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J Pharm Sci. Author manuscript; available in PMC 2010 August 10.

Published in final edited form as:

PMCID: PMC2919060

NIHMSID: NIHMS220452

Mohamed A. Kamal,^{1,2} David E. Smith,^{1} Jack Cook,^{3} Douglas Feltner,^{3} Allen Moton,^{3} and Daniele Ouellet^{3,4}

The publisher's final edited version of this article is available at J Pharm Sci

See other articles in PMC that cite the published article.

Categorical measures of lorazepam sleepiness and dizziness were modeled to identify differences in pharmacodynamic (PD) parameters between these adverse events (AEs). Differences in data-derived PD parameters were compared to relative incidence rates in the drug label (15.7% and 6.9%, respectively). Healthy volunteers (n=20) received single oral doses of 2 mg lorazepam or placebo in a randomized, double-blind, cross-over fashion. A 7-point categorical scale measuring the intensity of AEs was serially administered over 24 hr. The maximum score (MaxS), and area under the effect curve (AUEC) were determined by noncompartmental methods and compared using a paired t-test. Individual scores were modeled using a logistic function implemented in NONMEM. AUEC and MaxS for sleepiness were significantly higher than dizziness (20.35 vs. 9.76, p<0.01) and (2.35 vs.1.45, P<0.01). Model slope estimates were similar for sleepiness and dizziness (0.21 vs. 0.19 logits×ml/ng), but baseline logits were significantly higher for sleepiness (−2.81 vs. −4.34 logits). Data-derived PD parameters were in concordance with label incidence rates. The higher intensity of sleepiness may be directly related to baseline (no dug present) while the increase in intensity due to drug was relatively similar for both AEs.

Ordered categorical scales have been used in a variety of clinical settings to measure subjective effects and feelings which are clinically relevant yet difficult to measure using objective tests. A good example is pain where several analgesic trials used various categorical scales.^{1}^{,}^{2} Such scales have been reported to display high validity and reproducibility^{2}^{,}^{3} during repeated assessments and are usually quick and easy to administer.^{1}

Pharmacokinetic-pharmacodynamic (PK/PD) modeling of categorical responses may also provide insight into the PD of adverse events (AEs). The feasibility of using different subjective scales as biomarkers of AEs was investigated in a small clinical pharmacology study.^{4} As part of that study, seven-point ordered categorical scales measuring different types of subjective response (e.g. sleepiness, dizziness, etc) were administered serially after single dose administration to measure intensity of drug effects over 24 hours. Inspection of the effect-time profiles of the more common drug effects showed differential profiles for the different CNS agents, the onset and offset of response as well as the relationship to plasma concentrations.

The current analysis focuses on the categorical measures of two adverse effects (AEs) of one of the representative CNS drugs studied,^{4} namely lorazepam sleepiness and dizziness, with an aim to identify differences in relevant pharmacodynamic parameters using a PK/PD modeling approach. To date, no pharmacodynamic data, whether being categorical or continuous, have been published contrasting lorazepam induced sleepiness and dizziness in the context of population modeling. Their incidence rates in the drug label offer a unique benchmark for comparison. Thus, any differences found in PD measures between sleepiness and dizziness in the current analysis will be compared to differences in incidence rates in the drug label.^{5}

From the spectrum of CNS effects measured in the larger study,^{4} lorazepam sleepiness and dizziness were selected as the endpoints of interest because: 1) these effects showed a relatively high scale signal amplitude and highest statistical significance in the time- averaged-change- from -baseline differences with placebo, 2) sleepiness is a more common AE of lorazepam than dizziness according to incidence rates in the label,^{5} and 3) their pharmacology is thought to be conferred by benzodiazepine receptor activity in distinctly different areas of the CNS.^{6}^{, }^{7} It must be noted that modeling categorical data can not be performed using conventional nonlinear regression because it has a polynomial distribution which violates the assumption of homogeneity of variance.^{8} Therefore, the probabilities of reporting the effect categories as a function of time are typically modeled using logistic regression. The current study employs a logistic function^{9}^{,}^{10} to model sleepiness and dizziness categorical scores and assesses model performance using previously published pharmacometric methodology.^{11}^{,}^{12}

