diff --git a/_freeze/chapter_11/execute-results/html.json b/_freeze/chapter_11/execute-results/html.json index 7fff046..9f1f44b 100644 --- a/_freeze/chapter_11/execute-results/html.json +++ b/_freeze/chapter_11/execute-results/html.json @@ -1,7 +1,7 @@ { - "hash": "3aa5604f0f0c029129672ddf63b3032a", + "hash": "12fb8d715d1d2ead348f6ec7153a3975", "result": { - "markdown": "---\ntitle: \"Individual Participant Data Meta-analysis of clinical trials and real-world data\"\nauthors: \n - name: Pablo Verde\n affiliations:\n - ref: umcdusseldorf\n - name: Thomas Debray\n orcid: 0000-0002-1790-2719\n affiliations:\n - ref: smartdas\naffiliations:\n - id: smartdas\n name: Smart Data Analysis and Statistics B.V.\n city: Utrecht\n - id: umcdusseldorf\n name: Universitätsklinikum Düsseldorf\n city: Düsseldorf\nformat:\n html:\n toc: true\n number-sections: true\nexecute:\n cache: true\nbibliography: 'https://api.citedrive.com/bib/0d25b38b-db8f-43c4-b934-f4e2f3bd655a/references.bib?x=eyJpZCI6ICIwZDI1YjM4Yi1kYjhmLTQzYzQtYjkzNC1mNGUyZjNiZDY1NWEiLCAidXNlciI6ICIyNTA2IiwgInNpZ25hdHVyZSI6ICI0MGFkYjZhMzYyYWE5Y2U0MjQ2NWE2ZTQzNjlhMWY3NTk5MzhhNzUxZDNjYWIxNDlmYjM4NDgwOTYzMzY5YzFlIn0=/bibliography.bib'\n---\n\n\n\n\n## Introduction\n\n\n## Hierarchical Meta-Regression\nWe illustrate the implementation of hierarchical meta-regression using an example that involves the following data sources:\n\n* Aggregate data from 35 randomized trials investigating the efficacy of adjunctive treatments in managing diabetic foot problems compared with routine care\n* Individual participant data from a prospective cohort study investigating patient and limb survival in patients with diabetic foot ulcers \n\n### Aggregate data\nWe first retrieve the randomized evidence and summarize the treatment effect estimates using a random effects meta-analysis:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-2_f7cacc4b2068e8e0b49c42b0d14818e2'}\n\n```{.r .cell-code}\nlibrary(dplyr)\nlibrary(jarbes)\nlibrary(meta)\n\ndata(\"healing\")\n\nresults.ADJ <- metabin(event.c = y_c, n.c = n_c,\n event.e = y_t, n.e = n_t,\n studlab = Study, data = healing,\n sm = \"OR\", \n prediction = TRUE)\n```\n:::\n\n\nThe corresponding forest plot is depicted below. The endpoint is healing without amputations within a period less than or equal to 1 year.\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-3_ccb46ff31b59d1bcdf1839864e34eeb2'}\n::: {.cell-output-display}\n![](chapter_11_files/figure-html/unnamed-chunk-3-1.png){width=960}\n:::\n:::\n\n\nThe random effects meta-analysis yielded a pooled odds ratio of 1.90. However, substantial between-study heterogeneity was found, with $\\tau$ = 0.46.\n\n### Individual participant data\nSubsequently, we retrieve the individual participant data:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-4_98abfdc985b108064e02e2f47ea3d856'}\n\n```{.r .cell-code}\ndata(\"healingipd\")\nIPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy,\n first.ever.lesion, no.continuous.care, \n male, diab.typ2, insulin, HOCHD, \n HOS, CRF, dialysis, DNOAP, smoking.ever, \n diabdur, wagner.class)\n```\n:::\n\n\nBriefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 [@morbach_long-term_2012]. The baseline characteristics of the study population is summarized below:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-5_61ed19f8aa810f3baaa397ee20e963d7'}\n::: {.cell-output-display}\n```{=html}\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Overall
(N=260)
Age (years)
Mean (SD)68.9 (10.9)
Median [Min, Max]70.0 [25.0, 91.0]
Diabetes duration (years)
Mean (SD)15.9 (10.6)
Median [Min, Max]14.0 [0, 53.0]
Sex
Female106 (40.8%)
Male154 (59.2%)
Ever smoker
Yes154 (59.2%)
No106 (40.8%)
Diabetes type 2
Yes229 (88.1%)
No31 (11.9%)
Peripheral arterial disease
Yes148 (56.9%)
No112 (43.1%)
Neuropathy
Yes224 (86.2%)
No36 (13.8%)
First ever lesion
Yes114 (43.8%)
No146 (56.2%)
No continuous care
Yes177 (68.1%)
No83 (31.9%)
Insulin dependent
Yes174 (66.9%)
No86 (33.1%)
History of coronary events (CHD)
Yes52 (20.0%)
No208 (80.0%)
History of stroke
Yes55 (21.2%)
No205 (78.8%)
Charcot foot syndrome
Yes52 (20.0%)
No208 (80.0%)
Dialysis
Yes9 (3.5%)
No251 (96.5%)
DNOAP
Yes29 (11.2%)
No231 (88.8%)
Wagner score
1-2142 (54.6%)
3-4-5118 (45.4%)
\n
