncertainty in model predictions of exposure response at low exposures is a problem for risk assessment. A particular interest is the internal concentration of an agent in biological systems as a function of external exposure concentrations. Physiologically based pharmacokinetic (PBPK) models permit estimation of internal exposure concentrations in target tissues but most assume that model parameters are either fixed or instantaneously dose-dependent. Taking into account response times for biological regulatory mechanisms introduces new dynamic behaviors that have implications for low-dose exposure response in chronic exposure. A simple one-compartment simulation model is described in which internal concentrations summed over time exhibit significant nonlinearity and nonmonotonicity in relation to external concentrations due to delayed up- or downregulation of a metabolic pathway. These behaviors could be the mechanistic basis for homeostasis and for some apparent hormetic effects.     

Simple Relations Between Administered and Internal Doses in Compartmental Flow Models

It is sometimes argued that the use of increasingly complex "biologically-based" risk assessment (BBRA) models to capture increasing mechanistic understanding of carcinogenic processes may run into a practical barrier that cannot be overcome in the near term: the need for unrealistically large amounts of data about pharmacokinetic and pharmacodynamic parameters. This paper shows that, for a class of dynamical models widely used in biologically-based risk assessments, it is unnecessary to estimate the values of the individual parameters. Instead, the input-output properties of such a model–specifically, the ratio of the area-under-curve (AUC) for any selected output to the AUC of the input–is determined by a single aggregate "reduced" constant, which can be estimated from measured input and output quantities. Uncertainties about the many individual parameter values of the model, and even uncertainties about its internal structure, are irrelevant for purposes of quantifying and extrapolating its input-output (e.g., dose-response) behavior. We prove that this is the case for the class of linear, constant-coefficient, globally stable compartmental flow systems used in many classical pharmacokinetic and low-dose PBPK models. Examples are cited that suggest that the value of the reduced parameter representing such a system's aggregate behavior may be relatively insensitive to changes in (and hence to uncertainties about) the values of individual parameters. The theory is illustrated with a model of pharmacokinetics and metabolism of cyclophosphamide (CP), a drug widely used in cancer chemotherapy and as an immunosuppressive agent.     

An Adjustment Factor for Mode-of-Action Uncertainty with Dual-Mode Carcinogens: The Case of Naphthalene-Induced Nasal Tumors in Rats

The U.S. Environmental Protection Agency (USEPA) guidelines for cancer risk assessment recognize that some chemical carcinogens may have a site-specific mode of action (MOA) involving mutation and cell-killing-induced hyperplasia. The guidelines recommend that for such dual MOA (DMOA) carcinogens, judgment should be used to compare and assess results using separate "linear" (genotoxic) versus "nonlinear" (nongenotoxic) approaches to low-level risk extrapolation. Because the guidelines allow this only when evidence supports reliable risk extrapolation using a validated mechanistic model, they effectively prevent addressing MOA uncertainty when data do not fully validate such a model but otherwise clearly support a DMOA. An adjustment-factor approach is proposed to address this gap, analogous to reference-dose procedures used for classic toxicity endpoints. By this method, even when a "nonlinear" toxicokinetic model cannot be fully validated, the effect of DMOA uncertainty on low-dose risk can be addressed. Application of the proposed approach was illustrated for the case of risk extrapolation from bioassay data on rat nasal tumors induced by chronic lifetime exposure to naphthalene. Bioassay data, toxicokinetic data, and pharmacokinetic analyses were determined to indicate that naphthalene is almost certainly a DMOA carcinogen. Plausibility bounds on rat-tumor-type-specific DMOA-related uncertainty were obtained using a mechanistic two-stage cancer risk model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Bound-specific adjustment factors were then used to reduce naphthalene risk estimated by linear extrapolation (under the default genotoxic MOA assumption), to account for the DMOA exhibited by this compound.     

Comparison of the Cancer Risk of Methylene Chloride Predicted from Animal Bioassay Data with the Epidemiologic Evidence

Methylene chloride has been shown to be a lung and liver carcinogen in the mouse; yet, the current epidemiologic data show no adverse health effects associated with chronic exposure to this compound. Hearne et al. have compared the results of a large mortality study on occupational exposure to methylene chloride to the human risk predictions based on the rodent bioassay to point out the inconsistency between the animal toxicologic and human epidemiologic data. The maximum number of lung and liver cancers predicted due to methylene chloride exposure based on the rodent bioassay data was 24 compared to 14 deaths from these cancers actually observed in the Hearne et al. epidemiology study. We assess the minimum risk detectable by the human study in order to calculate the upperbound potency of methylene chloride and compare it to the potency derived from the bioassay data. Results from the epidemiology study imply an upperbound potency of 1.5 x 10(-2) per ppm, compared to 1.4 x 10(-2) per ppm calculated using the most conservative analysis of the animal data. We conclude that the negative epidemiology study of Hearne et al. is not sufficiently powerful to show that the risk is inconsistent with the human risk estimated by modeling the rodent bioassay data. Specifically, the doses to which the workers were exposed, the population studied, and the latency period were not adequate to determine that the risks are outside the bounds of the risk estimates predicted by low-dose modeling of the animal data.     

