httkpop: httkpop: Virtual population generator for HTTK.

In httk: High-Throughput Toxicokinetics

httkpop: Virtual population generator for HTTK.

Description

The httkpop package generates virtual population physiologies for use in population TK.

Details

To simulate inter-individual variability in the TK model, a MC approach is used: the model parameters are sampled from known or assumed distributions, and the model is evaluated for each sampled set of parameters. To simulate variability across subpopulations, the MC approach needs to capture the parameter correlation structure. For example, kidney function changes with age (Levey et al., 2009), thus the distribution of GFR is likely different in 6-year-olds than in 65-yearolds. To directly measure the parameter correlation structure, all parameters need to be measured in each individual in a representative sample population. Such direct measurements are extremely limited. However, the correlation structure of the physiological parameters can be inferred from their known individual correlations with demographic and anthropometric quantities for which direct population measurements do exist. These quantities are sex, race/ethnicity, age, height, and weight (Howgate et al., 2006; Jamei et al., 2009a; Johnson et al., 2006; McNally et al., 2014; Price et al., 2003). Direct measurements of these quantities in a large, representative sample of the U.S. population are publicly available from NHANES. NHANES also includes laboratory measurements, including both serum creatinine, which can be used to estimate GFR (Levey et al., 2009), and hematocrit. For conciseness, sex, race/ethnicity, age, height, weight, serum creatinine, and hematocrit will be called the NHANES quantities.

HTTK-Pop's correlated MC approach begins by sampling from the joint distribution of the NHANES quantities to simulate a population. Then, for each individual in the simulated population, HTTKePop predicts the physiological parameters from the NHANES quantities using regression equations from the literature (Barter et al., 2007; Baxter-Jones et al., 2011; Bosgra et al., 2012; Koo et al., 2000; Levey et al., 2009; Looker et al., 2013; McNally et al., 2014; Ogiu et al., 1997; Price et al., 2003; Schwartz and Work, 2009; Webber and Barr 2012). Correlations among the physiological parameters are induced by their mutual dependence on the correlated NHANES quantities. Finally, residual variability is added to the predicted physiological parameters using estimates of residual marginal variance (i.e., variance not explained by the regressions on the NHANES quantities) (McNally et al., 2014).

Data were combined from the three most recent publicly-available NHANES cycles: 2007-2008, 2009-2010, and 2011-2012. For each cycle, some NHANES quantities - height, weight, serum creatinine, and hematocrit - were measured only in a subset of respondents. Only these subsets were included in HTTKePop. The pooled subsets from the three cycles contained 29,353 unique respondents. Some respondents were excluded from analysis: those with age recorded as 80 years (because all NHANES respondents 80 years and older were marked as "80"); those with missing height, weight or hematocrit data; and those aged 12 years or older with missing serum creatinine data. These criteria excluded 4807 respondents, leaving 24,546 unique respondents. Each NHANES respondent was assigned a cycle-specific sample weight, which can be interpreted as the number of individuals in the total U.S. population represented by each NHANES respondent in each cycle (Johnson et al., 2013). Because data from three cycles were combined, the sample weights were rescaled (divided by the number of cycles being combined, as recommended in NHANES data analysis documentation) (Johnson et al., 2013). To handle the complex NHANES sampling structure, the R survey package was used to analyze the NHANES data (Lumley, 2004).

To allow generation of virtual populations specified by weight class, we coded a categorical variable for each NHANES respondent. The categories Underweight, Normal, Overweight, or Obese were assigned based on weight, age, and height/length (Grummer-Strawn et al., 2010; Kuczmarski et al., 2002; Ogden et al., 2014; WHO, 2006, 2010). We implemented two population simulation methods within HTTK-Pop: the direct-resampling method and the virtual-individuals method. The direct-resampling method simulated a population by sampling NHANES respondents with replacement, with probabilities proportional to the sample weights. Each individual in the resulting simulated population was an NHANES respondent, identified by a unique NHANES sequence number. By contrast, the second method generates "virtual individuals" - sets of NHANES quantities that obey the approximate joint distribution of the NHANES quantities (calculated using weighted smoothing functions and kernel density estimators), but do not necessarily correspond to any particular NHANES respondent. The direct-resampling method removed the possibility of generating unrealistic combinations of the NHANES quantities; the virtual-individuals method allowed the use of interpolation to simulate subpopulations represented by only a small number of NHANES respondents.