Twenty healthy volunteers were randomized in a double blind, single dose, 5-way crossover design.^{4} All subjects gave written informed consent to participate in the study. The study was conducted at the Clinical Pharmacology Unit of Pfizer (Ann Arbor, MI) in accordance with the principles of the Declaration of Helsinki. The study protocol was approved and performed in compliance with the Institutional Review Board/Independent Ethics Committee (IRB/IEC) and International Committee on Harmonization (ICH) Good Clinical Practice guidelines. Each subject received an oral dose of either lorazepam 2 mg, as one of four CNS drugs, or placebo. All study drugs were commonly used marketed compounds within their respective therapeutic indications and were selected to produce different AE profiles which could potentially be measurable after single dose administration. Each regimen was separated by a one week washout period for a total trial period of five consecutive weeks. Based on the half-life of each study drug, this washout period was deemed adequate to ensure lack of any period effect on baseline PD measures. Blood samples were drawn before dosing and at 0.5, 1, 2, 3, 4, 6, 8, 10, 12, 24, 48, and 72 hr after the morning dose.

Prior to each blood collection during the first 24 hr, a 70 item questionnaire was administered. Items on the questionnaire covered various complaints, symptoms, or feelings the subject experienced. For each statement the subject was to answer how strongly he or she felt the complaint, symptom, or feeling on a seven-point ordered categorical scale. The seven effect categories were 0=none, 1=minimum, 2=mild, 3=moderate, 4=significant, 5=severe, 6=extreme.

Plasma levels of lorazepam were determined using liquid chromatography tandem mass spectrometry (LC/MS/MS) at PPD Development (Richmond, VA). Briefly, 0.1 mL of human plasma containing sodium heparin was extracted by a liquid-liquid extraction using methyl t-butyl ether. The organic extract was dried and reconstituted in 0.2 mL of formic acid/methanol/5 mM ammonium formate (0.1:50:50, v/v/v), and an aliquot was injected into the LC/MS/MS system. The compounds were separated by reverse phase on a C_{18} column (2.0 mm × 50 mm, 5 µm) by gradient elution using a binary mobile phase consisting of formic acid/methanol/water (0.1:10:90, v/v/v) and 0.1% formic acid in methanol (v/v). The analytes were ionized in the mass spectrometer in a Turbo IonSpray source with positive ion atmospheric pressure electrospray ionization and detected with multiple-reaction monitoring modes. The nominal ion transitions monitored were *m/z* = 321 > 275 for lorazepam and *m/z* 327 > 281 for the internal standard (lorazepam-d_{4}). These transition ions were selected based on predominant fragmentation pathways of lorazepam and internal standard and their intensity, as observed in their product ion mass spectra. The lorazepam standard curve was linear over the range of 0.5 ng/mL (the lower limit of quantitation) to 50 ng/mL when 0.1 mL plasma was used for the analysis (*r*^{2} > 0.998). The intra- and inter-assay variations were less than 15% for the spiked standard curve and quality control samples. The variations for the quality control samples during the long-term study were <12%.

A non-compartmental analysis^{13} was performed using WinNonLin version 5.2 (Pharsight Inc, Mountain View, CA) on lorazepam plasma concentration-time profiles to determine maximal concentration (C_{max}), time to maximal concentration (T_{max}), area under the curve from time zero to infinity (AUC_{0-∞}) and the terminal half-life (t_{1/2}). Compartmental population analyses were conducted in NONMEM V^{14} using the first order conditional estimation method with interaction. The general model building strategy is based on modification of different approaches discussed by Beal and Sheiner,^{14} Mandema et al,^{15} and Ette and Ludden.^{16} During model building, the goodness of fit of different models to the data was evaluated using the following criteria: change in the minimum objective function (MOF), visual inspection of concordance and residual plots, precision of the parameter estimates, and decreases in both inter-individual and residual variability. A decrease in the MOF of at least 3.8 upon addition of a parameter was considered statistically significant. This corresponds to a nominal p value of <0.05 and one degree of freedom in the chi square distribution of the difference of MOF between hierarchical models.

The initial PK model was a one-compartment model defined in terms of the following structural parameters: oral clearance (CL/F), volume of distribution (V1/F), and first-order rate constant for absorption (ka). Other models tested include a term for lag time in absorption (tlag) and/or 2-compartments. Inter-subject variability on mean PK parameters was modeled using an exponential error term and was estimated sequentially on structural parameters such as oral clearance (CL/F), volume of distribution in the central and peripheral compartments (V1/F, V2/F), and on the first order absorption rate constant (Ka). Various models of residual variability were tested including additive, proportional and combined additive/proportional error models. During model building, the off-diagonal elements of the variance-covariance matrix were fixed to 0, i.e., it was assumed that there was no correlation between PK parameters. In the final step, the correlation between all parameters was estimated in NONMEM.