Comparing Toxicologic and Epidemiologic Studies: Methylene Chloride-A Case Study

Exposure to methylene chloride induces lung and liver cancers in mice. The mouse bioassay data have been used as the basis for several cancer risk assessments. ^(1,2) The results from epidemiologic studies of workers exposed to methylene chloride have been mixed with respect to demonstrating an increased cancer risk. The results from a negative epidemiologic study of Kodak workers have been used by two groups of investigators to test the predictions from the EPA risk assessment models.^(3,4) These two groups used very different approaches to this problem, which resulted in opposite conclusions regarding the consistency between the animal model predictions and the Kodak study results. The results from the Kodak study are used to test the predictions from OSHA's multistage models of liver and lung cancer risk. Confidence intervals for the standardized mortality ratios (SMRs) from the Kodak study are compared with the predicted confidence intervals derived from OSHA's risk assessment models. Adjustments for the "healthy worker effect," differences in length of follow-up, and dosimetry between animals and humans were incorporated into these comparisons. Based on these comparisons, we conclude that the negative results from the Kodak study are not inconsistent with the predictions from OSHA's risk assessment model.     

Benchmark Dose Risk Assessment for Formaldehyde Using Airflow Modeling and a Single-Compartment, DNA-Protein Cross-Link Dosimetry Model to Estimate Human Equivalent Doses

Formaldehyde induced squamous-cell carcinomas in the nasal passages of F344 rats in two inhalation bioassays at exposure levels of 6 ppm and above. Increases in rates of cell proliferation were measured by T. M. Monticello and colleagues at exposure levels of 0.7 ppm and above in the same tissues from which tumors arose. A risk assessment for formaldehyde was conducted at the CIIT Centers for Health Research, in collaboration with investigators from Toxicological Excellence in Risk Assessment (TERA) and the U.S. Environmental Protection Agency (U.S. EPA) in 1999. Two methods for dose-response assessment were used: a full biologically based modeling approach and a statistically oriented analysis by benchmark dose (BMD) method. This article presents the later approach, the purpose of which is to combine BMD and pharmacokinetic modeling to estimate human cancer risks from formaldehyde exposure. BMD analysis was used to identify points of departure (exposure levels) for low-dose extrapolation in rats for both tumor and the cell proliferation endpoints. The benchmark concentrations for induced cell proliferation were lower than for tumors. These concentrations were extrapolated to humans using two mechanistic models. One model used computational fluid dynamics (CFD) alone to determine rates of delivery of inhaled formaldehyde to the nasal lining. The second model combined the CFD method with a pharmacokinetic model to predict tissue dose with formaldehyde-induced DNA-protein cross-links (DPX) as a dose metric. Both extrapolation methods gave similar results, and the predicted cancer risk in humans at low exposure levels was found to be similar to that from a risk assessment conducted by the U.S. EPA in 1991. Use of the mechanistically based extrapolation models lends greater certainty to these risk estimates than previous approaches and also identifies the uncertainty in the measured dose-response relationship for cell proliferation at low exposure levels, the dose-response relationship for DPX in monkeys, and the choice between linear and nonlinear methods of extrapolation as key remaining sources of uncertainty.     

Interspecies Extrapolation of Physiological Pharmacokinetic Parameter Distributions

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is denned by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.     

A Calibrated Human PBPK Model for Benzene Inhalation with Urinary Bladder and Bone Marrow Compartments

A physiologically‐based pharmacokinetic (PBPK) model of benzene inhalation based on a recent mouse model was adapted to include bone marrow (target organ) and urinary bladder compartments. Empirical data on human liver microsomal protein levels and linked CYP2E1 activities were incorporated into the model, and metabolite‐specific conversion rate parameters were estimated by fitting to human biomonitoring data and adjusting for background levels of urinary metabolites. Human studies of benzene levels in blood and breath, and phenol levels in urine were used to validate the rate of human conversion of benzene to benzene oxide, and urinary benzene metabolites from Chinese benzene worker populations provided model validation for rates of human conversion of benzene to muconic acid (MA) and phenylmercapturic acid (PMA), phenol (PH), catechol (CA), hydroquinone (HQ), and benzenetriol (BT). The calibrated human model reveals that while liver microsomal protein and CYP2E1 activities are lower on average in humans compared to mice, the mouse also shows far lower rates of benzene conversion to MA and PMA, and far higher conversion of benzene to BO/PH, and of BO/PH to CA, HQ, and BT. The model also differed substantially from existing human PBPK models with respect to several metabolic rate parameters of importance to interpreting benzene metabolism and health risks in human populations associated with bone marrow doses. The model provides a new methodological paradigm focused on integrating linked human liver metabolism data and calibration using biomonitoring data, thus allowing for model uncertainty analysis and more rigorous validation.     

