{"generatedBy":"web/src/lib/stats/workflow.ts (computeWorkflow)","seeds":{"chains":[90125,90126,90127,90128],"ppc":90125},"thresholds":{"rhat":1.01,"ess":400},"corrected":{"samplers":[{"sampler":"mh","label":"Metropolis-Hastings","settings":"100,000 iterations, first 50,000 discarded, proposal N(θ, c²·vcov(GLM)) with c = 2.4/√2","iter":100000,"burnin":50000,"drawsPerChain":50000,"chains":[{"seed":90125,"init":[0.39309806169752365,-0.16006779893525433],"acceptRate":0.35846716934338685},{"seed":90126,"init":[-1.0462292713635244,-0.09985750026194619],"acceptRate":0.3593871877437549},{"seed":90127,"init":[0.4288642781801585,0.44475434358280697],"acceptRate":0.35192703854077084},{"seed":90128,"init":[0.36322972714596324,0.15189095440666925],"acceptRate":0.3609672193443869}],"params":[{"index":0,"label":"β₀ (Intercept)","mean":-0.8159029364258836,"sd":0.46373591291869687,"q025":-1.757702185387735,"q500":-0.8071994584042514,"q975":0.071923178515431,"mcseMean":0.002845424736154824,"mcseQ025":0.008470259980696615,"mcseQ500":0.002981611612169366,"mcseQ975":0.007472104699851129,"rhat":1.0001623351637987,"essBulk":26643.24120126508,"essTail":33115.30511545262,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":1,"label":"β₁ dose","mean":0.31535543245261866,"sd":0.13195538145897978,"q025":0.06538469175914857,"q500":0.31164674823020544,"q975":0.5852834263445804,"mcseMean":0.0008124917233396713,"mcseQ025":0.0013404061920271881,"mcseQ500":0.0009439905214922995,"mcseQ975":0.0021298201393817884,"rhat":1.0001444646070803,"essBulk":26503.60893696612,"essTail":33472.422160999486,"flags":{"rhat":false,"essBulk":false,"essTail":false}}],"flagged":[]},{"sampler":"hmc","label":"Hamiltonian Monte Carlo","settings":"10,000 iterations, first 1,000 discarded, L = 20 leapfrog steps of ε = 1/20, identity mass matrix","iter":10000,"burnin":1000,"drawsPerChain":9000,"chains":[{"seed":90125,"init":[0.39309806169752365,-0.16006779893525433],"acceptRate":0.9585555555555556},{"seed":90126,"init":[-1.0462292713635244,-0.09985750026194619],"acceptRate":0.9621111111111111},{"seed":90127,"init":[0.4288642781801585,0.44475434358280697],"acceptRate":0.9644444444444444},{"seed":90128,"init":[0.36322972714596324,0.15189095440666925],"acceptRate":0.9631111111111111}],"params":[{"index":0,"label":"β₀ (Intercept)","mean":-0.8156630517013257,"sd":0.46144290004247507,"q025":-1.7529809560733514,"q500":-0.8078299301381842,"q975":0.06771342359988672,"mcseMean":0.001509383677043414,"mcseQ025":0.008542431303535714,"mcseQ500":0.002572762351876756,"mcseQ975":0.008154573514700485,"rhat":1.0002313920731756,"essBulk":94387.26142687861,"essTail":29913.37762548516,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":1,"label":"β₁ dose","mean":0.3149099455814459,"sd":0.13255513632125077,"q025":0.062360610069156316,"q500":0.3126534222330958,"q975":0.58166300448383,"mcseMean":0.0004530505335307253,"mcseQ025":0.0019866549888164636,"mcseQ500":0.0005920547961685563,"mcseQ975":0.0021523865262405018,"rhat":1.000027417827771,"essBulk":87222.95576010934,"essTail":31864.396812963238,"flags":{"rhat":false,"essBulk":false,"essTail":false}}],"flagged":[]}],"ppc":{"seed":90125,"nDraws":36000,"nChains":4,"patientsPerDose":10,"cells":[{"dose":0,"outcome":"improved","observed":3,"repMean":3.1506666666666665,"rep05":1,"rep25":2,"rep50":3,"rep75":4,"rep95":6,"pValue":0.5085694444444444,"mcse":0.0021665727192254707},{"dose":1,"outcome":"improved","observed":5,"repMean":3.7960555555555557,"rep05":1,"rep25":3,"rep50":4,"rep75":5,"rep95":7,"pValue":0.24783333333333332,"mcse":0.0019426569181642999},{"dose":2,"outcome":"improved","observed":4,"repMean":4.551972222222222,"rep05":2,"rep25":3,"rep50":5,"rep75":6,"rep95":7,"pValue":0.6171805555555555,"mcse":0.002171395171671983},{"dose":3,"outcome":"improved","observed":4,"repMean":5.31875,"rep05":3,"rep25":4,"rep50":5,"rep75":6,"rep95":8,"pValue":0.7731944444444444,"mcse":0.0018758802239625917},{"dose":4,"outcome":"improved","observed":7,"repMean":6.085277777777778,"rep05":3,"rep25":5,"rep50":6,"rep75":7,"rep95":9,"pValue":0.31094444444444447,"mcse":0.0021289029608004438},{"dose":5,"outcome":"improved","observed":6,"repMean":6.7812222222222225,"rep05":4,"rep25":6,"rep50":7,"rep75":8,"rep95":9,"pValue":0.6836666666666666,"mcse":0.002050957461312924},{"dose":6,"outcome":"improved","observed":8,"repMean":7.3444722222222225,"rep05":4,"rep25":6,"rep50":8,"rep75":9,"rep95":10,"pValue":0.38240277777777776,"mcse":0.0020825863840352936},{"dose":0,"outcome":"not improved","observed":7,"repMean":6.849333333333333,"rep05":4,"rep25":6,"rep50":7,"rep75":8,"rep95":9,"pValue":0.49143055555555554,"mcse":0.0021665727192254707},{"dose":1,"outcome":"not