Parameter estimates of CL/F and t_{1/2} were compared to the non-compartmental results to ensure that model was adequate. Confidence intervals around parameter estimates were generated using nonparametric bootstrap procedure (n=1000 runs) as described by Ette et al ^{11}.

In order to produce a typical value versus time curve for sleepiness and dizziness categorical scores, the expected value at each time point was calculated. The expected value or average score of the categorical measure of sleepiness and dizziness at time t can be defined by the following equation:

$$E(X)={\displaystyle \sum _{X\in M}{x}_{t}\times P(x)}$$

(1)

where X is the discrete random variable denoting the categorical measure of sleepiness or dizziness, *x _{t}* is the categorical sleepiness or dizziness score at time t with a set of possible categorical values m ranging from 0–6, and P(x) is the probability (obtained as a frequency) of reporting a categorical score x at time t. To examine whether or not there were differences in sleepiness and dizziness intensities, a noncompartmental analysis of the time course of average sleepiness and dizziness scores was conducted. Effect intensity endpoints determined were maximum score (MaxS) and area under the effect curve (AUEC) over the entire dosing interval (24 hr). A paired t-test was used to determine whether differences in MaxS and AUEC between sleepiness and dizziness were statistically signficant.

Population modeling of the time course of sleepiness and dizziness scores was implemented in NONMEM^{14} using a logistic function^{9}^{,}^{10} with the second order Laplacian method of estimation.^{14} Since the intensity of pharmacodynamic effect was self-rated on the 7-point categorical scale (0–6), the logistic function was used to model the probability (P) of observing scores P≥m (m = 0 to 6) as a function of baseline effect, drug concentrations, and placebo effect. The logistic function used was:

$$g\{P({Y}_{t}\ge {m}_{\eta})\}={\displaystyle \sum _{i=1}^{m}{\beta}_{m}+drug+placebo+\eta}$$

(2)

where *g*{*P*(*Y _{t}* ≥

$$P({Y}_{t}\ge m)=\frac{{e}^{(g)}}{1+{e}^{(g)}}$$

(3)

Initial inspection of sleepiness data showed the highest reported effect category as 5 (severe). As such, the probabilities modeled over time were (P≥1, P≥2, P≥3, P≥4, P≥5). By definition, P≥0 =1, and this is not modeled. For the dizziness data, the highest reported category was three, and the probabilities modeled over time were (P≥1, P≥2, P≥3). Model building was conducted by adding the model components in equation (2) sequentially and observing the change in the MOF. Modeling was initialized on all data (placebo, baseline, and drug) with incorporation of the baseline model first followed by the drug model and then the placebo model.

First, baseline probabilities for each effect category were modeled as constants as described by Sheiner.^{9} From equation (2), β1 is the Y intercept (in logits) describing the baseline for reporting an effect category of at least minimum intensity (1 or more), β2 is the intercept added to β1 to determine the baseline logit contribution for reporting an effect category of at least mild (2 or more), and so forth.

The drug component was added by beginning with a simple linear slope function as described below:

$$\phantom{\rule{thinmathspace}{0ex}}\mathrm{E}=\mathrm{S}\times \mathrm{C}$$

(4)

Where E is the drug effect, S is the slope describing the relationship between drug effect in the logistic domain and drug concentrations C. Originally C was tested as concentration in the central compartment determined by posthoc individual PK parameter estimates. Addition of an effect compartment,^{17} where C in equation (4) now represents concentration in the effect compartment, was tested to account for any delay in effect with respect to peak plasma concentrations. This required addition of an extra parameter k_{eo}, the first order rate constant describing lag in effect in the biophase^{17} compared to central compartment concentrations. A Hill function without and with a sigmoidicity constant were also tested. Change in the MOF and inspection of the correlation matrix of estimates to ensure model stability was used to select final models.

For the placebo component of equation (2), several models were tested including a constant modeled as a theta^{14} parameter in logits and a Bateman-like function. Incorporation of the placebo component in this manner resulted in the covariance step being aborted. However, inspection of the individual placebo profiles revealed some subjects as non-responders and others as mild to moderate responders as shown in Figure 1. As such a mixture model^{18} on placebo response was tested. A mixture model assumes the population is composed of two or more subpopulations, each having a distinct population mean and random effects. Therefore, if the subject belonged to subpopulation 1 of non-responders, the placebo response was set to zero. If the subject belonged to subpopulation 2, the placebo response was modeled using a Bateman-like function, with a theta parameter in logits describing the amplitude of placebo effect, and first order rate constants describing the onset and offset of placebo effect.

