{"id":212,"date":"2019-11-28T19:56:20","date_gmt":"2019-11-28T19:56:20","guid":{"rendered":"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/?p=212"},"modified":"2021-04-03T21:57:04","modified_gmt":"2021-04-03T21:57:04","slug":"due-no-base64","status":"publish","type":"post","link":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/?p=212","title":{"rendered":"DUE, the Dose Utility Explorer  (no base64)"},"content":{"rendered":"<h4 class=\"author\">Roger Day, Marie Gerges<\/h4>\n<h4 class=\"date\">2019-11-28<\/h4>\n<p><!-- Check out http:\/\/rmarkdown.rstudio.com\/authoring_pandoc_markdown.html http:\/\/pandoc.org\/MANUAL.html https:\/\/yihui.name\/knitr\/options\/ --><\/p>\n<div id=\"introduction\" class=\"section level3\">\n<h3>Introduction<\/h3>\n<p>DUE, the Dose Utility Explorer package for R, is an interactive environment for exploring relationships between priors, utilities, and choice of dose, when toxicity and response are determined by patient-specific thresholds. A user can manipulate inputs describing a hypothetical dose choice scenario. A number of important aspects have been omitted, in order to focus on the factors that are patient-specific.<\/p>\n<p>The primary output is the expected utility, as a function of dose. Secondary outcomes are various probabilities of interest.<\/p>\n<p>This app is available at <a href=\"https:\/\/trials.shinyapps.io\/DUEshiny\" target=\"_blank\" rel=\"noopener\">https:\/\/trials.shinyapps.io\/DUEshiny<\/a> .<\/p>\n<div id=\"primary-uses\" class=\"section level5\">\n<h5><em>Primary uses<\/em><\/h5>\n<p>This package, with its app, is part of a broader effort to make clinical trials more responsive to patients, more rational, and more humane. One use is to explore the consequences of unconscious assumptions we tend to make as we plan clinical trials.<\/p>\n<ul>\n<li>Is the success of a clinical trial plot dependent on assumptions whose truth we do not know?<\/li>\n<li>Can a research plan be made more robust against assumptions?<\/li>\n<li>When does our subjective valuation of toxicity versus response matter?<\/li>\n<li>When is the expected utility strongly dependent on dose? When is it multimodal as a function of dose?<\/li>\n<li>When is the effect of pharmacokinetics variation important?<\/li>\n<li>How much improvement could we achieve if we could stratify on patient subgroup, or limit recruitment to, one of multiple subgroups of patients?<\/li>\n<\/ul>\n<p>In addition, there are potential uses for individual patients. One aspect of personalized medicine is personalized dose.<\/p>\n<\/div>\n<div id=\"contributions-and-history\" class=\"section level5\">\n<h5><em>Contributions and history<\/em><\/h5>\n<p>This package stemmed from a chapter of the doctoral dissertation of Meihua Wang. It was developed for eventual publication by Roger Day. Originally, it rested on tck\/tk for the graphics, requiring installation of R and the X window system, as well as tck\/tk. Therefore its reach was severely limited.<\/p>\n<p>In 2017, Marie Gerges, working with Day, spearheaded the conversion to RStudio shiny, which provides universal access through a published web page. In addition several new features were added. The tcl\/tk version is no longer supported.<\/p>\n<\/div>\n<\/div>\n<div id=\"inputs\" class=\"section level3\">\n<h3>Inputs<\/h3>\n<p>The factors accounted for are:<\/p>\n<ul>\n<li>The current \u201cprior\u201d or population joint distribution of dose thresholds for toxicity (<span class=\"math inline\">\\(T\\)<\/span>) and for response (<span class=\"math inline\">\\(R\\)<\/span>). (The four possible joint outcomes are: <span class=\"math inline\">\\(RT\\)<\/span>, <span class=\"math inline\">\\(Rt\\)<\/span>, <span class=\"math inline\">\\(rT\\)<\/span>, and <span class=\"math inline\">\\(rt\\)<\/span>, where <span class=\"math inline\">\\(T\\)<\/span> means toxicity occurs, <span class=\"math inline\">\\(t\\)<\/span> means it doesn\u2019t, <span class=\"math inline\">\\(R\\)<\/span> means toxicity occurs, <span class=\"math inline\">\\(r\\)<\/span> means it doesn\u2019t. )<\/li>\n<li>The distribution may be multimodal.