improved","observed":5,"repMean":6.203944444444445,"rep05":3,"rep25":5,"rep50":6,"rep75":7,"rep95":9,"pValue":0.7521666666666667,"mcse":0.0019426569181642999},{"dose":2,"outcome":"not improved","observed":6,"repMean":5.448027777777778,"rep05":3,"rep25":4,"rep50":5,"rep75":7,"rep95":8,"pValue":0.38281944444444443,"mcse":0.002171395171671983},{"dose":3,"outcome":"not improved","observed":6,"repMean":4.68125,"rep05":2,"rep25":4,"rep50":5,"rep75":6,"rep95":7,"pValue":0.22680555555555557,"mcse":0.0018758802239625917},{"dose":4,"outcome":"not improved","observed":3,"repMean":3.914722222222222,"rep05":1,"rep25":3,"rep50":4,"rep75":5,"rep95":7,"pValue":0.6890555555555555,"mcse":0.002128902960800444},{"dose":5,"outcome":"not improved","observed":4,"repMean":3.218777777777778,"rep05":1,"rep25":2,"rep50":3,"rep75":4,"rep95":6,"pValue":0.31633333333333336,"mcse":0.002050957461312924},{"dose":6,"outcome":"not improved","observed":2,"repMean":2.655527777777778,"rep05":0,"rep25":1,"rep50":2,"rep75":4,"rep95":6,"pValue":0.6175972222222222,"mcse":0.0020825863840352936}],"stats":[{"id":"total","label":"Total improved","description":"Patients improved across all seven doses (observed 37 of 70). The intercept and slope are fitted to this, so a well-specified model should put it near the middle.","kind":"count","observed":37,"pValue":0.5028472222222222,"ess":43345.915677418016,"mcse":0.0023124894567910915,"interval":[0.49831482617228307,0.5073796182721614],"intervalMethod":"normal","distribution":[{"value":14,"share":0.00005555555555555556},{"value":15,"share":0.00002777777777777778},{"value":16,"share":0.00005555555555555556},{"value":17,"share":0.00008333333333333333},{"value":18,"share":0.00016666666666666666},{"value":19,"share":0.0005},{"value":20,"share":0.0008055555555555556},{"value":21,"share":0.0010833333333333333},{"value":22,"share":0.0019166666666666666},{"value":23,"share":0.003416666666666667},{"value":24,"share":0.004944444444444444},{"value":25,"share":0.007194444444444444},{"value":26,"share":0.009777777777777778},{"value":27,"share":0.014555555555555556},{"value":28,"share":0.019833333333333335},{"value":29,"share":0.025277777777777777},{"value":30,"share":0.030944444444444445},{"value":31,"share":0.04055555555555555},{"value":32,"share":0.04841666666666666},{"value":33,"share":0.05494444444444444},{"value":34,"share":0.059944444444444446},{"value":35,"share":0.06469444444444444},{"value":36,"share":0.07155555555555555},{"value":37,"share":0.07280555555555555},{"value":38,"share":0.06933333333333333},{"value":39,"share":0.06580555555555556},{"value":40,"share":0.06202777777777778},{"value":41,"share":0.05552777777777778},{"value":42,"share":0.04763888888888889},{"value":43,"share":0.042194444444444444},{"value":44,"share":0.034166666666666665},{"value":45,"share":0.0255},{"value":46,"share":0.019583333333333335},{"value":47,"share":0.015194444444444444},{"value":48,"share":0.010888888888888889},{"value":49,"share":0.0075},{"value":50,"share":0.004722222222222222},{"value":51,"share":0.002361111111111111},{"value":52,"share":0.001888888888888889},{"value":53,"share":0.0010833333333333333},{"value":54,"share":0.0006388888888888889},{"value":55,"share":0.00022222222222222223},{"value":56,"share":0.00005555555555555556},{"value":57,"share":0.00005555555555555556},{"value":58,"share":0.00005555555555555556}]},{"id":"drops","label":"Dose-to-dose drops","description":"How often the count falls from one dose to the next (observed: 5 to 4 and 7 to 6, so 2). Checks whether the noise around a smooth logistic curve is as large as binomial noise predicts.","kind":"count","observed":2,"pValue":0.3869861111111111,"ess":38331.41627186777,"mcse":0.001848191373151686,"interval":[0.3833637225831962,0.390608499639026],"intervalMethod":"normal","distribution":[{"value":0,"share":0.07094444444444445},{"value":1,"share":0.3294722222222222},{"value":2,"share":0.42519444444444443},{"value":3,"share":0.15838888888888888},{"value":4,"share":0.01572222222222222},{"value":5,"share":0.0002777777777777778}]},{"id":"dose0","label":"Improved at dose 0","description":"The lowest-dose cell (observed 3 of 10): does the curve fit its lower end?","kind":"count","observed":3,"pValue":0.5085694444444444,"ess":41733.218012679725,"mcse":0.0021665727192254707,"interval":[0.5043230399448755,0.5128158489440133],"intervalMethod":"normal","distribution":[{"value":0,"share":0.04572222222222222},{"value":1,"share":0.1333888888888889},{"value":2,"share":0.20425},{"value":3,"share":0.21613888888888888},{"value":4,"share":0.18330555555555555},{"value":5,"share":0.12125},{"value":6,"share":0.06202777777777778},{"value":7,"share":0.024583333333333332},{"value":8,"share":0.007638888888888889},{"value":9,"share":0.0014166666666666668},{"value":10,"share":0.0002777777777777778}]},{"id":"dose6","label":"Improved