Nonparametric bootstrapping^{11} and simulation based on bootstrap estimates were performed using SPLUS VI software (Insightful Corporation, Seattle, Washington). One thousand bootstrap runs were conducted to determine confidence intervals of parameter estimates. This analysis was repeated using successful bootstrap runs only. Simulations were then performed using five-hundred sets of bootstrap estimates to generate five hundred sets of data as described by Ette et al.^{11} Using this simulated data, cumulative probability plots of reporting at least an effect intensity m ( P≥m ) as a function of time were constructed to show the performance of the model across effect categories. Ninety percent prediction intervals of the time course of categorical scores were also constructed to visually depict the degree of uncertainty in the models due to random effects and parameter estimate uncertainty. In addition, posterior distributions of relevant PD endpoints were constructed and overlaid on the observed mean values as described by Yano et al.^{12} The PD endpoints selected were those determined in the PD noncompartmental analysis (i.e., MaxS and AUEC), as well as the proportion of subjects reporting an AE of at least mild and moderate intensity.

The current logistic model assumes independence of two consecutive categorical observations measured as a function of time. To test that this assumption is reasonable, the posterior distribution of the number of different transitions^{19}^{,}^{20} from the logistic model were generated for both lorazepam sleepiness and dizziness and overlaid on the observed mean value.

The relative ratio of label incidence of lorazepam sleepiness and dizziness was compared to the relative ratio of various data-derived PD parameters including MaxS, AUEC, and the maximum probability of reporting at least a particular effect category m (P≥1, P≥2, P≥3). The relative ratio of model-derived PD parameters such as slope was also compared to the ratio of label incidence of sleepiness and dizziness.

Table 1 shows the demographic information of the twenty study subjects. The time course of observed mean ± SD, mean predicted, and individual plasma concentrations after single oral dose administration of lorazepam 2 mg are shown in Figure 2. A noncompartmental analysis yielded mean (CV%) estimates for Cmax of 26.8 ng/ml (22.9), Tmax of 1.7 hr (40.8), t_{1/2} of 16.8 hrs (21.3) and a total systemic exposure or AUC_{0-∞} of 551 ng*hr/ml (31.0). Significant decreases in the MOF, residual and inter-individual variability, and inspection of concordance and residual plots indicated that a two-compartment model with first order absorption adequately described the time course of plasma concentrations of 2 mg oral lorazepam.

Observed individual, Observed mean ± SD, and predicted mean plasma concentrations versus time. Error bars represent one standard deviation above and below the observed mean data.

Table 2 shows the final pharmacokinetic population parameter estimates. The population mean parameter estimates were in good agreement with parameters derived using non-compartmental analysis for both CL/F (3.63 vs. 4.02 L/hr) and the derived half-life (16.7 vs. 16.8 hrs). Epsilon shrinkage^{21} was 45%. Results of the non-parametric bootstrap analysis are included in Table 2. The model was robust with 87% of the runs minimizing successfully. The parameter estimates and confidence intervals obtained from the bootstrap procedure which included all runs (even those which failed) were generally comparable to the estimates derived from NONMEM. Similar bootstrap estimates and confidence intervals were obtained using only successful runs.

Noncompartmental analyses conducted on the effect-time profiles of sleepiness and dizziness scores showed significant differences between these AEs in the maximum score (MaxS) and area under the effect curve (AUEC) endpoints. The MaxS of lorazepam sleepiness (±SE) was significantly higher then dizziness (2.35 ± 0.26 vs. 1.45 ± 0.22, p<0.01), as was the AUEC (20.35 ± 3.58 vs. 9.76 ± 2.45, p<0.01). The time to reach MaxS for lorazepam sleepiness scores was delayed (3.98 hr, Figure 3) compared to time of maximal lorazepam concentrations (1.71 hr, Figure 2). This observation justified addition of the effect compartment^{17} to describe drug effect in the lorazepam sleepiness model. In contrast, the dizziness effect peaked (2.55 hr, Figure3) at a time similar to that observed for peak plasma drug concentrations.