<\/li>\n<li>Response-limiting toxicity (<span class=\"math inline\">\\(RLT\\)<\/span>), representing the case where a patient with a low threshold for toxicity has enough toxicity to require coming off the treatment before response could be achieved.<\/li>\n<li>Refractoriness, representing a portion of tumors entirely unable to respond regardless of the dose.<\/li>\n<li>The combined personal utility of the toxicity (T) and response (R) outcome events.<\/li>\n<\/ul>\n<p>Not included are:<\/p>\n<ul>\n<li>The possibility that probabilities of events might be non-monotonic in dose.<\/li>\n<li>Priors for the parameters describing the joint distribution (hyperparameters).<\/li>\n<li>Updating of the threshold distribution for the pair of thresholds with data.<\/li>\n<li>The scientific, commercial, or prestige-related value of the information to be gained.<\/li>\n<li>Costs of the drug or of dealing with adverse events, not incurred by the patient.<\/li>\n<li>Multiple degrees of the response and toxicity outcomes, for example complete versus partial response, or mild versus severe adverse events.<\/li>\n<\/ul>\n<p>The inputs are difficult to assign values to. In principle one could estimate the \u201cprior\u201d, the joint threshold distribution. But this would require treating many patients at many doses. Each patient\u2019s outcome would tell us only which quadrant the patient\u2019s joint threshold is in. Therefore this program is best thought of as a platform for thought experiments.<\/p>\n<\/div>\n<div id=\"overview-of-the-interface\" class=\"section level3\">\n<h3>Overview of the interface<\/h3>\n<p>The package presents a window that includes:<\/p>\n<ul>\n<li><strong>upper left<\/strong>: a graph of the threshold distribution<\/li>\n<li><strong>upper right<\/strong>: a graph of the mappings from dose to the expected utility, together with probabilities of events and event combinations,<\/li>\n<li><strong>lower left<\/strong>: controllers for the threshold distribution<\/li>\n<li><strong>lower right<\/strong>: controllers for the utility values<\/li>\n<\/ul>\n<p>Here is a view of the full interface. (Close-ups of sections appear below.)<img decoding=\"async\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/single-population-20.png\" alt=\".\" \/><\/p>\n<p>Other views for various examples appear in the section <a href=\"#examples\"><em>Examples<\/em><\/a>.<\/p>\n<div id=\"the-threshold-distribution-inputs\" class=\"section level4\">\n<h4><em>The threshold distribution inputs<\/em><\/h4>\n<div id=\"the-joint-threshold-model\" class=\"section level5\">\n<h5>The joint threshold model<\/h5>\n<p>We assume that each patient has a pair of thresholds, <span class=\"math inline\">\\(\\theta_{R}\\)<\/span> for response and <span class=\"math inline\">\\(\\theta_{T}\\)<\/span> for toxicity. If the dose exceeds the threshold, then the corresponding event, <span class=\"math inline\">\\(R\\)<\/span> or <span class=\"math inline\">\\(T\\)<\/span>, occurs.<\/p>\n<p>The model for the joint distribution of toxicity and response thresholds is a mixture of joint lognormal distributions. The groups in the mixture might differ by differences in pharmacokinetics, affecting both thresholds, so that one expects them to be centered along a line. Pharmacokinetics processes mediate the conversion of the dose into the delivered concentration.<\/p>\n<p><!-- --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-342 size-medium\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-LEFT-e1617419574487-300x240.png\" alt=\"\" width=\"300\" height=\"240\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-LEFT-e1617419574487-300x240.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-LEFT-e1617419574487-768x616.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-LEFT-e1617419574487.png 993w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-341 size-medium\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-RIGHT-e1617419678262-300x279.png\" alt=\"\" width=\"300\" height=\"279\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-RIGHT-e1617419678262-300x279.