at dose 6","description":"The highest-dose cell (observed 8 of 10): does the curve fit its upper end?","kind":"count","observed":8,"pValue":0.38240277777777776,"ess":40560.77946068047,"mcse":0.0020825863840352936,"interval":[0.37832098347037507,0.38648457208518044],"intervalMethod":"normal","distribution":[{"value":0,"share":0.00005555555555555556},{"value":1,"share":0.0009166666666666666},{"value":2,"share":0.0033055555555555555},{"value":3,"share":0.012861111111111111},{"value":4,"share":0.036694444444444446},{"value":5,"share":0.08202777777777778},{"value":6,"share":0.14930555555555555},{"value":7,"share":0.21191666666666667},{"value":8,"share":0.24102777777777779},{"value":9,"share":0.18491666666666667},{"value":10,"share":0.07697222222222222}]},{"id":"chisq","label":"Chi-square discrepancy","description":"Pearson's X² = Σ (y − n p)² / (n p (1 − p)) at each draw's probabilities, computed for the observed and the replicated table. An omnibus check of overall fit.","kind":"discrepancy","observed":null,"pValue":0.7405833333333334,"ess":31346.003879034368,"mcse":0.002475681736841991,"interval":[0.7357018141078143,0.7454058927165957],"intervalMethod":"wilson"}]},"prior":[{"scale":0.25,"beta0":{"mean":-0.16437868581646572,"sd":0.21286850166794855,"q025":-0.5819780626242119,"q975":0.252886102984428},"beta1":{"mean":0.1477866948720285,"sd":0.08176885443471155,"q025":-0.010475542282960142,"q500":0.14703014666430722,"q975":0.3103502030593379},"pBeta1Positive":0.9662594911009871,"oddsRatio":1.1583888840643013,"shiftSd":[1.4023338614537215,-1.2594582184784027]},{"scale":0.5,"beta0":{"mean":-0.4196677261581596,"sd":0.32790568205524623,"q025":-1.0663827737308484,"q975":0.22025841096438506},"beta1":{"mean":0.21579179179541824,"sd":0.10356843572859402,"q025":0.01592006166691382,"q500":0.21462724406188896,"q975":0.42228283856466503},"pBeta1Positive":0.9829597009675264,"oddsRatio":1.2393998172083673,"shiftSd":[0.8514138388224917,-0.7451714831520238]},{"scale":1,"beta0":{"mean":-0.6578231669501591,"sd":0.41157302014422137,"q025":-1.4783493716829155,"q975":0.13764363198485913},"beta1":{"mean":0.27551269240507564,"sd":0.12095501505033572,"q025":0.04362470271972918,"q500":0.2735896750805824,"q975":0.5183260837237909},"pBeta1Positive":0.9903507937820437,"oddsRatio":1.3146752475349195,"shiftSd":[0.33746854506735463,-0.29353376193986314]},{"scale":2.5,"beta0":{"mean":-0.7839878023184511,"sd":0.45337638021097454,"q025":-1.6956616490982401,"q975":0.08520183580159957},"beta1":{"mean":0.3068395785774913,"sd":0.13002883309819752,"q025":0.05899311836549907,"q500":0.3042485422462923,"q975":0.569419738748008},"pBeta1Positive":0.9927481855816688,"oddsRatio":1.3556059395683566,"shiftSd":[0.06520216152292765,-0.05662501911868375]},{"scale":5,"beta0":{"mean":-0.8064111763512023,"sd":0.4608024563661016,"q025":-1.7347467718740412,"q975":0.07562032651925542},"beta1":{"mean":0.3123969807365954,"sd":0.13166211801934544,"q025":0.06174328713219806,"q500":0.30966149824767875,"q975":0.5786090255431802},"pBeta1Positive":0.9930988715428872,"oddsRatio":1.3629636704460395,"shiftSd":[0.01681196931938776,-0.014597313217151483]},{"scale":10,"beta0":{"mean":-0.8122385306836117,"sd":0.4627352958665581,"q025":-1.7449161971088503,"q975":0.07311478724089776},"beta1":{"mean":0.31384084366162357,"sd":0.13208818040393705,"q025":0.062459148506565455,"q500":0.31106638876527737,"q975":0.5810033947935154},"pBeta1Positive":0.9931867733617349,"oddsRatio":1.3648798308651189,"shiftSd":[0.004236395466337866,-0.00367813827930732]},{"scale":null,"beta0":{"mean":-0.8142016202223509,"sd":0.4633867528038222,"q025":-1.7483432096221696,"q975":0.07226934242213309},"beta1":{"mean":0.3143272107658095,"sd":0.1322318703791418,"q025":0.06270040545123225,"q500":0.31153949059468766,"q975":0.5818104299631636},"pBeta1Positive":0.9932160933392015,"oddsRatio":1.3655257107814642,"shiftSd":[0,0]}],"comparison":{"reference":{"draws":36000,"chains":4},"rows":[{"method":"laplace","label":"Laplace (GLM)","basis":"Gaussian approximation (closed form)","mean":[-0.7800814267831959,0.3015761287116181],"mcse":null,"sd":[0.4540030115029675,0.1292260745900142],"beta1Interval":[0.0482976766517037,0.5548545807715325],"shiftSd":[0.07710948616795993,-0.10059072201859601],"w1Reference":[0.03558164215357985,0.013335619753535671],"w1Exact":[0.034119622330250884,0.012750893916026485],"klGaussian":0.006297383960472719},{"method":"mh","label":"Metropolis-Hastings","basis":"4 chains × 50,000 draws = 