Symmetry, Identifiability, and Prediction Uncertainties in Multistage Clonal Expansion (MSCE) Models of Carcinogenesis

Many models of exposure-related carcinogenesis, including traditional linearized multistage models and more recent two-stage clonal expansion (TSCE) models, belong to a family of models in which cells progress between successive stages-possibly undergoing proliferation at some stages-at rates that may depend (usually linearly) on biologically effective doses. Biologically effective doses, in turn, may depend nonlinearly on administered doses, due to PBPK nonlinearities. This article provides an exact mathematical analysis of the expected number of cells in the last ("malignant") stage of such a "multistage clonal expansion" (MSCE) model as a function of dose rate and age. The solution displays symmetries such that several distinct sets of parameter values provide identical fits to all epidemiological data, make identical predictions about the effects on risk of changes in exposure levels or timing, and yet make significantly different predictions about the effects on risk of changes in the composition of exposure that affect the pharmacodynamic dose-response relation. Several different predictions for the effects of such an intervention (such as reducing carcinogenic constituents of an exposure) that acts on only one or a few stages of the carcinogenic process may be equally consistent with all preintervention epidemiological data. This is an example of nonunique identifiability of model parameters and predictions from data. The new results on nonunique model identifiability presented here show that the effects of an intervention on changing age-specific cancer risks in an MSCE model can be either large or small, but that which is the case cannot be predicted from preintervention epidemiological data and knowledge of biological effects of the intervention alone. Rather, biological data that identify which rate parameters hold for which specific stages are required to obtain unambiguous predictions. From epidemiological data alone, only a set of equally likely alternative predictions can be made for the effects on risk of such interventions.     

Structure and Parameterization of Pharmacokinetic Models: Their Impact on Model Predictions

There has been an increasing interest in physiologically based pharmacokinetic (PBPK)models in the area of risk assessment. The use of these models raises two important issues: (1)How good are PBPK models for predicting experimental kinetic data? (2)How is the variability in the model output affected by the number of parameters and the structure of the model? To examine these issues, we compared a five-compartment PBPK model, a three-compartment PBPK model, and nonphysiological compartmental models of benzene pharmacokinetics. Monte Carlo simulations were used to take into account the variability of the parameters. The models were fitted to three sets of experimental data and a hypothetical experiment was simulated with each model to provide a uniform basis for comparison. Two main results are presented: (1)the difference is larger between the predictions of the same model fitted to different data se1ts than between the predictions of different models fitted to the dame data; and (2)the type of data used to fit the model has a larger effect on the variability of the predictions than the type of model and the number of parameters.     

Evaluation of the Uncertainty in an Oral Reference Dose for Methylmercury Due to Interindividual Variability in Pharmacokinetics

An analysis of the uncertainty in guidelines for the ingestion of methylmercury (MeHg) due to human pharmacokinetic variability was conducted using a physiologically based pharmacokinetic (PBPK) model that describes MeHg kinetics in the pregnant human and fetus. Two alternative derivations of an ingestion guideline for MeHg were considered: the U.S. Environmental Protection Agency reference dose (RfD) of 0.1 g/kg/day derived from studies of an Iraqi grain poisoning episode, and the Agency for Toxic Substances and Disease Registry chronic oral minimal risk level (MRL) of 0.5 g/kg/day based on studies of a fish-eating population in the Seychelles Islands. Calculation of an ingestion guideline for MeHg from either of these epidemiological studies requires calculation of a dose conversion factor (DCF) relating a hair mercury concentration to a chronic MeHg ingestion rate. To evaluate the uncertainty in this DCF across the population of U.S. women of child-bearing age, Monte Carlo analyses were performed in which distributions for each of the parameters in the PBPK model were randomly sampled 1000 times. The 1st and 5th percentiles of the resulting distribution of DCFs were a factor of 1.8 and 1.5 below the median, respectively. This estimate of variability is consistent with, but somewhat less than, previous analyses performed with empirical, one-compartment pharmacokinetic models. The use of a consistent factor in both guidelines of 1.5 for pharmacokinetic variability in the DCF, and keeping all other aspects of the derivations unchanged, would result in an RfD of 0.2 g/kg/day and an MRL of 0.3 g/kg/day.     