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-RIGHT-e1617419678262-768x714.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacokinetic-example-two-groups-RIGHT-e1617419678262.png 933w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>The groups can also differ in the pharmacodynamics: the effect of the concentration at the affected tissues. Pharmacodynamics processes mediate the effects of exposure on the tissues. A discrete factor affecting pharmacodynamics of response affects only <span class=\"math inline\">\\(\\theta_{R}\\)<\/span>, so that groups are placed horizontally on the plot.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-346 size-medium alignnone\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-LEFT-e1617419896325-300x230.png\" alt=\"\" width=\"300\" height=\"230\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-LEFT-e1617419896325-300x230.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-LEFT-e1617419896325-1024x787.png 1024w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-LEFT-e1617419896325-768x590.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-LEFT-e1617419896325.png 1031w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-345 size-medium\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-RIGHT-e1617419979131-300x284.png\" alt=\"\" width=\"300\" height=\"284\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-RIGHT-e1617419979131-300x284.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-RIGHT-e1617419979131-768x726.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-response-two-groups-RIGHT-e1617419979131.png 912w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><!-- --> A discrete factor affecting pharmacodynamics of toxicity affects only <span class=\"math inline\">\\(\\theta_{T}\\)<\/span>, and the groups are placed vertically. <!-- --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-344 size-medium\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-LEFT-e1617420090785-300x226.png\" alt=\"\" width=\"300\" height=\"226\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-LEFT-e1617420090785-300x226.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-LEFT-e1617420090785-768x578.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-LEFT-e1617420090785.png 1000w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-343 size-medium\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-RIGHT-e1617420142600-300x284.png\" alt=\"\" width=\"300\" height=\"284\" srcset=\"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-RIGHT-e1617420142600-300x284.png 300w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-RIGHT-e1617420142600-768x726.png 768w, https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Pharmacodynamics-toxicity-two-groups-RIGHT-e1617420142600.png 914w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>The number of groups is set in the input box labeled <span class=\"math inline\">\\(Number\\ of\\ groups\\)<\/span> (with value <span class=\"math inline\">\\(input\\$nPops\\)<\/span> ); if increased or decreased, reasonable adjustments take place elsewhere.<\/p>\n<p>A vector the length of the number of groups describes the probabilities of each component of the mixture distribution.<\/p>\n<p>To select which group the parameters refer to, there is an input box labeled <span class=\"math inline\">\\(This\\ group\\ \\#\\)<\/span>. Another input box labeled <span class=\"math inline\">\\(This\\ group&#8217;s\\ fraction\\)<\/span> holds the fraction belonging to this group within the total population. Because the probabilities of the components must add to one, wen the groups\u2019 fraction changes another group\u2019s fraction must change in the opposite direction. When there are more than 2 groups, there is more than one choice for which group changes. We provide a box labeled <span class=\"math inline\">\\(Dependent\\ group\\ \\#\\)<\/span>, to select one component that will adjust to accommodate a change in another component\u2019s probability.