200,000","mean":[-0.8159029364258836,0.31535543245261866],"mcse":[0.002845424736154824,0.0008124917233396713],"sd":[0.46373591291869687,0.13195538145897978],"beta1Interval":[0.06538469175914857,0.5852834263445804],"shiftSd":[-0.0005198578730696202,0.0033607665725820606],"w1Reference":[0.0027181675786932236,0.0013944219235668331],"w1Exact":[0.0022653075839484697,0.0010773033340469793],"klGaussian":0.0001867802871363066},{"method":"hmc","label":"HMC (reference)","basis":"4 chains × 9,000 draws = 36,000","mean":[-0.8156630517013257,0.3149099455814459],"mcse":[0.001509383677043414,0.0004530505335307253],"sd":[0.46144290004247507,0.13255513632125077],"beta1Interval":[0.062360610069156316,0.58166300448383],"shiftSd":[-2.6465795160685285e-15,-1.6751112864227338e-15],"w1Reference":[0,0],"w1Exact":[0.0027560570295275307,0.0008504956267396876],"klGaussian":-2.220446049250313e-16},{"method":"ep","label":"Expectation propagation","basis":"Gaussian approximation (closed form)","mean":[-0.8138718102609034,0.31420054124547425],"mcse":null,"sd":[0.4626271360878421,0.13188459888844806],"beta1Interval":[0.05571147730860487,0.5726896051823436],"shiftSd":[0.003881826852804987,-0.005351767993754887],"w1Reference":[0.008751673807602096,0.0023417664879782046],"w1Exact":[0.008088332652891932,0.0026644496461416894],"klGaussian":0.00011481212334259238},{"method":"exact","label":"Exact (quadrature)","basis":"2-D grid, trapezoidal rule","mean":[-0.8142016202223761,0.3143272107657908],"mcse":null,"sd":[0.4633867528038222,0.1322318703791418],"beta1Interval":[0.06270040545123225,0.5818104299631636],"shiftSd":[0.0031670906168756122,-0.004396169260790297],"w1Reference":[0.0027560570295275307,0.0008504956267396876],"w1Exact":[0,0],"klGaussian":0.00008501720103850415}],"noiseFloor":{"w1Halves":[0.005312122379742945,0.0011065678203009393],"klHalves":0.00017031831610484893,"w1ReferenceToExact":[0.0027560570295275307,0.0008504956267396876]},"exactKl":[{"label":"Laplace (GLM)","method":"laplace","kl":0.008495348383619428},{"label":"Expectation propagation","method":"ep","kl":0.002742647941407217},{"label":"Best possible Gaussian (the exact mean and covariance)","method":"moments","kl":0.0027326688463376048}]}},"asSubmitted":{"samplers":[{"sampler":"mh","label":"Metropolis-Hastings","settings":"100,000 iterations, first 50,000 discarded, proposal N(θ, c²·vcov(GLM)) with c = 2.4/√2","iter":100000,"burnin":50000,"drawsPerChain":50000,"chains":[{"seed":90125,"init":[0.39309806169752365,-0.16006779893525433,0.2611795544920177,-0.47044243483093534,-1.1819410492645384,1.0742630425744408,-0.210329152354665],"acceptRate":0.0498209964199284},{"seed":90126,"init":[-1.0462292713635244,-0.09985750026194619,0.7807093366398898,-1.1911495574235575,0.1913437390042044,0.21235828413235497,0.3814495579951366],"acceptRate":0.04898097961959239},{"seed":90127,"init":[0.4288642781801585,0.44475434358280697,0.3205116914924919,0.5277975341406045,-1.7307441329592501,-1.69411212265848,0.4292143513043847],"acceptRate":0.0495209904198084},{"seed":90128,"init":[0.36322972714596324,0.15189095440666925,0.8092039113673075,0.9176015580126077,0.42381495024287363,0.3604570599698374,0.38667568522356377],"acceptRate":0.04712094241884838}],"params":[{"index":0,"label":"β₀ (Intercept)","mean":-1.1224704854406933,"sd":0.571205766829858,"q025":-2.240982243939583,"q500":-1.1133477312580433,"q975":-0.03075814252113568,"mcseMean":0.011956013264926898,"mcseQ025":0.02525219813119617,"mcseQ500":0.014690709061975116,"mcseQ975":0.01607770529962707,"rhat":1.0017069255771303,"essBulk":2284.6914795032358,"essTail":3493.425873694953,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":1,"label":"β₁ dose1","mean":0.3144783100715814,"sd":0.13190639233235296,"q025":0.062314281676384836,"q500":0.3121763341968149,"q975":0.5805916111020589,"mcseMean":0.002531639748595233,"mcseQ025":0.005593545270954084,"mcseQ500":0.003048227486181304,"mcseQ975":0.005857500552806316,"rhat":1.0012041060901904,"essBulk":2721.8586904203103,"essTail":3958.805213792343,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":2,"label":"β₂ dose2","mean":-27.726908656764227,"sd":69.84423296876972,"q025":-136.47357930900728,"q500":-42.02305244633054,"q975":88.07772034504099,"mcseMean":34.032867318365426,"mcseQ025":18.613999779713758,"mcseQ500":25.2888231318587,"mcseQ975":2.7109833880456193,"rhat":2.6909689753721633,"essBulk":4.65849022305071,"essTail":11.154812632887571,"flags":{"rhat":true,"essBulk":true,"essTail":true}},{"index":3,"label":"β₃ dose3","mean":-10.685973535564218,"sd":42.48131912687035,"q025":-75.46968903359381,"q500":-7.116916215852746,"q975":74.94076923888551,"mcseMean":20.236919632335933,"mcseQ025":1.347044504681314,"mcseQ500":31.66564358846678,"mcseQ975":19.245186250297944,"rhat":2.3073967823913457,"essBulk":5.0063566702251565,"essTail":11.39588582356653,"flags":{"rhat":true,"essBulk":true,"essTail":true}},{"index":4,"label":"β₄ dose4","mean":-17.373409461837223,"sd":40.09303109168395,"q025":-91.32816222926554,"q500":-7.99810264885237,"q975":38.319232328704544,"mcseMean":18.350316254007833,"mcseQ025":3.5253999975739774,"mcseQ500":12.062375446793338,"mcseQ975":6.983064964167335,"rhat":1.721736191519774,"essBulk":6.463180101173254,"essTail":22.317826957135313,"flags":{"rhat":true,"essBulk":true,"essTail":true}},{"index":5,"label":"β₅ dose5","mean":21.988430186174856,"sd":50.67107396865001,"q025":-56.23681040999117,"q500":5.060031517548699,"q975":116.57078620525334,"mcseMean":23.967991079603394,"mcseQ025":9.931369555141782,"mcseQ500":33.25123576492668,"mcseQ975":12.15415460482415,"rhat":2.2903008023277374,"essBulk":5.032209307972416,"essTail":11.32927628348479,"flags":{"rhat":true,"essBulk":true,"essTail":true}},{"index":6,"label":"β₆ dose6","mean":-15.074945651618673,"sd":103.44015449393524,"q025":-209.05025009763912,"q500":7.55505535351766,"q975":168.26143467973236,"mcseMean":50.50014278388607,"mcseQ025":17.187444156382966,"mcseQ500":27.75053049747177,"mcseQ975":31.890925393090235,"rhat":2.757125041988959,"essBulk":4.639951839245903,"essTail":11.592327022767062,"flags":{"rhat":true,"essBulk":true,"essTail":true}}],"flagged":[2,3,4,5,6]},{"sampler":"hmc","label":"Hamiltonian Monte Carlo","settings":"10,000 iterations, first 1,000 discarded, L = 20 leapfrog steps of ε = 1/20, identity mass matrix","iter":10000,"burnin":1000,"drawsPerChain":9000,"chains":[{"seed":90125,"init":[0.39309806169752365,-0.16006779893525433,0.2611795544920177,-0.47044243483093534,-1.1819410492645384,1.0742630425744408,-0.210329152354665],"acceptRate":0.9994444444444445},{"seed":90126,"init":[-1.0462292713635244,-0.09985750026194619,0.7807093366398898,-1.1911495574235575,0.1913437390042044,0.21235828413235497,0.3814495579951366],"acceptRate":0.9988888888888889},{"seed":90127,"init":[0.4288642781801585,0.44475434358280697,0.3205116914924919,0.5277975341406045,-1.7307441329592501,-1.69411212265848,0.4292143513043847],"acceptRate":0.9993333333333333},{"seed":90128,"init":[0.36322972714596324,0.15189095440666925,0.8092039113673075,0.9176015580126077,0.42381495024287363,0.3604570599698374,0.38667568522356377],"acceptRate":0.9993333333333333}],"params":[{"index":0,"label":"β₀ (Intercept)","mean":-2.683396102332736,"sd":1.3569310290010934,"q025":-5.960181022105244,"q500":-2.4775105884335504,"q975":-0.6517061627197627,"mcseMean":0.06780803684899304,"mcseQ025":0.34348601641706145,"mcseQ500":0.044611900496761336,"mcseQ975":0.02933404281245272,"rhat":1.0035630811710083,"essBulk":519.1476722472036,"essTail":538.1957819720534,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":1,"label":"β₁ dose1","mean":-0.043402052622237626,"sd":1.91434433493025,"q025":-3.849351800122123,"q500":-0.04022899993621393,"q975":3.861507589745016,"mcseMean":0.07574907032844927,"mcseQ025":0.09608979752099511,"mcseQ500":0.054952170986154104,"mcseQ975":0.26584204240224896,"rhat":1.0051987132882643,"essBulk":692.1476875015937,"essTail":694.0976200812086,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":2,"label":"β₂ dose2","mean":-0.07172364636874762,"sd":1.9141712457519906,"q025":-3.897781123254318,"q500":-0.07682606638232843,"q975":3.807577724925399,"mcseMean":0.07467388619111373,"mcseQ025":0.1029733873589822,"mcseQ500":0.053870797396606926,"mcseQ975":0.28352390580351683,"rhat":1.0016875583969038,"essBulk":709.1696696683687,"essTail":719.5695939137067,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":3,"label":"β₃ dose3","mean":-0.05343230052345284,"sd":1.9138186540934765,"q025":-3.8673094464923543,"q500":-0.06915112385441616,"q975":3.8094927971020978,"mcseMean":0.07743756981077551,"mcseQ025":0.12050440200763335,"mcseQ500":0.054330724437302906,"mcseQ975":0.32041544881146744,"rhat":1.0031018624492096,"essBulk":675.0430094893733,"essTail":650.08245906669,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":4,"label":"β₄ dose4","mean":-0.01929132449351774,"sd":1.8713450599222787,"q025":-3.759133368663812,"q500":-0.025245834480300548,"q975":3.758423491321453,"mcseMean":0.07565381269377883,"mcseQ025":0.10840725991152556,"mcseQ500":0.054551234543962435,"mcseQ975":0.3004860558557927,"rhat":1.0028539205740288,"essBulk":681.6189338207616,"essTail":617.95598643107,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":5,"label":"β₅ dose5","mean":-0.042835726042942696,"sd":1.9157791882195974,"q025":-3.8878463407703006,"q500":-0.04722032330014161,"q975":3.853774529348814,"mcseMean":0.07747383450346465,"mcseQ025":0.10919435183414095,"mcseQ500":0.055328178936230134,"mcseQ975":0.29296946801928536,"rhat":1.0030330152045357,"essBulk":650.1395610259439,"essTail":630.7706733520268,"flags":{"rhat":false,"essBulk":false,"essTail":false}},{"index":6,"label":"β₆ dose6","mean":-0.030343314524295242,"sd":1.9136862431768644,"q025":-3.8427639851264455,"q500":-0.0537744393540856,"q975":3.863126764354316,"mcseMean":0.07770392720124553,"mcseQ025":0.10469412783553933,"mcseQ500":0.05887995408067026,"mcseQ975":0.2924766446424998,"rhat":1.003174929617748,"essBulk":663.0133360792682,"essTail":668.1146132644102,"flags":{"rhat":false,"essBulk":false,"essTail":false}}],"flagged":[]}],"ppc":{"seed":90125,"nDraws":36000,"nChains":4,"patientsPerDose":10,"cells":[{"dose":0,"outcome":"improved","observed":3,"repMean":1.0330833333333334,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.09408333333333334,"mcse":0.004098836425238584},{"dose":1,"outcome":"improved","observed":5,"repMean":0.9932777777777778,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.015152777777777777,"mcse":0.0005971746306072023},{"dose":2,"outcome":"improved","observed":4,"repMean":0.9813333333333333,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.035277777777777776,"mcse":0.0009522775518847973},{"dose":3,"outcome":"improved","observed":4,"repMean":0.9985555555555555,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.03798611111111111,"mcse":0.0010116330145994409},{"dose":4,"outcome":"improved","observed":7,"repMean":0.9966111111111111,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.0016527777777777778,"mcse":0.00018946160728634947},{"dose":5,"outcome":"improved","observed":6,"repMean":0.9958333333333333,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.005083333333333333,"mcse":0.000325539680419907},{"dose":6,"outcome":"improved","observed":8,"repMean":1.0039722222222223,"rep05":0,"rep25":0,"rep50":1,"rep75":2,"rep95":4,"pValue":0.0004027777777777778,"mcse":0.0000888397490060818},{"dose":0,"outcome":"not improved","observed":7,"repMean":8.966916666666666,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9059166666666667,"mcse":0.004098836425238584},{"dose":1,"outcome":"not improved","observed":5,"repMean":9.006722222222223,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9848472222222222,"mcse":0.0005971746306072024},{"dose":2,"outcome":"not improved","observed":6,"repMean":9.018666666666666,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9647222222222223,"mcse":0.0009522775518847976},{"dose":3,"outcome":"not improved","observed":6,"repMean":9.001444444444445,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9620138888888888,"mcse":0.0010116330145994409},{"dose":4,"outcome":"not improved","observed":3,"repMean":9.003388888888889,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9983472222222223,"mcse":0.00018946160728634947},{"dose":5,"outcome":"not improved","observed":4,"repMean":9.004166666666666,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9949166666666667,"mcse":0.000325539680419907},{"dose":6,"outcome":"not improved","observed":2,"repMean":8.996027777777778,"rep05":6,"rep25":8,"rep50":9,"rep75":10,"rep95":10,"pValue":0.9995972222222222,"mcse":0.0000888397490060818}],"stats":[{"id":"total","label":"Total improved","description":"Patients improved across all seven doses (observed 37 of 70). The intercept and slope are fitted to this, so a well-specified model should put it near the middle.","kind":"count","observed":37,"pValue":0,"ess":519.1476722472036,"mcse":0,"interval":[0,0.007345198193412172],"intervalMethod":"wilson","distribution":[{"value":0,"share":0.0055},{"value":1,"share":0.021027777777777777},{"value":2,"share":0.04533333333333334},{"value":3,"share":0.07308333333333333},{"value":4,"share":0.1005},{"value":5,"share":0.11444444444444445},{"value":6,"share":0.12261111111111112},{"value":7,"share":0.11411111111111111},{"value":8,"share":0.10136111111111111},{"value":9,"share":0.08538888888888889},{"value":10,"share":0.06591666666666667},{"value":11,"share":0.04883333333333333},{"value":12,"share":0.03663888888888889},{"value":13,"share":0.024583333333333332},{"value":14,"share":0.015583333333333333},{"value":15,"share":0.010388888888888888},{"value":16,"share":0.006194444444444444},{"value":17,"share":0.003638888888888889},{"value":18,"share":0.0022222222222222222},{"value":19,"share":0.00125},{"value":20,"share":0.00044444444444444447},{"value":21,"share":0.00044444444444444447},{"value":22,"share":0.00038888888888888887},{"value":23,"share":0.00008333333333333333},{"value":24,"share":0.00002777777777777778}]},{"id":"drops","label":"Dose-to-dose drops","description":"How often the count falls from one dose to the next (observed: 5 to 4 and 7 to 6, so 2). Checks whether the noise around a smooth logistic curve is as large as binomial noise