\n```\n:::\n:::\n\n\nAs depicted above, IPD are available from 260 patients. Some of these patients have similar characteristics to those enrolled in the randomized trials. However, other patients have comorbidities, where one or more risk factors prevent them to participate in the RCTs due to ethical reasons. For example,\n118 patients have severe ulcer lesions (Wagner score 3 to 4), and 77 patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice?\n\n### Hierarchical metaregression\nWe fitted an HMR model to the available RWD and published AD: \n\n\n::: {.cell hash='chapter_11_cache/html/hmr_fit_2740671afa49efcae98d1899c9eb7d7e'}\n\n```{.r .cell-code}\nset.seed(2022)\n\nAD <- healing %>% dplyr::select(yc = y_c, nc = n_c, \n yt = y_t, nt = n_t, Study = Study)\n\nmx2 <- hmr(data = AD, # Published aggregate data\n two.by.two = FALSE, # \n dataIPD = IPD, # Data frame of the IPD \n re = \"sm\", # Random effects model: \"sm\" scale mixtures \n link = \"logit\", # Link function of the random effects\n sd.mu.1 = 1, # Scale parameter for the prior of mu.1\n sd.mu.2 = 1, # Scale parameter for the prior of mu.2 \n sd.mu.phi = 1, # Scale parameter for the prior of mu.phi \n sigma.1.upper = 5, # Upper bound of the prior of sigma.1 \n sigma.2.upper = 5, # Upper bound of the prior of sigma.2\n sigma.beta.upper = 5, # Upper bound of the prior of sigma.beta\n sd.Fisher.rho = 1.25, # Scale parameter for the prior of rho\n df.estimate = TRUE, # If TRUE the degrees of freedom are estimated\n df.lower = 3, # Lower bound of the df's prior\n df.upper = 10, # Upper bound of the df's prior\n nr.chains = 2, # Number of MCMC chains\n nr.iterations = 10000, # Total number of iterations\n nr.adapt = 1000, # Number of iteration for burnin \n nr.thin = 1) # Thinning rate\n```\n:::\n\n\nWe start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of $\\mu_{\\phi}$, which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass on the right of zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs.\n\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-6_34ac7ace045f4a230f5a3d0b1500214c'}\n::: {.cell-output-display}\n![Conflict of evidence analysis. The left panel shows the prior to posterior sensitivity analysis of bias mean between the RCTs and the IPD-NRS. The right panel depicts the posterior distribution of the outliers detection weights.](chapter_11_files/figure-html/unnamed-chunk-6-1.png){width=1056}\n:::\n:::\n\n\n\nThe figure below presents the posterior distribution of the weights $w_{i}$ for each study included in the HMR. These posteriors are summarized using a forest plot, where posterior intervals substantially greater than one indicate outliers. One important aspect of the HMR is that those outliers are automatically down-weighted in the analysis.\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-7_669c7187ffda5a3eea5d552f61a5f2a9'}\n::: {.cell-output-display}\n![Posterior distribution of the weights for each study included in the HMR](chapter_11_files/figure-html/unnamed-chunk-7-1.png){width=1056}\n:::\n:::\n\n\n\n## Version info {.unnumbered}\nThis chapter was rendered using the following version of R and its packages:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-8_097e9efc1fec5df7c7a25885223b5cef'}\n::: {.cell-output .cell-output-stdout}\n```\nR version 4.2.3 (2023-03-15 ucrt)\nPlatform: x86_64-w64-mingw32/x64 (64-bit)\nRunning under: Windows 10 x64 (build 19045)\n\nMatrix products: default\n\nlocale:\n[1] LC_COLLATE=Dutch_Netherlands.utf8 LC_CTYPE=Dutch_Netherlands.utf8 \n[3] LC_MONETARY=Dutch_Netherlands.utf8 LC_NUMERIC=C \n[5] LC_TIME=Dutch_Netherlands.utf8 \n\nattached base packages:\n[1] stats graphics grDevices utils datasets methods base \n\nother attached packages:\n [1] meta_6.5-0 table1_1.4.3 tableone_0.13.2 dplyr_1.1.2 \n [5] jarbes_2.0.0 GGally_2.1.2 R2jags_0.7-1 rjags_4-14 \n [9] mcmcplots_0.4.3 coda_0.19-4 gridExtra_2.3 ggplot2_3.4.4 \n[13] kableExtra_1.3.4\n\nloaded via a namespace (and not attached):\n [1] httr_1.4.7 tidyr_1.3.0 sfsmisc_1.1-16 \n [4] jsonlite_1.8.7 viridisLite_0.4.2 splines_4.2.3 \n [7] Formula_1.2-5 shiny_1.8.0 metafor_4.4-0 \n[10] yaml_2.3.7 numDeriv_2016.8-1.1 R2WinBUGS_2.1-21 \n[13] pillar_1.9.0 lattice_0.21-8 glue_1.6.2 \n[16] digest_0.6.31 RColorBrewer_1.1-3 promises_1.2.1 \n[19] minqa_1.2.6 rvest_1.0.3 colorspace_2.1-0 \n[22] htmltools_0.5.5 httpuv_1.6.12 Matrix_1.5-4.1 \n[25] survey_4.2-1 plyr_1.8.8 pkgconfig_2.0.3 \n[28] purrr_1.0.1 xtable_1.8-4 scales_1.2.1 \n[31] webshot_0.5.5 svglite_2.1.1 later_1.3.1 \n[34] metadat_1.2-0 lme4_1.1-35.1 tibble_3.2.1 \n[37] generics_0.1.3 ellipsis_0.3.2 withr_2.5.2 \n[40] cli_3.6.1 survival_3.5-5 magrittr_2.0.3 \n[43] mime_0.12 evaluate_0.23 fansi_1.0.4 \n[46] nlme_3.1-162 MASS_7.3-60 xml2_1.3.4 \n[49] tools_4.2.3 mitools_2.4 lifecycle_1.0.4 \n[52] stringr_1.5.1 munsell_0.5.0 compiler_4.2.3 \n[55] systemfonts_1.0.4 rlang_1.1.1 nloptr_2.0.3 \n[58] grid_4.2.3 rstudioapi_0.15.0 CompQuadForm_1.4.3 \n[61] htmlwidgets_1.6.2 miniUI_0.1.1.1 rmarkdown_2.25 \n[64] boot_1.3-28.1 gtable_0.3.4 abind_1.4-5 \n[67] DBI_1.1.3 reshape_0.8.9 R6_2.5.1 \n[70] knitr_1.45 denstrip_1.5.4 fastmap_1.1.1 \n[73] utf8_1.2.3 mathjaxr_1.6-0 ggExtra_0.10.1 \n[76] stringi_1.7.12 parallel_4.2.3 Rcpp_1.0.10 \n[79] vctrs_0.6.3 tidyselect_1.2.0 xfun_0.39 \n```\n:::\n:::\n\n\n## References {.unnumbered}\n\n", + "markdown": "---\ntitle: \"Individual Participant Data Meta-analysis of clinical trials and real-world data\"\nauthors: \n - name: Pablo Verde\n affiliations:\n - ref: umcdusseldorf\n - name: Thomas Debray\n orcid: 0000-0002-1790-2719\n affiliations:\n - ref: smartdas\naffiliations:\n - id: smartdas\n name: Smart Data Analysis and Statistics B.V.