<\/p>\n<p>The joint lognormal density for each group in the mixture is described by these parameters:<\/p>\n<ul>\n<li>the two medians of the corresponding normal distributions, <span class=\"math inline\">\\(\\mu_{R} = \\exp(E(\\log \\theta_{R}))\\)<\/span> and <span class=\"math inline\">\\(\\mu_{T} = \\exp(E(\\log \\theta_{T}))\\)<\/span>,<\/li>\n<li>its two coefficients of variation <span class=\"math inline\">\\(CV_{R}\\)<\/span> and <span class=\"math inline\">\\(CV_{T}\\)<\/span>, and<\/li>\n<li><span class=\"math inline\">\\(\\rho\\)<\/span>, the correlation between <span class=\"math inline\">\\(\\log\\mu_{R}\\)<\/span> and <span class=\"math inline\">\\(\\log\\mu_{T}\\)<\/span>.<\/li>\n<\/ul>\n<p>(The corresponding input values are: <span class=\"math inline\">\\(input\\$thetaRmedian\\)<\/span>, <span class=\"math inline\">\\(input\\$thetaTmedian\\)<\/span>, <span class=\"math inline\">\\(input\\$thetaR.CV\\)<\/span>, <span class=\"math inline\">\\(input\\$thetaT.CV\\)<\/span>, <span class=\"math inline\">\\(input\\$correlation\\)<\/span>.)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"response-limiting-toxicity\" class=\"section level3\">\n<h3>Response-limiting toxicity<\/h3>\n<p>Response-limiting toxicity represents the case where a patient with a low threshold for toxicity has enough toxicity to prevent response, even if the response threshold is low enough. For example, a toxicity experience might require coming off the treatment or reducing the dose below the threshold. Or, a treatment-caused fatality might occur before a response which otherwise would have happened can occur. This idea is represented by a parameter called <span class=\"math inline\">\\(Kdeath\\)<\/span> in the code. Its input box is labeled as <span class=\"math inline\">\\(RLT:\\ log_{10}\\)<\/span> (response-limiting toxicity event) for converting <span class=\"math inline\">\\((RT\\to rT)\\)<\/span>. A response-limiting toxicity is a toxicity so severe that, although the patient would otherwise have responded, death or suspension of the treatment makes that impossible. This parameter is the gap between log10 of the patient\u2019s toxicity threshold and log10 of the dose at which toxicity is so severe that response cannot happen. It appears on the left-hand plot as a vertical distance below the <span class=\"math inline\">\\(Rt\/RT\\)<\/span> border to the border where the <span class=\"math inline\">\\(rT\\)<\/span> region encroaches into <span class=\"math inline\">\\(RT\\)<\/span>.<\/p>\n<p>The assumption is that this gap is the same for all patients. (This works similarly to the relationship between thresholds for different grades of toxicity introduced in Richard Simon\u2019s paper on accelerated titration designs; thus the letter <span class=\"math inline\">\\(K\\)<\/span> is borrowed notation.)<\/p>\n<div id=\"refractoriness\" class=\"section level4\">\n<h4><em>Refractoriness<\/em><\/h4>\n<p>Some proportion of patients may have disease which will not respond to the treatment at any dose. This parameter appears to be necessary to better reflect experience in cancer treatment.<\/p>\n<\/div>\n<div id=\"interaction-with-the-joint-threshold-distribution\" class=\"section level4\">\n<h4><em>Interaction with the joint threshold distribution<\/em><\/h4>\n<p>On the upper left side of the window is the contour plot for the joint threshold distribution. If one clicks on the graph close to one of the modes, then the parameter <span class=\"math inline\">\\(This\\ group\\ \\#\\)<\/span> should change to refer to the corresponding group If the click closer to the diagonal than any mode, then dose corresponding to the closest diagonal point (the geometric mean) becomes the new <span class=\"math inline\">\\(Selected\\ dose\\)<\/span>.