Ninety percent prediction intervals of sleepiness and dizziness scores in healthy volunteers as a function of time (n=20). Panel one shows lorazepam and placebo sleepiness, panel two lorazepam and placebo dizziness, and panel three lorazepam sleepiness **...**

Population PD model-building was initialized by addition of baseline logit intercepts for each effect category. As indicated in equation (2), these are added sequentially from i=1 to m in order to quantify the probability of experiencing a score category m or more in the absence of drug or placebo. Table 3 shows the final PD model estimates. As shown, β_{1} (which reperesents the probability in logits of reporting a score of 1 or more at baseline) was significantly higher for sleepiness (−2.81) than dizziness (−4.34) as indicated by the 95% confidence intervals.β_{4} and β_{5} were included in the sleepiness model as they resulted in significant decreases in the MOF. Addition of the drug component of the model as a slope as described in equation (4) resulted in a decrease in point reduction in the MOF of 216 and 174 points for sleepiness and dizziness models, respectively, indicating a significant drug effect. As shown in Table 3, slope estimates of sleepiness (0.21 logits/ml*ng) and dizziness (0.19) were not significantly different on inspection of the 95% confidence intervals. Addition of an effect compartment as described in equation (5) was significant for sleepiness but not dizziness, and the final estimate of k_{eo}, the first order rate constant describing lag in effect in the biophase compared to central compartment concentrations, was 2.44 hr^{−1}.

Pharmacodynamic Parameters in Healthy Volunteers after a 2 mg Oral Dose of Lorazepam or Placebo (n=20).

Placebo effect was modeled as a mixture of non-responders and responders in the final model, where the responder component was described using a Bateman-like function as shown in Figure 1. Modeling the placebo effect as a mixture, remedied the initial problem encountered with abortion of the covariance step and resulted in stabilization of the final model as indicated by the correlation matrix of estimates being devoid of high correlations (>0.8) among parameters. PLAC describes the amplitude of response and, as indicated in Table 3, was similar for sleepiness (3.6 logits) and dizziness (4.3 logits) as was k1, the first-order rate constant describing onset of placebo effect. When k2, the first-order rate constant describing offset of placebo effect, was modeled for sleepiness placebo, it resulted in over-parameterization as determined by inspection of the correlation matrix of estimates. However, given that the individual responder profiles showed a Bateman pattern of effect and not exponential decay, k2 was modeled as a fraction of k1 and the constant used to determine this fraction was determined using a sensitivity analysis. The majority of subjects were non-responders to placebo effect as indicated by P(1), the subpopulation proportion that was non-responder to placebo, and this estimate was similar between sleepiness (63%) and dizziness (71%). The inter-individual random effects parameter Ω1 was significantly higher for sleepiness effect (3.31 logits) compared to dizziness (0.32 logits).

As shown in Table 3, mean population parameter estimates obtained from the bootstrap procedure were generally comparable to the estimates from the final model. The NONMEM confidence intervals were also generally comparable to the bootstrap intervals for most parameters, with the exception of β_{5}, keo, PLAC, and P(1) of the sleepiness model; and PLAC, k1, and P(1), of the dizziness model, reflecting their asymmetric distribution. The success rate of bootstrap runs was 80% for the lorazepam sleepiness model and 83% for the dizziness model.

Figure 3 shows the observed (points) and overlaid mean simulated scores (lines) and 90% shaded prediction intervals (PIs) obtained from five hundred sets of bootstrap parameter estimates. The mean simulations adequately describe the time course of sleepiness and dizziness scores with the prediction intervals (shaded region) capturing the data and mean simulations. The one exception, however, is a data point of placebo sleepiness (at 6 hr) which is not captured by the model and lies slightly outside of the shaded interval. The shaded PI for lorazepam sleepiness is wider then that of lorazepam dizziness indicating the greater model uncertainty of sleepiness.

Figure 4 shows the observed and simulated cumulative probabilities of reporting a sleepiness and dizziness effect greater than or equal to a particular effect category over time (P>=m). The simulations describe the data adequately. As shown, the cumulative probabilities decrease with increasing effect category (m). Moreover, peak probabilities of reporting at least an effect category m at time of maximal effect are higher for lorazepam sleepiness (P≥1=1, P≥2=0.45, P≥3=0.25, P≥4=0.1, P≥5=0.05) then for lorazepam dizziness (P≥1=0.7, P≥2=0.3, P≥3=0. 15) as shown in Figure 4.

Cumulative probability plots of reporting sleepiness and dizziness. P≥l-5 is the cumulative probability of reporting an effect of at least minimum, mild, moderate, significant, and severe intensity on the categorical scale. Symbols indicate observed **...**

Figure 5 shows histograms of the simulated distribution of MaxS, AUEC, and the number of subjects reporting an AE of at least mild and moderate severity obtained from 500 sets of bootstrap parameter estimates, overlaid on the observed mean of these PD endpoints (represented by the vertical black bar). The panels indicate that that proposed models simulate posterior distributions of these parameters which are centered close to the observed means.