\n city: Utrecht\n - id: umcdusseldorf\n name: Universitätsklinikum Düsseldorf\n city: Düsseldorf\nformat:\n html:\n toc: true\n number-sections: true\nexecute:\n cache: true\nbibliography: 'https://api.citedrive.com/bib/0d25b38b-db8f-43c4-b934-f4e2f3bd655a/references.bib?x=eyJpZCI6ICIwZDI1YjM4Yi1kYjhmLTQzYzQtYjkzNC1mNGUyZjNiZDY1NWEiLCAidXNlciI6ICIyNTA2IiwgInNpZ25hdHVyZSI6ICI0MGFkYjZhMzYyYWE5Y2U0MjQ2NWE2ZTQzNjlhMWY3NTk5MzhhNzUxZDNjYWIxNDlmYjM4NDgwOTYzMzY5YzFlIn0=/bibliography.bib'\n---\n\n\n\n\n## Introduction\n\n\n## Hierarchical Meta-Regression\nWe illustrate the implementation of hierarchical meta-regression using an example that involves the following data sources:\n\n* Aggregate data from 35 randomized trials investigating the efficacy of adjunctive treatments in managing diabetic foot problems compared with routine care\n* Individual participant data from a prospective cohort study investigating patient and limb survival in patients with diabetic foot ulcers \n\n### Aggregate data\nWe first retrieve the randomized evidence and summarize the treatment effect estimates using a random effects meta-analysis:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-2_f7cacc4b2068e8e0b49c42b0d14818e2'}\n\n```{.r .cell-code}\nlibrary(dplyr)\nlibrary(jarbes)\nlibrary(meta)\n\ndata(\"healing\")\n\nresults.ADJ <- metabin(event.c = y_c, n.c = n_c,\n event.e = y_t, n.e = n_t,\n studlab = Study, data = healing,\n sm = \"OR\", \n prediction = TRUE)\n```\n:::\n\n\nThe corresponding forest plot is depicted below. The endpoint is healing without amputations within a period less than or equal to 1 year.\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-3_ccb46ff31b59d1bcdf1839864e34eeb2'}\n::: {.cell-output-display}\n![](chapter_11_files/figure-html/unnamed-chunk-3-1.png){width=960}\n:::\n:::\n\n\nThe random effects meta-analysis yielded a pooled odds ratio of 1.90. However, substantial between-study heterogeneity was found, with $\\tau$ = 0.46.\n\n### Individual participant data\nSubsequently, we retrieve the individual participant data:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-4_98abfdc985b108064e02e2f47ea3d856'}\n\n```{.r .cell-code}\ndata(\"healingipd\")\nIPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy,\n first.ever.lesion, no.continuous.care, \n male, diab.typ2, insulin, HOCHD, \n HOS, CRF, dialysis, DNOAP, smoking.ever, \n diabdur, wagner.class)\n```\n:::\n\n\nBriefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 [@morbach_long-term_2012]. The baseline characteristics of the study population are summarized below:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-5_a3fa5d48e7c6dee59e8f08278511b2b8'}\n::: {.cell-output-display}\n```{=html}\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Healing without amputation
(N=165)		No healing without amputation
(N=95)		Overall
(N=260)
Age (years)
Mean (SD)69.1 (10.9)68.5 (11.0)68.9 (10.9)
Median [Min, Max]70.0 [25.0, 90.0]69.0 [36.0, 91.0]70.0 [25.0, 91.0]
Diabetes duration (years)
Mean (SD)15.9 (10.3)15.9 (11.2)15.9 (10.6)
Median [Min, Max]14.0 [1.00, 53.0]14.0 [0, 50.0]14.0 [0, 53.0]
Sex
Female71 (43.0%)35 (36.8%)106 (40.8%)
Male94 (57.0%)60 (63.2%)154 (59.2%)
Ever smoker
Yes97 (58.8%)57 (60.0%)154 (59.2%)
No68 (41.2%)38 (40.0%)106 (40.8%)
Diabetes type 2
Yes150 (90.9%)79 (83.2%)229 (88.1%)
No15 (9.1%)16 (16.8%)31 (11.9%)
Peripheral arterial disease
Yes82 (49.7%)66 (69.5%)148 (56.9%)
No83 (50.3%)29 (30.5%)112 (43.1%)
Neuropathy
Yes144 (87.3%)80 (84.2%)224 (86.2%)
No21 (12.7%)15 (15.8%)36 (13.8%)
First ever lesion
Yes70 (42.4%)44 (46.3%)114 (43.8%)
No95 (57.6%)51 (53.7%)146 (56.2%)
No continuous care
Yes115 (69.7%)62 (65.3%)177 (68.1%)
No50 (30.3%)33 (34.7%)83 (31.9%)
Insulin dependent
Yes109 (66.1%)65 (68.4%)174 (66.9%)
No56 (33.9%)30 (31.6%)86 (33.1%)
History of coronary events (CHD)
Yes31 (18.8%)21 (22.1%)52 (20.0%)
No134 (81.2%)74 (77.9%)208 (80.0%)
History of stroke
Yes36 (21.8%)19 (20.0%)55 (21.2%)
No129 (78.2%)76 (80.0%)205 (78.8%)
Charcot foot syndrome
Yes28 (17.0%)24 (25.3%)52 (20.0%)
No137 (83.0%)71 (74.7%)208 (80.0%)