<\/p>\n<p>The <span class=\"math inline\">\\(Selected\\ dose\\)<\/span>, whether selected by clicking or by entering into the <span class=\"math inline\">\\(Selected\\ dose\\)<\/span> input, will divide the graph into four quadrants, corresponding to four outcomes:<\/p>\n<ul>\n<li><em>rt<\/em>: neither response nor toxicity<\/li>\n<li><em>rT<\/em>: only toxicity<\/li>\n<li><em>Rt<\/em>: only response<\/li>\n<li><em>RT<\/em>: both response and toxicity<\/li>\n<\/ul>\n<p>If the <span class=\"math inline\">\\(Response-limiting\\ toxicity\\)<\/span> parameter <span class=\"math inline\">\\(input\\$Kdeath\\)<\/span> is small enough, then there also appears an incursion of the <span class=\"math inline\">\\(rT\\)<\/span> region towards the left at the bottom, invading the <span class=\"math inline\">\\(RT\\)<\/span> region. This is discussed above: <a href=\"#response-limiting-toxicity\">Response-limiting toxicity<\/a> . If <span class=\"math inline\">\\(input\\$Kdeath\\)<\/span> equals 1, then the vertical distance between the horizontal <span class=\"math inline\">\\(Selected\\ dose\\)<\/span> line and the incursion line is one order of magnitude.<\/p>\n<\/div>\n<div id=\"log-normal-conversions\" class=\"section level4\">\n<h4><em>Log-normal conversions<\/em><\/h4>\n<p>The choice of log-normal distributions entails conversion between log and native dose scales. The graph is a log-log graph, so the labeling is on the unlogged dose scale while the spacing is on the logged scale. The contour lines correspond to the density in log-bivariate-normal space.<\/p>\n<\/div>\n<\/div>\n<div id=\"probabilities-and-utilities\" class=\"section level2\">\n<h2><em>Probabilities and utilities<\/em><\/h2>\n<div id=\"calculation-of-probabilities\" class=\"section level3\">\n<h3><em>Calculation of probabilities<\/em><\/h3>\n<p>For each dose in a vector of doses of interest, the probabilities of each of the four regions are computed by integration. Varying the dose gives the mapping from dose to each outcome probability.<\/p>\n<\/div>\n<div id=\"utility-parameters-and-expected-utility\" class=\"section level3\">\n<h3><em>Utility parameters and expected utility<\/em><\/h3>\n<p>For decision analysis, a necessary input is the utility function which values outcomes.<\/p>\n<p>The scale\/text pairs on the lower right specify the utility values for these four outcomes. There are also buttons to set the utilities to specific values: <span class=\"math inline\">\\(Additive, Simple, Cautious, Aggressive\\)<\/span>.<\/p>\n<p>All four of these utilities set <span class=\"math inline\">\\(U_{rt}=0\\)<\/span>, since <span class=\"math inline\">\\(rt\\)<\/span> is the outcome without any treatment (dose = 0). all four also set <span class=\"math inline\">\\(Rt\\)<\/span> equal to 1, so that the optimal result, a dose at which <span class=\"math inline\">\\(Pr(Rt) = 1\\)<\/span>, has the same utility regardless of any other parameter.<\/p>\n<p>The <span class=\"math inline\">\\(Simple\\)<\/span> utility assignment considers only the <span class=\"math inline\">\\(Rt\\)<\/span> outcome to be valuable, with utility value = 1, and sets the other three utility values to zero. It is commonly used in studies of Phase I and II clinical trial designs. It expresses the idea that only <span class=\"math inline\">\\(Rt\\)<\/span> is a worthy outcome. But it equates <span class=\"math inline\">\\(rt\\)<\/span> with <span class=\"math inline\">\\(rT\\)<\/span>, as if toxicity is no concern as long as <span class=\"math inline\">\\(R\\)<\/span> is achieved.<\/p>\n<p>The other three utility assignments all penalize the outcome <span class=\"math inline\">\\(rT\\)<\/span> with a utility of -1. They differ in the valuation of the <span class=\"math inline\">\\(RT\\)<\/span> outcome:<\/p>\n<table>\n<thead>\n<tr class=\"header\">\n<th>Option<\/th>\n<th><span class=\"math inline\">\\(U(RT)\\)<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td><span class=\"math inline\">\\(Cautious\\)<\/span><\/td>\n<td>-1<\/td>\n<\/tr>\n<tr class=\"even\">\n<td><span class=\"math inline\">\\(Additive\\)<\/span><\/td>\n<td>\u00a00<\/td>\n<\/tr>\n<tr class=\"odd\">\n<td><span class=\"math inline\">\\(Aggressive\\)<\/span><\/td>\n<td>+1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In addition to these defaults, the input boxes allow any assignments to the four utilities.