predicts.","kind":"count","observed":2,"pValue":0.5192222222222223,"ess":13049.641959361556,"mcse":0.0031875735802321097,"interval":[0.5129746928068959,0.5254697516375486],"intervalMethod":"normal","distribution":[{"value":0,"share":0.022472222222222223},{"value":1,"share":0.2242222222222222},{"value":2,"share":0.4681666666666667},{"value":3,"share":0.25369444444444444},{"value":4,"share":0.031},{"value":5,"share":0.00044444444444444447}]},{"id":"dose0","label":"Improved at dose 0","description":"The lowest-dose cell (observed 3 of 10): does the curve fit its lower end?","kind":"count","observed":3,"pValue":0.09408333333333334,"ess":3992.7921696982075,"mcse":0.004098836425238584,"interval":[0.0860497615613448,0.10211690510532187],"intervalMethod":"normal","distribution":[{"value":0,"share":0.46305555555555555},{"value":1,"share":0.2645},{"value":2,"share":0.14205555555555555},{"value":3,"share":0.07261111111111111},{"value":4,"share":0.03383333333333333},{"value":5,"share":0.015583333333333333},{"value":6,"share":0.006027777777777778},{"value":7,"share":0.0015277777777777779},{"value":8,"share":0.0007222222222222222},{"value":9,"share":0.00008333333333333333}]},{"id":"dose6","label":"Improved at dose 6","description":"The highest-dose cell (observed 8 of 10): does the curve fit its upper end?","kind":"count","observed":8,"pValue":0.0004027777777777778,"ess":36055.478082641355,"mcse":0.0000888397490060818,"interval":[0.00022865506933027942,0.0005769004862252762],"intervalMethod":"normal","distribution":[{"value":0,"share":0.4775277777777778},{"value":1,"share":0.2565},{"value":2,"share":0.1395},{"value":3,"share":0.07136111111111111},{"value":4,"share":0.03336111111111111},{"value":5,"share":0.013305555555555555},{"value":6,"share":0.0055},{"value":7,"share":0.0023055555555555555},{"value":8,"share":0.00047222222222222224},{"value":9,"share":0.00016666666666666666}]},{"id":"chisq","label":"Chi-square discrepancy","description":"Pearson's X² = Σ (y − n p)² / (n p (1 − p)) at each draw's probabilities, computed for the observed and the replicated table. An omnibus check of overall fit.","kind":"discrepancy","observed":null,"pValue":0,"ess":519.1476722472036,"mcse":0,"interval":[0,0.007345198193412172],"intervalMethod":"wilson"}]}},"hmcTuning":[{"L":5,"epsilon":0.2,"mass":"identity","length":1,"original":false,"stuck":true,"acceptMean":0.0005,"acceptRange":[0,0.001],"rhatMax":3.878944037020405,"essBulk":4.530184505340733,"essTail":4.008016032064128,"efficiencyChainRange":[0,0],"gradients":96000,"essPer1000Gradients":0},{"L":10,"epsilon":0.1,"mass":"identity","length":1,"original":false,"stuck":false,"acceptMean":0.897875,"acceptRange":[0.8925,0.90425],"rhatMax":1.0008198157727466,"essBulk":34801.971849146954,"essTail":9421.24067762574,"efficiencyChainRange":[44.97672109506307,58.60474619203206],"gradients":176000,"essPer1000Gradients":53.52977657741898},{"L":20,"epsilon":0.05,"mass":"identity","length":1,"original":true,"stuck":false,"acceptMean":0.9640000000000001,"acceptRange":[0.95975,0.96725],"rhatMax":1.00015131412689,"essBulk":38516.93132502652,"essTail":14016.197703021811,"efficiencyChainRange":[38.75796929107491,42.88341549807399],"gradients":336000,"essPer1000Gradients":41.71487411613634},{"L":40,"epsilon":0.025,"mass":"identity","length":1,"original":false,"stuck":false,"acceptMean":0.9908750000000001,"acceptRange":[0.99025,0.99175],"rhatMax":1.0001458667443905,"essBulk":37433.39263303037,"essTail":15369.262298392887,"efficiencyChainRange":[21.462911133411527,24.219119446972602],"gradients":656000,"essPer1000Gradients":23.42875350364769},{"L":5,"epsilon":0.05,"mass":"identity","length":0.25,"original":false,"stuck":false,"acceptMean":0.9803124999999999,"acceptRange":[0.97775,0.9825],"rhatMax":1.0047192613011233,"essBulk":1604.0818312395957,"essTail":3326.272107683013,"efficiencyChainRange":[11.832381107813594,19.78534590540276],"gradients":96000,"essPer1000Gradients":16.70918574207912},{"L":10,"epsilon":0.05,"mass":"identity","length":0.5,"original":false,"stuck":false,"acceptMean":0.965375,"acceptRange":[0.962,0.96975],"rhatMax":1.000570191213404,"essBulk":4944.951344479736,"essTail":7933.735344802476,"efficiencyChainRange":[22.707083436906533,31.427505516167894],"gradients":176000,"essPer1000Gradients":28.096314457271227},{"L":40,"epsilon":0.05,"mass":"identity","length":2,"original":false,"stuck":false,"acceptMean":0.97125,"acceptRange":[0.969,0.9735],"rhatMax":1.0004187977344394,"essBulk":45162.807788610095,"essTail":12012.023754992699,"efficiencyChainRange":[15.361601232836296,20.162573495443375],"gradients":656000,"essPer1000Gradients":18.311011821635212},{"L":10,"epsilon":0.2,"mass":"identity","length":2,"original":false,"stuck":true,"acceptMean":0,"acceptRange":[