For either method, HTTK-Pop takes optional specifications about the population to be simulated and then samples from the appropriate conditional joint distribution of the NHANES quantities.

Once HTTK-Pop has simulated a population characterized by the NHANES quantities, the physiological parameters of the TK model are predicted from the NHANES quantities using regression equations from the literature. Liver mass was predicted for individuals over age 18 using allometric scaling with height from Reference Man (Valentin, 2002), and for individuals under 18 using regression relationships with height and weight published by Ogiu et al. (1997). Residual marginal variability was added for each individual as in PopGen (McNally et al., 2014). Similarly, hepatic portal vein blood flows (in L/h) are predicted as fixed fractions of a cardiac output allometrically scaled with height from Reference Man (Valentin, 2002), and residual marginal variability is added for each individual (McNally et al., 2014). Glomerular filtration rate (GFR) (in L/h/1.73 m2 body surface area) is predicted from age, race, sex, and serum creatinine using the CKD-EPI equation, for individuals over age 18 (Levey et al., 2009). For individuals under age 18, GFR is estimated from body surface area (BSA) (Johnson et al., 2006); BSA is predicted using Mosteller's formula (Verbraecken et al., 2006) for adults and Haycock's formula (Haycock et al., 1978) for children. Hepatocellularity (in millions of cells per gram of liver tissue) is predicted from age using an equation developed by Barter et al. (2007). Hematocrit is estimated from NHANES data for individuals 1 year and older. For individuals younger than 1 year, for whom NHANES did not measure hematocrit directly, hematocrit was predicted from age in months, using published reference ranges (Lubin, 1987).

In addition to the HTTK physiological parameters, the HTTK models include chemical-specific parameters representing the fraction of chemical unbound in plasma (Fup) and intrinsic clearance (CLint). Because these parameters represent interactions of the chemical with the body, their values will vary between individuals. To simulate this variability, Fub and CLint were included in MC simulations, by sampling from estimated or assumed distributions for the parameters defining them.

Variability in hematocrit was simulated either using NHANES data (for individuals ages 1 and older) or using age-based reference ranges (for individuals under age 1). Fup was treated as a random variable obeying a distribution censored below the average limit of quantification (LOQ) of the in vitro assay. Specifically, Fup was assumed to obey a normal distribution truncated below at 0 and above at 1, centered at the Fup value measured in vitro, with a 30 the average LOQ (0.01), Fup was instead drawn from a uniform distribution between 0 and 0.01. Fup was assumed to be independent of all other parameters. This censored normal distribution was chosen to match that used in Wambaugh et al. (2015).

Variability in hepatocellularity (106 cells/g liver) and Mliver (kg) were simulated. The remaining source of variability in CLint,h is variability in CLint, which was simulated using a Gaussian mixture distribution to represent the population proportions of poor metabolizers (PMs) and non-PMs of each substance. The true prevalence of PMs is isozyme-specific (Ma et al., 2002; Yasuda et al., 2008); however, isozyme- specific metabolism data were not available for the majority of chemicals considered. We therefore made a simplifying assumption that 5 slower than average. With 95 a normal distribution truncated below at zero, centered at the value measured in vitro, with a 30 CLint was drawn from a PM distribution: a truncated normal distribution centered on one-tenth of the in vitro value with 30 Both CLint itself and the probability of being a PM were assumed to be independent of all other parameters. The truncated normal nonePM distribution was chosen because it has been used (with 100 in previous work (Rotroff et al., 2010; Wambaugh et al., 2015; Wetmore et al., 2014; Wetmore et al., 2015; Wetmore et al., 2012); the PM distribution was chosen to comport with the nonePM distribution.

Main function to generate a population

If you just want to generate a table of (chemical-independent) population physiology parameters, use httkpop_generate.

Using HTTK-Pop with HTTK

To generate a population and then run an HTTK model for that population, the workflow is as follows:

1. Generate a population using httkpop_generate.

2. For a given HTTK chemical and general model, convert the population data to corresponding sets of HTTK model parameters using httkpop_mc.

Author(s)

Caroline Ring

References

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httk documentation built on Sept. 11, 2024, 9:32 p.m.