<\/p>\n<\/div>\n<div id=\"expected-utility\" class=\"section level3\">\n<h3>Expected utility<\/h3>\n<p>The expected utility <span class=\"math inline\">\\(EU\\)<\/span> for each dose is calculated as the weighted average of the four utilities, weighted by the four event probabilities:<\/p>\n<p><span class=\"math inline\">\\(EU = U(Rt) Pr(Rt) + U(rt) Pr(rt) + U(rT) Pr(rT) + U(RT) Pr(RT)\\)<\/span><\/p>\n<\/div>\n<div id=\"display-of-the-expected-utility-and-probabilities\" class=\"section level3\">\n<h3>Display of the expected utility and probabilities<\/h3>\n<p>On the upper right side of the window is a graph showing these probabilities (left-side scale) and expected utilities (right-side scale). The vertical green line corresponds to the <span class=\"math inline\">\\(Selected\\ dose\\)<\/span> indicated by the green cross in the contour plot. The black dotted vertical line picks out the dose maximizing expected utility, which we can label <span class=\"math inline\">\\(OptDose\\)<\/span> for short.<\/p>\n<p>The horizontal red line shows the dose corresponding to <span class=\"math inline\">\\(Pr(T) = 1\/3\\)<\/span>. This dose we will call the TRUE \u201c<span class=\"math inline\">\\(MTD\\)<\/span>\u201d (MTD = \u201cmaximum tolerated dose\u201d), since in some views this would ideally be the best dose to report forward for further study, if one could somehow identify it without doing an experiment at all. The idea is that a dose should be sufficiently toxic reflecting potential for enough activity to counterbalance the risk, but not so toxic as to be unusable. Below we explore how suitable this rule of thumb is, under what circumstances. The traditional Phase I trial generally produces a MTD intended to estimate the true MTD.<\/p>\n<p>Sometimes the true <span class=\"math inline\">\\(MTD\\)<\/span> is very close to <span class=\"math inline\">\\(OptDose\\)<\/span>, justifying the <span class=\"math inline\">\\(Pr(T) = 1\/3\\)<\/span> target; and sometimes not. This is discussed further later.<\/p>\n<p>The eight boxes at the top of the graph are three-way toggles, which cycle each of the curves through the settings <code>thick line<\/code>, <code>thin line<\/code>, and <code>invisible<\/code>.<\/p>\n<p>To the right of the plot is a table of quantities of interest for the current plot. They include:<\/p>\n<ul>\n<li>highest.EU,<\/li>\n<li>OptDose.EU,<\/li>\n<li>EUatMTDdose,<\/li>\n<li>MTDdose,<\/li>\n<li>lowest.EU,<\/li>\n<li>highest.Rt,<\/li>\n<li>best.dose.Rt.<\/li>\n<\/ul>\n<\/div>\n<div id=\"other-features-of-the-interface\" class=\"section level3\">\n<h3><em>Other features of the interface<\/em><\/h3>\n<div id=\"in-the-middle-column\" class=\"section level4\">\n<h4><em>In the middle column:<\/em><\/h4>\n<ul>\n<li>There is an <span class=\"math inline\">\\(Information\\)<\/span> button, which launches this document.<\/li>\n<li>A user can click a button to change the dose range and number of ticks on the dose scales.<\/li>\n<li>A numeric input box allows setting the <span class=\"math inline\">\\(Selected\\ dose\\)<\/span>, or selected dose. This only has the effect of moving the green lines in both plots.<\/li>\n<li>The <span class=\"math inline\">\\(Phase\\ I\\)<\/span> button brings up a pop-up window with the probabilities of stopping at each dose level. The dose levels are initially set at the doses at which the ticks occur in the graphs. The user can change these doses within the pop-up window.<\/li>\n<\/ul>\n<\/div>\n<div id=\"at-the-top\" class=\"section level4\">\n<h4><em>At the top<\/em><\/h4>\n<p>Clicking the checkbox at the left of the grey band opens a <span class=\"math inline\">\\(file\\ panel\\)<\/span>, a facility for saving and loading files with parameter values for the joint threshold distribution and the utility values. (For convenience, the middle column also has a toggle for this <span class=\"math inline\">\\(file \\ panel\\)<\/span>.)<\/p>\n<\/div>\n<div id=\"at-the-bottom\" class=\"section level4\">\n<h4><em>At the bottom<\/em><\/h4>\n<p>Clicking the checkbox at the left of the grey band opens an instance of <code>shinyDebuggingPanel<\/code>, allowing access to R and Javascript expressions.