Posterior distributions of MaxS, AUEC, and the proportion reporting an AE of at least mild and moderate intensity for lorazepam sleepiness and dizziness in healthy volunteers after a 2 mg oral dose of lorazepam (n=20). The vertical line in each plot indicates **...**

Figures 6a and 6b show the posterior distributions of the number of different categorical transitions for lorazepam sleepiness and dizziness, respectively, overlaid on the observed mean. The panels indicate that the observed population mean lies within the posterior distributions of the transitions counts for all simulated transitions. The posterior distributions capture the observed mean adequately overall with the exception of few transitions which lie at the tail of the posterior distribution (transition 1 to 1 in Figures 6a and the transitions 1 to 0, 2 to 2, 3 to 1, and 3 to 0 in in6b6b).

Figure 6a. Posterior distributions of the number of different categorical transitions for lorazepam sleepiness. Transition permuations of the first 4 of the reported 6 categories are shown (categories 0,1,2,3). The vertical line in each plot indicates **...**

Finally, Table 4 relates the various data-derived PD parameters, and the model-derived PD parameter, slope, to the incidence rates of the adverse events in the more general population, as reported in the drug label.^{5} The ratio of the sleepiness/dizziness endpoints was calculated across these parameters. As shown by the relative ratios, Max (P≥2), Max (P≥3) and AUEC, show the greatest concordance to label incidence, followed by MaxS and Max (P≥1). However, the ratio of sleepiness to dizziness slope parameters was very close to 1 indicating that drug effect may not explain the differences between sleepiness and dizziness across these PD parameters.

The current PK/PD analysis of a 7-point ordered categorical measure aims to differentiate the pharmacodynamics of two of the most common AEs of lorazepam, sleepiness and dizziness. The 2 mg dose of drug selected in this study is within the range of recommended daily doses of lorazepam for maintenance treatment of generalized anxiety disorder. Studies modeling the intensity of drug AEs over time are relatively uncommon,^{19}^{,}^{20} and no studies have formally applied population PK/PD analyses in differentiation of AEs.

PK estimates obtained from the noncompartmental and compartmental analysis of the concentration-time profiles are consistent with previous reports^{22} and showed that lorazepam is rapidly absorbed (K_{a}=1.04 h^{−1}), has peak plasma concentrations occurring at about 2 hours post dose and that it has relatively moderate steady state volume of distribution (90 L), low systemic clearance (4 L/h), and moderate terminal half-life (16.7 hr).

The noncompartmental analysis of the effect-time profiles of sleepiness and dizziness scores indicated that the MaxS of sleepiness was significantly higher than dizziness (2.35 vs. 1.45, p<0.01) as was the AUEC (20.35 vs. 9.76, p<0.01). As shown in Table 4, the ratios of sleepiness/dizziness of these PD parameters are in concordance to the ratio of label incidence, with AUEC showing stronger concordance. While sleepiness and dizziness are the most commonly reported AEs of lorazepam according to the drug label,^{5} these effects show minimal to moderate amplitude on the categorical scale as shown in Figure 3. This observation may underscore the sensitivity of the seven-point categorical scale in discerning small differences between relatively mild to moderate AEs over time.

Differences in reporting various categories of effect intensity between these AEs are seen in the cumulative effect probability plots in Figure 4. Maximum probabilities of reporting at least a minimal effect, Max (P≥1), are higher for lorazepam sleepiness (P=1) than dizziness (P=0.7). Likewise, maximum probabilities of reporting at least mild and moderate intensity, Max(P≥2) and Max(P≥3), are higher for lorazepam induced sleepiness (P≥2=0.45, P≥3=0.25) than for dizziness (P≥2=0.3, P≥3=0.15). Since these represent the cumulative probabilities (which is a frequency) of reporting an effect of given intensity in a conceptual population, their relationship to label incidence is more direct than MaxS and AUEC which reflect effect intensity rather than effect frequency. As shown in Table 4, the sleepiness/dizziness ratio across these PD parameters are also in concordance to the ratio of label incidence with Max (P≥2) and Max (P≥3) showing the highest concordance followed by Max (P≥1). The stronger concordance of Max (P≥2) and Max (P≥3) to label incidence seems to suggest that the frequency of reporting categorical effects of higher intensity may be better related to incidence in the more general population.

