Evaluating Pharmacokinetic/Pharmacodynamic Models Using the Posterior Predictive Check View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2001-04

AUTHORS

Yoshitaka Yano, Stuart L. Beal, Lewis B. Sheiner

ABSTRACT

The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, "real" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical "sufficiency") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with "statistics" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found. More... »

PAGES

171-192

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1011555016423

DOI

http://dx.doi.org/10.1023/a:1011555016423

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1032175473

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/11381569


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Area Under Curve", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Models, Biological", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Pharmacokinetics", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Pharmacology", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "familyName": "Yano", 
        "givenName": "Yoshitaka", 
        "type": "Person"
      }, 
      {
        "familyName": "Beal", 
        "givenName": "Stuart L.", 
        "id": "sg:person.01076410040.36", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01076410040.36"
        ], 
        "type": "Person"
      }, 
      {
        "familyName": "Sheiner", 
        "givenName": "Lewis B.", 
        "id": "sg:person.0705422657.60", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0705422657.60"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02353487", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008091929", 
          "https://doi.org/10.1007/bf02353487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/bimj.4710320615", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014289857"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/bimj.4710320615", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014289857"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1146/annurev.pharmtox.40.1.67", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014703851"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1020930626404", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018407227", 
          "https://doi.org/10.1023/a:1020930626404"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/sim.4780140805", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020806436"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/(sici)1097-0258(19981030)17:20<2313::aid-sim935>3.0.co;2-v", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032769225"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aoms/1177706645", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043005266"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aos/1176346785", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051641329"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00401706.1991.10484873", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058286616"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1985.10478157", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058303134"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1987.10478408", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058303385"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1988.10478649", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058303626"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1994.10476823", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058304687"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1996.10476708", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058304991"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biomet/75.4.661", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059419870"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biomet/76.3.435", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059419947"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1147/sj.82.0136", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1063185174"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2531491", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069976933"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2001-04", 
    "datePublishedReg": "2001-04-01", 
    "description": "The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, \"real\" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical \"sufficiency\") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with \"statistics\" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1023/a:1011555016423", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.2515642", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1016394", 
        "issn": [
          "1567-567X", 
          "2168-5789"
        ], 
        "name": "Journal of Pharmacokinetics and Pharmacodynamics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "28"
      }
    ], 
    "name": "Evaluating Pharmacokinetic/Pharmacodynamic Models Using the Posterior Predictive Check", 
    "pagination": "171-192", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9946c51f7e834ff32544d45debf7bfe22f4f155aa17dc1350371afe9333a6142"
        ]
      }, 
      {
        "name": "pubmed_id", 
        "type": "PropertyValue", 
        "value": [
          "11381569"
        ]
      }, 
      {
        "name": "nlm_unique_id", 
        "type": "PropertyValue", 
        "value": [
          "101096520"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1023/a:1011555016423"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1032175473"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1023/a:1011555016423", 
      "https://app.dimensions.ai/details/publication/pub.1032175473"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T16:39", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8669_00000500.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1023/A:1011555016423"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1023/a:1011555016423'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1011555016423'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1011555016423'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1011555016423'


 

This table displays all metadata directly associated to this object as RDF triples.