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"examples\" class=\"section level2\">\n<h2><em>Examples<\/em><\/h2>\n<div id=\"a-single-population\" class=\"section level4\">\n<h4><em>A single population<\/em><\/h4>\n<div class=\"figure\">\n<p><img decoding=\"async\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/single-population-20.png\" alt=\".\" \/><\/p>\n<p class=\"caption\">.<\/p>\n<\/div>\n<p>In this ideal situation, there is a fairly sharp peak in the expected utility EU, with an optimal dose somewhere between <span class=\"math inline\">\\(\\mu_{R} = 100\\)<\/span> and <span class=\"math inline\">\\(\\mu_{T} = 200\\)<\/span>. Only the <code>Aggressive<\/code> utility function has substantially different optimal, driving the optimal dose near the top of the dose range.<\/p>\n<p>When the correlation equals 0, all the variation is due to independent response pharmacodynamics and toxicity pharmacodynamics. When it equals 1, the variation is thresholds is all pharmacokinetics, so shared between the two thresholds. As the correlation increases from 0 to 1, the utility curve flattens slightly, while the optimal EU dose is unchanged.<\/p>\n<p>Lowering the median value <span class=\"math inline\">\\(\\mu_{T} = 100\\)<\/span> to equal <span class=\"math inline\">\\(\\mu_{R}\\)<\/span>, then toxicity is highly likely, response less so. In that case, the utility choice has profound effects. Only the <code>Simple<\/code> utility shows a local EU peak at 100. With the <code>Additive<\/code> utility, the EU curve is flat. A 3+3 phase I trial on 7 tiers logarithmically spaced from 50 to 200, would stop at tier 100, with maximum tolerated dose (MTD) = 79.4 with probability 72%.<\/p>\n<\/div>\n<\/div>\n<div id=\"is-prtoxicity-33-a-good-proxy-for-optimal-expected-utility\" class=\"section level2\">\n<h2>Is Pr(toxicity) = 33% a good proxy for optimal expected utility?<\/h2>\n<p>In this figure, the \u201cT\u201d curve is made visible, for comparison with the EU curve. The optimal dose is nearly the same as the dose at which the probability of toxicity is 33%.<\/p>\n<table>\n<thead>\n<tr class=\"header\">\n<th>Additive utility settings<\/th>\n<th>Probabilities and E(U)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td><img decoding=\"async\" style=\"width: 95.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Utility_settings-additive.png\" alt=\".\" \/><\/td>\n<td><img decoding=\"async\" style=\"width: 95.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/EU-is-at-T_0.33-additive.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The venerable \u201c3+3\u201d Phase I design is sometimes described as aiming to estimate the dose tier closest to Pr(toxicity) = 33%. To rationalize this in vague terms, lowering the dose might decrease the response probability too much, while raising it would of course increase the risk, and possibly entail \u201cresponse limiting events\u201d that would mask or make irrelevant an increase in response rate.<\/p>\n<div id=\"effect-of-the-utility-function\" class=\"section level3\">\n<h3>Effect of the utility function<\/h3>\n<p>The utility function in the figure is \u201cAdditive\u201d: <span class=\"math inline\">\\(U_{RT}\\)<\/span>=0. At the other three default utility functions, here are the comparable curves:<\/p>\n<table>\n<colgroup>\n<col width=\"33%\" \/>\n<col width=\"33%\" \/>\n<col width=\"33%\" \/> <\/colgroup>\n<thead>\n<tr class=\"header\">\n<th>\u201cCautious\u201d: <span class=\"math inline\">\\(U_{RT}\\)<\/span> = -1<\/th>\n<th>\u201cAggressive\u201d: <span class=\"math inline\">\\(U_{RT}\\)<\/span> = +1<\/th>\n<th>\u201cSimple\u201d: <span class=\"math inline\">\\(U_{RT}\\)<\/span> = <span class=\"math inline\">\\(U_{Rt}\\)<\/span> = 0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td><img decoding=\"async\" style=\"width: 90.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/EU-lower-than-T_0.33-cautious.png\" alt=\".\" \/><\/td>\n<td><img decoding=\"async\" style=\"width: 90.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/EU-is-above-T_0.33-aggressive.png\" alt=\".\" \/><\/td>\n<td><img decoding=\"async\" style=\"width: 90.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/EU-is-at-T_0.33-simple.