The lack of significant difference between the model estimate of slope for sleepiness (0.21) and dizziness (0.19) at the 95% confidence level suggests that the drug does not contribute to the observed differences in intensity of these AEs. β_{1}, the baseline intercept parameter of effect category 1 (likelihood of having a response of at least minimum intensity), is the only parameter that is significantly different between these AEs at the 95% confidence level. The difference between this estimate for sleepiness and dizziness is 1.5 logits. As shown in Figure 7, which shows the relationship between the probability and logistic domains, the majority of the probability domain (0.1 ≤y≤ 0.9) occurs in the logit range −3≤x≤3, and 0 logits corresponds to the inflection point at y=0.5. In this range, 1.5 logits corresponds to a probability of 0.82. Since 0 logits corresponds to P=0.5, the difference P=0.82–0.5=0.32 corresponds to the greater likelihood of reporting sleepiness than dizziness due to the baseline difference. From Figure 4, the difference in observed cumulative effect (P≥1) at Tmax between sleepiness and dizziness is 1-0.7=0.3 equivalent to the value determined above. Since (P≥1) is the cumulative effect across all effect categories, differences in this endpoint between sleepiness and dizziness at Tmax closely resembles differences in Max Score.

It is unclear from a physiological standpoint why the difference in baseline effect exists between sleepiness and dizziness, but one possible explanation may be the time of day in which the data was collected. Given that the scale was first applied in the morning, some subjects may have experienced a residual sleepiness in the morning that was reported at baseline. Another explanation may be that subjects may have a greater tendency to report a sleepiness effect than dizziness even in the absence of any drug. However, no placebo response rates of these effects are reported in the lorazepam label to confirm this. Placebo data in the current study, as shown in Figure 3, show a slightly greater sleepiness response at earlier time points (at 0.5 hrs post dose administration), suggesting that differences in reporting sleepiness and dizziness in the absence of drug may be related to time of day.

The PK/PD temporal patterns of sleepiness and dizziness are shown in Figure 8, depicting the counterclockwise hysteresis for lorazepam sleepiness and the closed hysteresis loop for dizziness. The same PK-PD temporal relationships of these AEs were recorded on the Visual Analog Scale ^{2}^{, }^{3} administered in the same study^{4} as shown in Figure 8 further corroborating this finding. Other studies have shown the counterclockwise hysteresis pattern with amnesic,^{23} psychomotor,^{24}^{,}^{25} and cognitive^{24}^{,}^{25} effects after administration of 2 mg oral lorazepam in healthy adults. These studies estimated greater delays with slightly lower keo values (keo=1.3–1.7 h^{−1}) compared to the current study (2.4 h^{−1}). However, although correlated to the sedative effect of lorazepam,^{26} these amnesic and psychomotor effects are different from sleepiness. On the other hand, in the current study, dizziness showed no such significant delay and the time to MaxS was close to the Tmax of lorazepam concentrations. While this temporal difference between AEs is unclear, one pharmacologic explanation may be distributional, i.e. lorazepam induced sleepiness may require traversing of the blood brain barrier while dizziness may not. In fact, if indeed the subjects were reporting vertigo as dizziness,^{27} this would require binding to the GABA receptors in the vestibular system of the inner ear which does not require traversing the blood brain barrier. However, the distributional delay is less likely given the high log P of lorazepam. Moreover, GABA receptor inhibition of the vestibular axis by lorazepam would actually be therapeutic to vertigo,^{28} suggesting that the biophase of lorazepam dizziness is most likely the brain itself and not the inner ear. Another explanation is that these AEs may originate from distinct anatomical locations in the brain. It is known that lorazepam induced sleepiness is the result of binding to and inhibition of benzodiazepine receptors of GABA complexes in the thalamus and sensory cortex of the brain.^{6}^{,}^{7} The receptor binding causes downstream inhibition of glucose metabolism,^{6}^{,}^{7} which might account for the delayed sensation of sleepiness recorded by the scale. On the other hand, lorazepam induced dizziness is conferred by benzodiazepine action in receptors of the cerebellum (responsible for maintenance of balance) and these receptors may have a different subunit composition,^{29} altering rates of downstream signaling. If such a pharmacologic scenario is indeed valid, this delay may be described using a transduction model.^{30}

Upper panel: Sleepiness and dizziness scores recorded on the 7-point categorical scale versus lorazepam concentrations. Lower panel: Sleepiness and dizziness scores recorded on the Visual Analog Scale (VAS) versus lorazepam concentrations.