Dialysis
Yes3 (1.8%)6 (6.3%)9 (3.5%)
No162 (98.2%)89 (93.7%)251 (96.5%)
DNOAP
Yes19 (11.5%)10 (10.5%)29 (11.2%)
No146 (88.5%)85 (89.5%)231 (88.8%)
Wagner score
1-2115 (69.7%)27 (28.4%)142 (54.6%)
3-4-550 (30.3%)68 (71.6%)118 (45.4%)
\n
\n```\n:::\n:::\n\n\nAs depicted above, IPD are available from 260 patients. Some of these patients have similar characteristics to those enrolled in the randomized trials. However, other patients have comorbidities, where one or more risk factors prevent them to participate in the RCTs due to ethical reasons. For example,\n118 patients have severe ulcer lesions (Wagner score 3 to 5), and 77 patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice?\n\n### Hierarchical metaregression\nWe fitted an HMR model to the available RWD and published AD: \n\n\n::: {.cell hash='chapter_11_cache/html/hmr_fit_2740671afa49efcae98d1899c9eb7d7e'}\n\n```{.r .cell-code}\nset.seed(2022)\n\nAD <- healing %>% dplyr::select(yc = y_c, nc = n_c, \n yt = y_t, nt = n_t, Study = Study)\n\nmx2 <- hmr(data = AD, # Published aggregate data\n two.by.two = FALSE, # \n dataIPD = IPD, # Data frame of the IPD \n re = \"sm\", # Random effects model: \"sm\" scale mixtures \n link = \"logit\", # Link function of the random effects\n sd.mu.1 = 1, # Scale parameter for the prior of mu.1\n sd.mu.2 = 1, # Scale parameter for the prior of mu.2 \n sd.mu.phi = 1, # Scale parameter for the prior of mu.phi \n sigma.1.upper = 5, # Upper bound of the prior of sigma.1 \n sigma.2.upper = 5, # Upper bound of the prior of sigma.2\n sigma.beta.upper = 5, # Upper bound of the prior of sigma.beta\n sd.Fisher.rho = 1.25, # Scale parameter for the prior of rho\n df.estimate = TRUE, # If TRUE the degrees of freedom are estimated\n df.lower = 3, # Lower bound of the df's prior\n df.upper = 10, # Upper bound of the df's prior\n nr.chains = 2, # Number of MCMC chains\n nr.iterations = 10000, # Total number of iterations\n nr.adapt = 1000, # Number of iteration for burnin \n nr.thin = 1) # Thinning rate\n```\n:::\n\n\nWe start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of $\\mu_{\\phi}$, which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass on the right of zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs.\n\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-6_34ac7ace045f4a230f5a3d0b1500214c'}\n::: {.cell-output-display}\n![Conflict of evidence analysis. The left panel shows the prior to posterior sensitivity analysis of bias mean between the RCTs and the IPD-NRS. The right panel depicts the posterior distribution of the outliers detection weights.](chapter_11_files/figure-html/unnamed-chunk-6-1.png){width=1056}\n:::\n:::\n\n\n\nThe figure below presents the posterior distribution of the weights $w_{i}$ for each study included in the HMR. These posteriors are summarized using a forest plot, where posterior intervals substantially greater than one indicate outliers. One important aspect of the HMR is that those outliers are automatically down-weighted in the analysis.\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-7_7bf6c90185feaf660fc83a48724970b6'}\n::: {.cell-output-display}\n![Posterior distribution of the weights for each study included in the HMR](chapter_11_files/figure-html/unnamed-chunk-7-1.png){width=1056}\n:::\n:::\n\n\n\n## Version info {.unnumbered}\nThis chapter was rendered using the following version of R and its packages:\n\n\n::: {.cell hash='chapter_11_cache/html/unnamed-chunk-8_097e9efc1fec5df7c7a25885223b5cef'}\n::: {.cell-output .cell-output-stdout}\n```\nR version 4.2.3 (2023-03-15 ucrt)\nPlatform: x86_64-w64-mingw32/x64 (64-bit)\nRunning under: Windows 10 x64 (build 19045)\n\nMatrix products: default\n\nlocale:\n[1] LC_COLLATE=Dutch_Netherlands.utf8 LC_CTYPE=Dutch_Netherlands.utf8 \n[3] LC_MONETARY=Dutch_Netherlands.utf8 LC_NUMERIC=C \n[5] LC_TIME=Dutch_Netherlands.utf8 \n\nattached base packages:\n[1] stats graphics grDevices utils datasets methods base \n\nother attached packages:\n [1] meta_6.5-0 table1_1.4.3 tableone_0.13.2 dplyr_1.1.2 \n [5] jarbes_2.0.0 GGally_2.1.2 R2jags_0.7-1 rjags_4-14 \n [9] mcmcplots_0.4.3 coda_0.19-4 gridExtra_2.3 ggplot2_3.4.4 \n[13] kableExtra_1.3.4\n\nloaded via a namespace (and not attached):\n [1] httr_1.4.7 tidyr_1.3.0 sfsmisc_1.1-16 \n [4] jsonlite_1.8.7 viridisLite_0.4.2 splines_4.2.3 \n [7] Formula_1.2-5 shiny_1.8.0 metafor_4.4-0 \n[10] yaml_2.3.7 numDeriv_2016.8-1.1 R2WinBUGS_2.1-21 \n[13] pillar_1.9.0 lattice_0.21-8 glue_1.6.2 \n[16] digest_0.6.31 RColorBrewer_1.1-3 promises_1.2.1 \n[19] minqa_1.2.6 rvest_1.0.3 colorspace_2.1-0 \n[22] htmltools_0.5.5 httpuv_1.6.12 Matrix_1.5-4.1 \n[25] survey_4.2-1 plyr_1.8.8 