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The cautious assignment lowers the optimal dose somewhat. The aggressive assignment sends it all the way to the maximum dose on the scale. Changing the utility values to the simple scheme, which credits only the outcome <code>Rt<\/code> and does not penalize more for <code>rT<\/code>, does not change the optimum dose, but enhances its optimality (from <span class=\"math inline\">\\(E(U)\\)<\/span>=0.38 to <span class=\"math inline\">\\(E(U)\\)<\/span>=0.47).<\/p>\n<p>From here on we stick with the additive utility assignment. Certainly a user can explore different values of <span class=\"math inline\">\\(U_{RT}\\)<\/span> and <span class=\"math inline\">\\(U_{rT}\\)<\/span> if desired, setting those values with reference to the desired outcome <span class=\"math inline\">\\(Rt\\)<\/span> assigned utility of 1. A response is no cure, but a toxicity is no fun.<\/p>\n<\/div>\n<div id=\"effect-of-the-correlation\" class=\"section level3\">\n<h3>Effect of the correlation<\/h3>\n<p>In the foregoing, we set the correlation between the thresholds <span class=\"math inline\">\\(\\theta_{R}\\)<\/span> and <span class=\"math inline\">\\(\\theta_{T}\\)<\/span> to zero. Let\u2019s investigate what happens as we move the correlation to the other extreme, nearly one (0.99). This could occur if the pharmacodynamics (PD) of toxicity and response are strongly correlated across the population. More likely, the two PD processes are independent, but the population variation in pharmacokinetics generates the correlation.<\/p>\n<p>With the \u201cAdditive\u201d utility, changing to correlation = 0.99 does not change the <span class=\"math inline\">\\(E(U)\\)<\/span> curve at all; th maximum is still 0.38. But switching to \u201cSimple\u201d utility does not enhance the optimal E(U).<\/p>\n<table>\n<thead>\n<tr class=\"header\">\n<th>Thresholds<\/th>\n<th>Probabilities and E(U)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td><img decoding=\"async\" style=\"width: 90.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Thresholds_corr_0.99.png\" alt=\".\" \/><\/td>\n<td><img decoding=\"async\" style=\"width: 90.0%;\" src=\"http:\/\/www.professorbeautiful.org\/IveBeenThinkin\/wp-content\/uploads\/Probs_corr_0.99.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>These observation are not generally true. A broad investigation may clarify when the correlation governing PK and PD really matters.<\/p>\n<\/div>\n<\/div>\n<div id=\"effect-of-multimodality\" class=\"section level2\">\n<h2>Effect of multimodality<\/h2>\n<\/div>\n<p><!-- dynamically load mathjax for compatibility with self-contained --><br \/>\n<script>\n  (function () {\n    var script = document.createElement(\"script\");\n    script.type = \"text\/javascript\";\n    script.src  = \"https:\/\/mathjax.rstudio.com\/latest\/MathJax.js?config=TeX-AMS-MML_HTMLorMML\";\n    document.getElementsByTagName(\"head\")[0].appendChild(script);\n  })();\n<\/script><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Roger Day, Marie Gerges 2019-11-28 Introduction DUE, the Dose Utility Explorer package for R, is an interactive environment for exploring relationships between priors, utilities, and choice of dose, when toxicity and response are determined by patient-specific thresholds. A user can manipulate inputs describing a hypothetical dose choice scenario. A number of important aspects have been [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-212","post","type-post","status-publish","format-standard","hentry","category-r-blog"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/posts\/212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=212"}],"version-history":[{"count":10,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/posts\/212\/revisions"}],"predecessor-version":[{"id":348,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=\/wp\/v2\/posts\/212\/revisions\/348"}],"wp:attachment":[{"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professorbeautiful.org\/IveBeenThinkin\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}