150 TRIPLES      21 PREDICATES      51 URIs      25 LITERALS      13 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1023/a:1011555016423 schema:about N23dc32328e85429193024b337a82aaf6
2 N77c51691759945a8bc59190f3c49e533
3 Nd81c51257d6c4a85b7c3ea6cf81b5d16
4 Ne7b3693d814544ea991826f7e941d9e7
5 anzsrc-for:01
6 anzsrc-for:0104
7 schema:author N5c05163714b54905b9363541712b56c4
8 schema:citation sg:pub.10.1007/bf02353487
9 sg:pub.10.1023/a:1020930626404
10 https://doi.org/10.1002/(sici)1097-0258(19981030)17:20<2313::aid-sim935>3.0.co;2-v
11 https://doi.org/10.1002/bimj.4710320615
12 https://doi.org/10.1002/sim.4780140805
13 https://doi.org/10.1080/00401706.1991.10484873
14 https://doi.org/10.1080/01621459.1985.10478157
15 https://doi.org/10.1080/01621459.1987.10478408
16 https://doi.org/10.1080/01621459.1988.10478649
17 https://doi.org/10.1080/01621459.1994.10476823
18 https://doi.org/10.1080/01621459.1996.10476708
19 https://doi.org/10.1093/biomet/75.4.661
20 https://doi.org/10.1093/biomet/76.3.435
21 https://doi.org/10.1146/annurev.pharmtox.40.1.67
22 https://doi.org/10.1147/sj.82.0136
23 https://doi.org/10.1214/aoms/1177706645
24 https://doi.org/10.1214/aos/1176346785
25 https://doi.org/10.2307/2531491
26 schema:datePublished 2001-04
27 schema:datePublishedReg 2001-04-01
28 schema:description The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, "real" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical "sufficiency") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with "statistics" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found.
29 schema:genre research_article
30 schema:inLanguage en
31 schema:isAccessibleForFree false
32 schema:isPartOf N96d562f7ada949e385ad46b42c4577da
33 Nd6d326a02a28405b991c87cc25218f79
34 sg:journal.1016394
35 schema:name Evaluating Pharmacokinetic/Pharmacodynamic Models Using the Posterior Predictive Check
36 schema:pagination 171-192
37 schema:productId N1f8c726c67ef4a28b493396ecbcdab4d
38 N5d8e8dbd486948c6af4cad2831519bf7
39 N82cbc056913d4108b1f3d02a7c462039
40 Ncfb43acd45134669bbf34c0363900078
41 Ndfbc8f7d96284b52903b5722feedbac5
42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032175473
43 https://doi.org/10.1023/a:1011555016423
44 schema:sdDatePublished 2019-04-10T16:39
45 schema:sdLicense https://scigraph.springernature.com/explorer/license/
46 schema:sdPublisher N255826d32c9641c8a61e49dcdf1948fb
47 schema:url http://link.springer.com/10.1023/A:1011555016423
48 sgo:license sg:explorer/license/
49 sgo:sdDataset articles
50 rdf:type schema:ScholarlyArticle
51 N1f8c726c67ef4a28b493396ecbcdab4d schema:name nlm_unique_id
52 schema:value 101096520
53 rdf:type schema:PropertyValue
54 N23dc32328e85429193024b337a82aaf6 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
55 schema:name Models, Biological
56 rdf:type schema:DefinedTerm
57 N255826d32c9641c8a61e49dcdf1948fb schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 N3c9adc211b6f40ff94be5a7422005598 schema:familyName Yano
60 schema:givenName Yoshitaka
61 rdf:type schema:Person
62 N5c05163714b54905b9363541712b56c4 rdf:first N3c9adc211b6f40ff94be5a7422005598
63 rdf:rest Nce07852b7687428987a58391acd4cc41
64 N5d8e8dbd486948c6af4cad2831519bf7 schema:name dimensions_id
65 schema:value pub.1032175473
66 rdf:type schema:PropertyValue
67 N77c51691759945a8bc59190f3c49e533 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
68 schema:name Pharmacokinetics
69 rdf:type schema:DefinedTerm
70 N82cbc056913d4108b1f3d02a7c462039 schema:name doi
71 schema:value 10.1023/a:1011555016423
72 rdf:type schema:PropertyValue
73 N96d562f7ada949e385ad46b42c4577da schema:volumeNumber 28
74 rdf:type schema:PublicationVolume
75 Nce07852b7687428987a58391acd4cc41 rdf:first sg:person.01076410040.36
76 rdf:rest Nf3c11d360b794f058b301c3dfede37f8
77 Ncfb43acd45134669bbf34c0363900078 schema:name pubmed_id
78 schema:value 11381569
79 rdf:type schema:PropertyValue
80 Nd6d326a02a28405b991c87cc25218f79 schema:issueNumber 2
81 rdf:type schema:PublicationIssue
82 Nd81c51257d6c4a85b7c3ea6cf81b5d16 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
83 schema:name Pharmacology
84 rdf:type schema:DefinedTerm
85 Ndfbc8f7d96284b52903b5722feedbac5 schema:name readcube_id
86 schema:value 9946c51f7e834ff32544d45debf7bfe22f4f155aa17dc1350371afe9333a6142
87 rdf:type schema:PropertyValue
88 Ne7b3693d814544ea991826f7e941d9e7 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
89 schema:name Area Under Curve
90 rdf:type schema:DefinedTerm
91 Nf3c11d360b794f058b301c3dfede37f8 rdf:first sg:person.0705422657.60
92 rdf:rest rdf:nil
93 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
94 schema:name Mathematical Sciences
95 rdf:type schema:DefinedTerm
96 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
97 schema:name Statistics
98 rdf:type schema:DefinedTerm
99 sg:grant.2515642 http://pending.schema.org/fundedItem sg:pub.10.1023/a:1011555016423
100 rdf:type schema:MonetaryGrant
101 sg:journal.1016394 schema:issn 1567-567X
102 2168-5789
103 schema:name Journal of Pharmacokinetics and Pharmacodynamics
104 rdf:type schema:Periodical
105 sg:person.01076410040.36 schema:familyName Beal
106 schema:givenName Stuart L.
107 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01076410040.36
108 rdf:type schema:Person
109 sg:person.0705422657.60 schema:familyName Sheiner
110 schema:givenName Lewis B.
111 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0705422657.60
112 rdf:type schema:Person
113 sg:pub.10.1007/bf02353487 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008091929
114 https://doi.org/10.1007/bf02353487
115 rdf:type schema:CreativeWork
116 sg:pub.10.1023/a:1020930626404 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018407227
117 https://doi.org/10.1023/a:1020930626404
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1002/(sici)1097-0258(19981030)17:20<2313::aid-sim935>3.0.co;2-v schema:sameAs https://app.dimensions.ai/details/publication/pub.1032769225
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1002/bimj.4710320615 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014289857
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1002/sim.4780140805 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020806436
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1080/00401706.1991.10484873 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058286616
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1080/01621459.1985.10478157 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058303134
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1080/01621459.1987.10478408 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058303385
130 rdf:type schema:CreativeWork
131 https://doi.org/10.1080/01621459.1988.10478649 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058303626
132 rdf:type schema:CreativeWork
133 https://doi.org/10.1080/01621459.1994.10476823 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058304687
134 rdf:type schema:CreativeWork
135 https://doi.org/10.1080/01621459.1996.10476708 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058304991
136 rdf:type schema:CreativeWork
137 https://doi.org/10.1093/biomet/75.4.661 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059419870
138 rdf:type schema:CreativeWork
139 https://doi.org/10.1093/biomet/76.3.435 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059419947
140 rdf:type schema:CreativeWork
141 https://doi.org/10.1146/annurev.pharmtox.40.1.67 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014703851
142 rdf:type schema:CreativeWork
143 https://doi.org/10.1147/sj.82.0136 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063185174
144 rdf:type schema:CreativeWork
145 https://doi.org/10.1214/aoms/1177706645 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043005266
146 rdf:type schema:CreativeWork
147 https://doi.org/10.1214/aos/1176346785 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051641329
148 rdf:type schema:CreativeWork
149 https://doi.org/10.2307/2531491 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069976933
150 rdf:type schema:CreativeWork
 




Preview window. Press ESC to close (or click here)


...