pkgconfig_2.0.3 \n[28] purrr_1.0.1 xtable_1.8-4 scales_1.2.1 \n[31] webshot_0.5.5 svglite_2.1.1 later_1.3.1 \n[34] metadat_1.2-0 lme4_1.1-35.1 tibble_3.2.1 \n[37] generics_0.1.3 ellipsis_0.3.2 withr_2.5.2 \n[40] cli_3.6.1 survival_3.5-5 magrittr_2.0.3 \n[43] mime_0.12 evaluate_0.23 fansi_1.0.4 \n[46] nlme_3.1-162 MASS_7.3-60 xml2_1.3.4 \n[49] tools_4.2.3 mitools_2.4 lifecycle_1.0.4 \n[52] stringr_1.5.1 munsell_0.5.0 compiler_4.2.3 \n[55] systemfonts_1.0.4 rlang_1.1.1 nloptr_2.0.3 \n[58] grid_4.2.3 rstudioapi_0.15.0 CompQuadForm_1.4.3 \n[61] htmlwidgets_1.6.2 miniUI_0.1.1.1 rmarkdown_2.25 \n[64] boot_1.3-28.1 gtable_0.3.4 abind_1.4-5 \n[67] DBI_1.1.3 reshape_0.8.9 R6_2.5.1 \n[70] knitr_1.45 denstrip_1.5.4 fastmap_1.1.1 \n[73] utf8_1.2.3 mathjaxr_1.6-0 ggExtra_0.10.1 \n[76] stringi_1.7.12 parallel_4.2.3 Rcpp_1.0.10 \n[79] vctrs_0.6.3 tidyselect_1.2.0 xfun_0.39 \n```\n:::\n:::\n\n\n## References {.unnumbered}\n\n", "supporting": [], "filters": [ "rmarkdown/pagebreak.lua" diff --git a/_freeze/chapter_11/figure-html/unnamed-chunk-7-1.png b/_freeze/chapter_11/figure-html/unnamed-chunk-7-1.png index da43eb2..bae7f56 100644 Binary files a/_freeze/chapter_11/figure-html/unnamed-chunk-7-1.png and b/_freeze/chapter_11/figure-html/unnamed-chunk-7-1.png differ diff --git a/_quarto.yml b/_quarto.yml index c3e1eae..09822f5 100644 --- a/_quarto.yml +++ b/_quarto.yml @@ -27,6 +27,7 @@ book: - chapter_12.qmd - chapter_16.qmd - chapter_18.qmd + - authors.qmd bibliography: 'https://api.citedrive.com/bib/0d25b38b-db8f-43c4-b934-f4e2f3bd655a/references.bib?x=eyJpZCI6ICIwZDI1YjM4Yi1kYjhmLTQzYzQtYjkzNC1mNGUyZjNiZDY1NWEiLCAidXNlciI6ICIyNTA2IiwgInNpZ25hdHVyZSI6ICI0MGFkYjZhMzYyYWE5Y2U0MjQ2NWE2ZTQzNjlhMWY3NTk5MzhhNzUxZDNjYWIxNDlmYjM4NDgwOTYzMzY5YzFlIn0=/bibliography.bib' diff --git a/authors.qmd b/authors.qmd new file mode 100644 index 0000000..b85c15a --- /dev/null +++ b/authors.qmd @@ -0,0 +1,23 @@ +--- +title: "Book Authors" +authors: + - name: Thomas Debray + orcid: 0000-0002-1790-2719 + affiliations: + - ref: smartdas +affiliations: + - id: smartdas + name: Smart Data Analysis and Statistics B.V. + city: Utrecht +format: + html: + toc: true + number-sections: true +execute: + cache: true +bibliography: 'https://api.citedrive.com/bib/0d25b38b-db8f-43c4-b934-f4e2f3bd655a/references.bib?x=eyJpZCI6ICIwZDI1YjM4Yi1kYjhmLTQzYzQtYjkzNC1mNGUyZjNiZDY1NWEiLCAidXNlciI6ICIyNTA2IiwgInNpZ25hdHVyZSI6ICI0MGFkYjZhMzYyYWE5Y2U0MjQ2NWE2ZTQzNjlhMWY3NTk5MzhhNzUxZDNjYWIxNDlmYjM4NDgwOTYzMzY5YzFlIn0=/bibliography.bib' +--- + +## About this book + +We gratefully acknowledge the contribution from the following authors: diff --git a/chapter_11.qmd b/chapter_11.qmd index 7ddaf8f..ea0bb48 100644 --- a/chapter_11.qmd +++ b/chapter_11.qmd @@ -99,7 +99,7 @@ IPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy, diabdur, wagner.class) ``` -Briefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 [@morbach_long-term_2012]. The baseline characteristics of the study population is summarized below: +Briefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 [@morbach_long-term_2012]. The baseline characteristics of the study population are summarized below: ```{r} #| echo: false @@ -108,7 +108,8 @@ wagner.groups <- table(IPD$wagner.class) IPD.and.wagner <- table(IPD$PAD, IPD$wagner.class) -dstbl <- healingipd %>% mutate(PAD = factor(PAD , levels = c(1,0), labels = c("Yes", "No")), +dstbl <- healingipd %>% mutate(healing.without.amp = factor(healing.without.amp , levels = c(1,0), labels = c("Healing without amputation", "No healing without amputation")), + PAD = factor(PAD , levels = c(1,0), labels = c("Yes", "No")), neuropathy = factor(neuropathy, levels = c(1,0), labels = c("Yes", "No")), first.ever.lesion = factor(first.ever.lesion, levels = c(1,0), labels = c("Yes", "No")), no.continuous.care = factor(no.continuous.care, levels = c(1,0), labels = c("Yes", "No")), @@ -122,6 +123,7 @@ dstbl <- healingipd %>% mutate(PAD = factor(PAD , levels = c(1,0), labels = c("Y DNOAP = factor(DNOAP, levels = c(1,0), labels = c("Yes", "No")), smoking.ever = factor(smoking.ever, levels = c(1,0), labels = c("Yes", "No"))) +label(dstbl$healing.without.amp) <- "Healing without amputation" label(dstbl$age) <- "Age" label(dstbl$PAD) <- "Peripheral arterial disease" label(dstbl$neuropathy) <- "Neuropathy" @@ -144,14 +146,49 @@ units(dstbl$diabdur) <- "years" table1(~ age + diabdur + gender + smoking.ever + diab.typ2 + PAD + neuropathy + first.ever.lesion + no.continuous.care + insulin + HOCHD + - HOS + CRF + dialysis + DNOAP + wagner.class, data = dstbl) + HOS + CRF + dialysis + DNOAP + wagner.class | healing.without.amp, data = dstbl) ``` As depicted above, IPD