The performance of the final population models was assessed by a number of diagnostics including the mean simulations in Figure 3 which adequately capture the time course of drug and placebo scores, and the simulations in Figure 4 which capture the observed cumulative probabilities. As a further check to ensure the models simulate realistic data, posterior predictive checks (PPCs)^{12} in Figure 5 were performed and show that the simulated distributions of MaxS and AUEC were centered close to the observed mean. These PD parameters were selected based on them being clinically relevant, data-derived parameters which could be determined using the profile of an individual subject. These parameters condense the PD profiles to a single metric (either AUEC or MaxS) that capture evaluation of peak response and extent of response similar to a PK analysis. Use of analogous metrics (AUC and Cmax) for the PPC is recommended for PK models as discussed by Yano et al.^{12} Two other PPC metrics were analyzed: proportion of subjects reporting a categorical effect of at least mild and moderate intensity. As shown in Figure 5, the simulated distributions of these metrics were centered close to the observed mean as well. The 90% PIs in Figure 3 show the model uncertainty conferred by both random effects and uncertainty in estimating the parameter estimates. Typically, the 90% as opposed to 95% PI is assessed, because some confidence to detect a type I error is compromised to compensate for the increased uncertainty incurred by random effects. As shown in Figure 3, the PI of lorazepam sleepiness is wider then dizziness indicating greater model uncertainty. This may be the result of the greater random effects as shown in Table 3 (Ω is higher for sleepiness). Since overlaying PIs of these effects shows separation beyond 2 hours, one can make the conclusion that, given uncertainty in the model estimates and random effects, the models can detect a difference between the time course (at Tmax and beyond) of these effects at the 90% confidence level.

The current logistic or proportional odds model assumes independence of neighboring consecutive categorical observations as a function of time. The Markov or transition model^{19}^{,}^{20} which determines the conditional probability of reporting an observation at time t given the previous observation, and therefore assumes dependence between these observations, would be a valid model to test since data were collected frequently and longitudinally over time. The PPC analysis of the number of different categorical transitions for both lorazepam sleepiness and dizziness simulated form the logistic models, show that the observed population mean lies within the posterior distributions for the number of the different transitions. The posterior distributions capture the observed mean adequately overall with the exception of few transitions which lie at the tail of the posterior distribution as shown in Figure 6a (lorazepam sleepiness) and and6b6b (lorazepam dizziness). As an additional check, the individual simulations (not shown) were explored in relation to the observed individual data. Random individual simulations from random trials were inspected visually against the observed individual data to evaluate the individual pattern. One might expect the individual simulated score from a logistic model to go back and forth between the different transitions while the observation typically only goes up or down once as the intensity progresses. From inspection of the individual simulations against observed data, transitions between scores were noted in the observations as well and the individual simulations were found to mimic the individual patterns adequately.

Finally, certain study caveats should be acknowledged. First, the current study differentiates two AEs of a single drug. It would also be of interest to differentiate the same AE between 2 drugs in a similar therapeutic class, however the drugs included in the larger study^{4} were of different therapeutic classifications. Second, the low incidence of other AEs observed in this study precluded application of this modeling approach to other AEs (of lower intensity).^{4} Nevertheless, the model proposed, may serve as platform to determine the minimal quantifiable categorical signal, given a particular study design and power, by conducting a sensitivity analysis^{31} on model parameters. Third, only a single therapeutic dose was investigated. Use of higher doses would better elucidate the maximal categorical response for such AEs. This information would have allowed determination of maximal capacity (Emax) of the system and sensitivity (EC50) of AEs, enhancing the interpretability of the current analysis. Such an analysis may be feasible in ascending dose studies of compounds under development. Fourth, the study was conducted on healthy volunteers as opposed to patients with anxiety. Extrapolation of adverse event endpoints from healthy volunteers to patients may not be straightforward, as the tolerance of these different populations to AEs may be quite different. This has been seen in certain CNS indications such as schizophrenia where patients have shown higher tolerance to AEs of antipsychotic medications.^{32} Despite the limitations of the study, we believe the current analysis has demonstrated the feasibility of differentiating certain AEs using the pharmacometric approach described and may provide a framework for future studies with a similar aim.

Lorazepam sleepiness and dizziness have shown distinct temporal PK/PD patterns and were recorded with significantly different intensity on the 7-point categorical scale. Differences in the PD endpoints described may be due to differences in baseline parameters. The differences between data-derived PD measures of sleepiness and dizziness were consistent with differences in incidence rates reported in the drug label.

The authors thank Bill Frame for helpful discussions regarding the pharmacometric analysis. This work was supported by Pfizer Inc. MAK was supported by the Pharmacological Sciences Training Program of the National Institutes of Health Grant number GM007767. Responsibility for opinions, conclusions, and interpretation of the data lies with the authors.

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