Efficient Sensitivity/Uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems

Estimation of uncertainties associated with model predictions is an important component of the application of environmental and biological models. "Traditional" methods for propagating uncertainty, such as standard Monte Carlo and Latin Hypercube Sampling, however, often require performing a prohibitive number of model simulations, especially for complex, computationally intensive models. Here, a computationally efficient method for uncertainty propagation, the Stochastic Response Surface Method (SRSM) is coupled with another method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of "well-behaved" standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the model outputs with respect to inputs or transformed inputs. The calculated model outputs and the derivatives at a set of sample points are used to approximate the unknown coefficients in the series expansions of outputs. A framework for the coupling of the SRSM and ADIFOR is developed and presented here. Two case studies are presented, involving (1) a physiologically based pharmacokinetic model for perchloroethylene for humans, and (2) an atmospheric photochemical model, the Reactive Plume Model. The results obtained agree closely with those of traditional Monte Carlo and Latin hypercube sampling methods, while reducing the required number of model simulations by about two orders of magnitude.     

Quantitative Cancer Risk Estimation for Formaldehyde

Of primary concern are irreversible effects, such as cancer induction, that formaldehyde exposure could have on human health. Dose-response data from human exposure situations would provide the most solid foundation for risk assessment, avoiding problematic extrapolations from the health effects seen in nonhuman species. However, epidemiologic studies of human formaldehyde exposure have provided little definitive information regarding dose-response. Reliance must consequently be placed on laboratory animal evidence. An impressive array of data points to significantly nonlinear relationships between rodent tumor incidence and administered dose, and between target tissue dose and administered dose (the latter for both rodents and Rhesus monkeys) following exposure to formaldehyde by inhalation. Disproportionately less formaldehyde binds covalently to the DNA of nasal respiratory epithelium at low than at high airborne concentrations. Use of this internal measure of delivered dose in analyses of rodent bioassay nasal tumor response yields multistage model estimates of low-dose risk, both point and upper bound, that are lower than equivalent estimates based upon airborne formaldehyde concentration. In addition, risk estimates obtained for Rhesus monkeys appear at least 10-fold lower than corresponding estimates for identically exposed Fischer-344 rats.     

A Trichloroethylene Risk Assessment Using a Monte Carlo Analysis of Parameter Uncertainty in Conjunction with Physiologically-Based Pharmacokinetic Modeling

A Monte Carlo simulation is incorporated into a risk assessment for trichloroethylene (TCE) using physiologically-based pharmacokinetic (PBPK) modeling coupled with the linearized multistage model to derive human carcinogenic risk extrapolations. The Monte Carlo technique incorporates physiological parameter variability to produce a statistically derived range of risk estimates which quantifies specific uncertainties associated with PBPK risk assessment approaches. Both inhalation and ingestion exposure routes are addressed. Simulated exposure scenarios were consistent with those used by the Environmental Protection Agency (EPA) in their TCE risk assessment. Mean values of physiological parameters were gathered from the literature for both mice (carcinogenic bioassay subjects) and for humans. Realistic physiological value distributions were assumed using existing data on variability. Mouse cancer bioassay data were correlated to total TCE metabolized and area-under-the-curve (blood concentration) trichloroacetic acid (TCA) as determined by a mouse PBPK model. These internal dose metrics were used in a linearized multistage model analysis to determine dose metric values corresponding to 10^-6 lifetime excess cancer risk. Using a human PBPK model, these metabolized doses were then extrapolated to equivalent human exposures (inhalation and ingestion). The Monte Carlo iterations with varying mouse and human physiological parameters produced a range of human exposure concentrations producing a 10^-6 risk.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Stochasticity in Physiologically Based Kinetics Models: Implications for Cancer Risk Assessment

In case of low-dose exposure to a substance, its concentration in cells is likely to be stochastic. Assessing the consequences of this stochasticity in toxicological risk assessment requires the coupling of macroscopic dynamics models describing whole-body kinetics with microscopic tools designed to simulate stochasticity. In this article, we propose an approach to approximate stochastic cell concentration of butadiene in the cells of diverse organs. We adapted the dynamics equations of a physiologically based pharmacokinetic (PBPK) model and used a stochastic simulator for the system of equations that we derived. We then coupled kinetics simulations with a deterministic hockey stick model of carcinogenicity. Stochasticity induced substantial modifications relative to dose-response curve, compared with the deterministic situation. In particular, there was nonlinearity in the response and the stochastic apparent threshold was lower than the deterministic one. The approach that we developed could easily be extended to other biological studies to assess the influence of stochasticity at macroscopic scale for compound dynamics at the cell level.