are available from `r nrow(healingipd)` patients. Some of these patients have similar characteristics to those enrolled in the randomized trials. However, other patients have comorbidities, where one or more risk factors prevent them to participate in the RCTs due to ethical reasons. For example, -`r wagner.groups[2]` patients have severe ulcer lesions (Wagner score 3 to 4), and `r IPD.and.wagner[2,2]` patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice? +`r wagner.groups[2]` patients have severe ulcer lesions (Wagner score 3 to 5), and `r IPD.and.wagner[2,2]` patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice? ### Hierarchical metaregression +We first investigate the event rate of patients receiving routine care: + +```{r} +#| warning: false +#| message: false +#| echo: false +#| fig-width: 10 +#| fig-height: 10 +healingplus <- healing %>% dplyr::select(Study, y_c, n_c) %>% + mutate("Source" = "RCT", cil = NA, ciu = NA) %>% + add_row(data.frame(Study = "Morbach 2012", + y_c = nrow(healingipd %>% filter(healing.without.amp==1)), + n_c = nrow(healingipd), + Source = "RWD")) %>% + mutate(prop = y_c/n_c) %>% + arrange(prop) + +for (i in seq(nrow(healingplus))) { + proptest <- prop.test(x = healingplus$y_c[i], n = healingplus$n_c[i], correct=FALSE) + healingplus$cil[i] <- proptest$conf.int[1] + healingplus$ciu[i] <- proptest$conf.int[2] +} + +ggplot(healingplus, aes(x=prop, y=reorder(Study, prop))) + + geom_errorbar(aes(xmin = cil, xmax = ciu, color = Source)) + + geom_point(aes(color = Source)) + + xlab("Recovery within one year (%)") + + ylab("")+ + theme(legend.position = "bottom") + + scale_x_continuous(labels = scales::percent) +``` + +The forest plot above indicates that the baseline risk in the observational study from Morbach et al. is much higher than most trials. + + We fitted an HMR model to the available RWD and published AD: ```{r hmr_fit} @@ -184,7 +221,7 @@ mx2 <- hmr(data = AD, # Published aggregate data nr.thin = 1) # Thinning rate ``` -We start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of $\mu_{\phi}$, which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass on the right of zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs. +We start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of $\mu_{\phi}$, which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass below zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs. ```{r} @@ -238,15 +275,16 @@ w.l <- apply(w, 2, quantile, prob = 0.25) n.studies <- length(w.s) w.col <- ifelse(w.s < 1.5, "grey", "red") w.col[length(w.s)] <- "black" -study.names = c(as.character(mx2$data$Study), "Cohort (individual data)") +study.names = c(as.character(mx2$data$Study), "RWD (Morbach 2012)") dat.weights = data.frame(x = study.names, y = w.s, ylo = w.l, yhi = w.u) ggplot(dat.weights, aes(x = x, y = y, ymin = ylo, ymax = yhi, size = 0.5)) + geom_pointrange(colour = w.col, lwd = 1, shape = 23, size = 0.3) + coord_flip() + - geom_hline(yintercept = 1, lty = 2) + xlab("Study") + - ylab("Outlier detection weight") + ggtitle("Weights") + - theme_bw() + geom_hline(yintercept = 1, lty = 2) + xlab("Study") + + ylab("Outlier detection weight") + + theme_bw() + + scale_y_log10() ``` diff --git a/chapter_11_files/figure-html/unnamed-chunk-7-1.png b/chapter_11_files/figure-html/unnamed-chunk-7-1.png index da43eb2..bae7f56 100644 Binary files a/chapter_11_files/figure-html/unnamed-chunk-7-1.png and b/chapter_11_files/figure-html/unnamed-chunk-7-1.png differ diff --git a/docs/chapter_11.html b/docs/chapter_11.html index 8c85368..432155d 100644 --- a/docs/chapter_11.html +++ b/docs/chapter_11.html @@ -228,6 +228,12 @@ 10  Visualization and interpretation of individualized treatment rule results + +
  • +
    + + 11  Book Authors +
    • @@ -337,19 +343,25 @@

    HOS, CRF, dialysis, DNOAP, smoking.ever, diabdur, wagner.class) -

    Briefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 (Morbach et al. 2012). The baseline characteristics of the study population is summarized below:

    -
    +

    Briefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 (Morbach et al. 2012). The baseline characteristics of the study population are summarized below:

    +
    --++++ + + @@ -358,193 +370,289 @@

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -553,7 +661,7 @@

    7.2.3 Hierarchical metaregression

    @@ -596,7 +704,7 @@

    \(w_{i}\) for each study included in the HMR. These posteriors are summarized using a forest plot, where posterior intervals substantially greater than one indicate outliers. One important aspect of the HMR is that those outliers are automatically down-weighted in the analysis.