0,0],"rhatMax":null,"essBulk":4.008016032064128,"essTail":null,"efficiencyChainRange":[0,0],"gradients":176000,"essPer1000Gradients":0},{"L":3,"epsilon":0.5,"mass":"identity","length":1.5,"original":false,"stuck":true,"acceptMean":0.0000625,"acceptRange":[0,0.00025],"rhatMax":7.1202847485558785,"essBulk":4.82574217800019,"essTail":null,"efficiencyChainRange":[0,0],"gradients":64000,"essPer1000Gradients":0},{"L":3,"epsilon":0.5,"mass":"glm","length":1.5,"original":false,"stuck":false,"acceptMean":0.9702500000000001,"acceptRange":[0.96775,0.97175],"rhatMax":1.0000723136050351,"essBulk":12730.760662849567,"essTail":12759.284294405106,"efficiencyChainRange":[188.47204257110928,200.15292335288714],"gradients":64000,"essPer1000Gradients":198.91813535702448},{"L":2,"epsilon":0.8,"mass":"glm","length":1.6,"original":false,"stuck":false,"acceptMean":0.9176874999999999,"acceptRange":[0.91375,0.92175],"rhatMax":0.9999402151230805,"essBulk":15411.506277202496,"essTail":14354.996929067838,"efficiencyChainRange":[275.1764404445946,304.76919347108907],"gradients":48000,"essPer1000Gradients":299.06243602224663}],"hmcTuningReplicates":{"seedSets":[[90125,90126,90127,90128],[90129,90130,90131,90132],[90133,90134,90135,90136],[90137,90138,90139,90140],[90141,90142,90143,90144],[90145,90146,90147,90148],[90149,90150,90151,90152],[90153,90154,90155,90156],[90157,90158,90159,90160],[90161,90162,90163,90164]],"rows":[{"L":20,"epsilon":0.05,"mass":"identity","original":true,"efficiency":[41.71487411613634,43.92746332325278,43.995677787905194,41.327157718295794,42.808944045375625,41.62838831631182,43.059524004077836,41.18543245373533,39.37558079424298,41.268280404039494],"efficiencyMedian":41.671631216224085,"efficiencyRange":[39.37558079424298,43.995677787905194],"ratio":[1,1,1,1,1,1,1,1,1,1],"ratioMedian":1,"ratioRange":[1,1]},{"L":10,"epsilon":0.1,"mass":"identity","original":false,"efficiency":[53.52977657741898,50.501246991941684,51.41648453067477,55.96275206755613,50.507706623522395,53.9051482885971,53.59107061220878,50.419732733230596,55.4304126481999,50.38134698193117],"efficiencyMedian":52.473130554046875,"efficiencyRange":[50.38134698193117,55.96275206755613],"ratio":[1.2832299680058807,1.149650882872836,1.1686712676309676,1.3541398721156443,1.179840048611954,1.2949131702866024,1.2445811200126964,1.2242127793575652,1.4077357471335195,1.2208249650499046],"ratioMedian":1.2343969496851308,"ratioRange":[1.149650882872836,1.4077357471335195]},{"L":3,"epsilon":0.5,"mass":"glm","original":false,"efficiency":[198.91813535702448,212.05902848665409,198.95208697585332,193.90211642408894,202.44876554501224,212.87384789724896,189.82048460697004,196.22189594556104,188.6136966022646,203.10906793865627],"efficiencyMedian":198.9351111664389,"efficiencyRange":[188.6136966022646,212.87384789724896],"ratio":[4.768518174194322,4.827481772078601,4.522082553994589,4.691881250237716,4.729123085363314,5.1136701781422484,4.4083275186459,4.764351962699001,4.790118464229521,4.921675096468889],"ratioMedian":4.766435068446661,"ratioRange":[4.4083275186459,5.1136701781422484]},{"L":2,"epsilon":0.8,"mass":"glm","original":false,"efficiency":[299.06243602224663,293.1417115865875,286.2861427221849,300.63680095061375,282.31229018486266,282.1398826220012,274.7555168410686,312.99062490879214,304.7408414353209,299.5455723019085],"efficiencyMedian":296.10207380441705,"efficiencyRange":[274.7555168410686,312.99062490879214],"ratio":[7.169203847760429,6.67331298940302,6.507142453909132,7.27455788273385,6.594703431264828,6.777583616213326,6.380830331869173,7.599546884942453,7.7393357834578635,7.25849415990175],"ratioMedian":6.973393731986878,"ratioRange":[6.380830331869173,7.7393357834578635]}]},"epVariants":[{"label":"Original: identity sites, no damping","initSitePrecision":1,"damping":1,"sweeps":5,"converged":true,"mean":[-0.8138718102609034,0.31420054124547425],"sd":[0.4626271360878421,0.13188459888844806],"maxDiffFromOriginal":0},{"label":"Near-flat initial sites (0.01 I)","initSitePrecision":0.01,"damping":1,"sweeps":5,"converged":true,"mean":[-0.8138718104593132,0.31420054130500025],"sd":[0.4626271363171899,0.13188459894043822],"maxDiffFromOriginal":2.2934776300331805e-10},{"label":"Strong initial sites (100 I)","initSitePrecision":100,"damping":1,"sweeps":5,"converged":true,"mean":[-0.8138718097440962,0.31420054110090634],"sd":[0.4626271354989971,0.13188459876071248],"maxDiffFromOriginal":5.888450282931501e-10},{"label":"Damped updates (0.5)","initSitePrecision":1,"damping":0.5,"sweeps":23,"converged":true,"mean":[-0.8138715296802577,0.3142004728888087],"sd":[0.4626269237253744,0.1318845537287991],"maxDiffFromOriginal":2.805806457173432e-7}],"stabilityLimit":0.14092255761772562}