    -
    +
    diff --git a/docs/chapter_11_files/figure-html/unnamed-chunk-7-1.png b/docs/chapter_11_files/figure-html/unnamed-chunk-7-1.png index da43eb2..bae7f56 100644 Binary files a/docs/chapter_11_files/figure-html/unnamed-chunk-7-1.png and b/docs/chapter_11_files/figure-html/unnamed-chunk-7-1.png differ diff --git a/docs/chapter_12.html b/docs/chapter_12.html index 66857f1..b071ca9 100644 --- a/docs/chapter_12.html +++ b/docs/chapter_12.html @@ -224,6 +224,12 @@ 10  Visualization and interpretation of individualized treatment rule results
    + +
  • +
    + + 11  Book Authors +
    • diff --git a/docs/search.json b/docs/search.json index 7c583cd..05f6db2 100644 --- a/docs/search.json +++ b/docs/search.json @@ -256,7 +256,7 @@ "href": "chapter_11.html#hierarchical-meta-regression", "title": "7  Individual Participant Data Meta-analysis of clinical trials and real-world data", "section": "7.2 Hierarchical Meta-Regression", - "text": "7.2 Hierarchical Meta-Regression\nWe illustrate the implementation of hierarchical meta-regression using an example that involves the following data sources:\n\nAggregate data from 35 randomized trials investigating the efficacy of adjunctive treatments in managing diabetic foot problems compared with routine care\nIndividual participant data from a prospective cohort study investigating patient and limb survival in patients with diabetic foot ulcers\n\n\n7.2.1 Aggregate data\nWe first retrieve the randomized evidence and summarize the treatment effect estimates using a random effects meta-analysis:\n\nlibrary(dplyr)\nlibrary(jarbes)\nlibrary(meta)\n\ndata(\"healing\")\n\nresults.ADJ <- metabin(event.c = y_c, n.c = n_c,\n event.e = y_t, n.e = n_t,\n studlab = Study, data = healing,\n sm = \"OR\", \n prediction = TRUE)\n\nThe corresponding forest plot is depicted below. The endpoint is healing without amputations within a period less than or equal to 1 year.\n\n\n\n\n\nThe random effects meta-analysis yielded a pooled odds ratio of 1.90. However, substantial between-study heterogeneity was found, with \\(\\tau\\) = 0.46.\n\n\n7.2.2 Individual participant data\nSubsequently, we retrieve the individual participant data:\n\ndata(\"healingipd\")\nIPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy,\n first.ever.lesion, no.continuous.care, \n male, diab.typ2, insulin, HOCHD, \n HOS, CRF, dialysis, DNOAP, smoking.ever, \n diabdur, wagner.class)\n\nBriefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 (Morbach et al. 2012). The baseline characteristics of the study population is summarized below:\n\n\n\n\n\n\n\n\n\n\n\n\nOverall\n(N=260)\n\n\n\n\nAge (years)\n\n\n\nMean (SD)\n68.9 (10.9)\n\n\nMedian [Min, Max]\n70.0 [25.0, 91.0]\n\n\nDiabetes duration (years)\n\n\n\nMean (SD)\n15.9 (10.6)\n\n\nMedian [Min, Max]\n14.0 [0, 53.0]\n\n\nSex\n\n\n\nFemale\n106 (40.8%)\n\n\nMale\n154 (59.2%)\n\n\nEver smoker\n\n\n\nYes\n154 (59.2%)\n\n\nNo\n106 (40.8%)\n\n\nDiabetes type 2\n\n\n\nYes\n229 (88.1%)\n\n\nNo\n31 (11.9%)\n\n\nPeripheral arterial disease\n\n\n\nYes\n148 (56.9%)\n\n\nNo\n112 (43.1%)\n\n\nNeuropathy\n\n\n\nYes\n224 (86.2%)\n\n\nNo\n36 (13.8%)\n\n\nFirst ever lesion\n\n\n\nYes\n114 (43.8%)\n\n\nNo\n146 (56.2%)\n\n\nNo continuous care\n\n\n\nYes\n177 (68.1%)\n\n\nNo\n83 (31.9%)\n\n\nInsulin dependent\n\n\n\nYes\n174 (66.9%)\n\n\nNo\n86 (33.1%)\n\n\nHistory of coronary events (CHD)\n\n\n\nYes\n52 (20.0%)\n\n\nNo\n208 (80.0%)\n\n\nHistory of stroke\n\n\n\nYes\n55 (21.2%)\n\n\nNo\n205 (78.8%)\n\n\nCharcot foot syndrome\n\n\n\nYes\n52 (20.0%)\n\n\nNo\n208 (80.0%)\n\n\nDialysis\n\n\n\nYes\n9 (3.5%)\n\n\nNo\n251 (96.5%)\n\n\nDNOAP\n\n\n\nYes\n29 (11.2%)\n\n\nNo\n231 (88.8%)\n\n\nWagner score\n\n\n\n1-2\n142 (54.6%)\n\n\n3-4-5\n118 (45.4%)\n\n\n\n\n\n\n\nAs depicted above, IPD are available from 260 patients. Some of these patients have similar characteristics to those enrolled in the randomized trials. However, other patients have comorbidities, where one or more risk factors prevent them to participate in the RCTs due to ethical reasons. For example, 118 patients have severe ulcer lesions (Wagner score 3 to 4), and 77 patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice?\n\n\n7.2.3 Hierarchical metaregression\nWe fitted an HMR model to the available RWD and published AD:\n\nset.seed(2022)\n\nAD <- healing %>% dplyr::select(yc = y_c, nc = n_c, \n yt = y_t, nt = n_t, Study = Study)\n\nmx2 <- hmr(data = AD, # Published aggregate data\n two.by.two = FALSE, # \n dataIPD = IPD, # Data frame of the IPD \n re = \"sm\", # Random effects model: \"sm\" scale mixtures \n link = \"logit\", # Link function of the random effects\n sd.mu.1 = 1, # Scale parameter for the prior of mu.1\n sd.mu.2 = 1, # Scale parameter for the prior of mu.2 \n sd.mu.phi = 1, # Scale parameter for the prior of mu.phi \n sigma.1.upper = 5, # Upper bound of the prior of sigma.1 \n sigma.2.upper = 5, # Upper bound of the prior of sigma.2\n sigma.beta.upper = 5, # Upper bound of the prior of sigma.beta\n sd.Fisher.rho = 1.25, # Scale parameter for the prior of rho\n df.estimate = TRUE, # If TRUE the degrees of freedom are estimated\n df.lower = 3, # Lower bound of the df's prior\n df.upper = 10, # Upper bound of the df's prior\n nr.chains = 2, # Number of MCMC chains\n nr.iterations = 10000, # Total number of iterations\n nr.adapt = 1000, # Number of iteration for burnin \n nr.thin = 1) # Thinning rate\n\nWe start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of \\(\\mu_{\\phi}\\), which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass on the right of zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs.\n\n\n\n\n\nConflict of evidence analysis. The left panel shows the prior to posterior sensitivity analysis of bias mean between the RCTs and the IPD-NRS. The right panel depicts the posterior distribution of the outliers detection weights.\n\n\n\n\nThe figure below presents the posterior distribution of the weights \\(w_{i}\\) for each study included in the HMR. These posteriors are summarized using a forest plot, where posterior intervals substantially greater than one indicate outliers. One important aspect of the HMR is that those outliers are automatically down-weighted in the analysis.\n\n\n\n\n\nPosterior distribution of the weights for each study included in the HMR" + "text": "7.2 Hierarchical Meta-Regression\nWe illustrate the implementation of hierarchical meta-regression using an example that involves the following data sources:\n\nAggregate data from 35 randomized trials investigating the efficacy of adjunctive treatments in managing diabetic foot problems compared with routine care\nIndividual participant data from a prospective cohort study investigating patient and limb survival in patients with diabetic foot ulcers\n\n\n7.2.1 Aggregate data\nWe first retrieve the randomized evidence and summarize the treatment effect estimates using a random effects meta-analysis:\n\nlibrary(dplyr)\nlibrary(jarbes)\nlibrary(meta)\n\ndata(\"healing\")\n\nresults.ADJ <- metabin(event.c = y_c, n.c = n_c,\n event.e = y_t, n.e = n_t,\n studlab = Study, data = healing,\n sm = \"OR\", \n prediction = TRUE)\n\nThe corresponding forest plot is depicted below. The endpoint is healing without amputations within a period less than or equal to 1 year.\n\n\n\n\n\nThe random effects meta-analysis yielded a pooled odds ratio of 1.90. However, substantial between-study heterogeneity was found, with \\(\\tau\\) = 0.46.\n\n\n7.2.2 Individual participant data\nSubsequently, we retrieve the individual participant data:\n\ndata(\"healingipd\")\nIPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy,\n first.ever.lesion, no.continuous.care, \n male, diab.typ2, insulin, HOCHD, \n HOS, CRF, dialysis, DNOAP, smoking.ever, \n diabdur, wagner.class)\n\nBriefly, these IPD were obtained from a prospective cohort study enrolling consecutive patients with diabetic foot ulcers (DFUs) and without previous major amputation in a single diabetes center between June 1998 and December 1999 (Morbach et al. 2012). The baseline characteristics of the study population are summarized below:\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nHealing without amputation\n(N=165)\nNo healing without amputation\n(N=95)\nOverall\n(N=260)\n\n\n\n\nAge (years)\n\n\n\n\n\nMean (SD)\n69.1 (10.9)\n68.5 (11.0)\n68.9 (10.9)\n\n\nMedian [Min, Max]\n70.0 [25.0, 90.0]\n69.0 [36.0, 91.0]\n70.0 [25.0, 91.0]\n\n\nDiabetes duration (years)\n\n\n\n\n\nMean (SD)\n15.9 (10.3)\n15.9 (11.2)\n15.9 (10.6)\n\n\nMedian [Min, Max]\n14.0 [1.00, 53.0]\n14.0 [0, 50.0]\n14.0 [0, 53.0]\n\n\nSex\n\n\n\n\n\nFemale\n71 (43.0%)\n35 (36.8%)\n106 (40.8%)\n\n\nMale\n94 (57.0%)\n60 (63.2%)\n154 (59.2%)\n\n\nEver smoker\n\n\n\n\n\nYes\n97 (58.8%)\n57 (60.0%)\n154 (59.2%)\n\n\nNo\n68 (41.2%)\n38 (40.0%)\n106 (40.8%)\n\n\nDiabetes type 2\n\n\n\n\n\nYes\n150 (90.9%)\n79 (83.2%)\n229 (88.1%)\n\n\nNo\n15 (9.1%)\n16 (16.8%)\n31 (11.9%)\n\n\nPeripheral arterial disease\n\n\n\n\n\nYes\n82 (49.7%)\n66 (69.5%)\n148 (56.9%)\n\n\nNo\n83 (50.3%)\n29 (30.5%)\n112 (43.1%)\n\n\nNeuropathy\n\n\n\n\n\nYes\n144 (87.3%)\n80 (84.2%)\n224 (86.2%)\n\n\nNo\n21 (12.7%)\n15 (15.8%)\n36 (13.8%)\n\n\nFirst ever lesion\n\n\n\n\n\nYes\n70 (42.4%)\n44 (46.3%)\n114 (43.8%)\n\n\nNo\n95 (57.6%)\n51 (53.7%)\n146 (56.2%)\n\n\nNo continuous care\n\n\n\n\n\nYes\n115 (69.7%)\n62 (65.3%)\n177 (68.1%)\n\n\nNo\n50 (30.3%)\n33 (34.7%)\n83 (31.9%)\n\n\nInsulin dependent\n\n\n\n\n\nYes\n109 (66.1%)\n65 (68.4%)\n174 (66.9%)\n\n\nNo\n56 (33.9%)\n30 (31.6%)\n86 (33.1%)\n\n\nHistory of coronary events (CHD)\n\n\n\n\n\nYes\n31 (18.8%)\n21 (22.1%)\n52 (20.0%)\n\n\nNo\n134 (81.2%)\n74 (77.9%)\n208 (80.0%)\n\n\nHistory of stroke\n\n\n\n\n\nYes\n36 (21.8%)\n19 (20.0%)\n55 (21.2%)\n\n\nNo\n129 (78.2%)\n76 (80.0%)\n205 (78.8%)\n\n\nCharcot foot syndrome\n\n\n\n\n\nYes\n28 (17.0%)\n24 (25.3%)\n52 (20.0%)\n\n\nNo\n137 (83.0%)\n71 (74.7%)\n208 (80.0%)\n\n\nDialysis\n\n\n\n\n\nYes\n3 (1.8%)\n6 (6.3%)\n9 (3.5%)\n\n\nNo\n162 (98.2%)\n89 (93.7%)\n251 (96.5%)\n\n\nDNOAP\n\n\n\n\n\nYes\n19 (11.5%)\n10 (10.5%)\n29 (11.2%)\n\n\nNo\n146 (88.5%)\n85 (89.5%)\n231 (88.8%)\n\n\nWagner score\n\n\n\n\n\n1-2\n115 (69.7%)\n27 (28.4%)\n142 (54.6%)\n\n\n3-4-5\n50 (30.3%)\n68 (71.6%)\n118 (45.4%)\n\n\n\n\n\n\n\nAs depicted above, IPD are available from 260 patients. Some of these patients have similar characteristics to those enrolled in the randomized trials. However, other patients have comorbidities, where one or more risk factors prevent them to participate in the RCTs due to ethical reasons. For example, 118 patients have severe ulcer lesions (Wagner score 3 to 5), and 77 patients suffer from severe ulcer lesions and peripheral arterial disease (PAD). The question is: Can we generalize the benefit of adjuvant therapies observed in the RCTs to the subgroups of patients encountered in clinical practice?\n\n\n7.2.3 Hierarchical metaregression\nWe fitted an HMR model to the available RWD and published AD:\n\nset.seed(2022)\n\nAD <- healing %>% dplyr::select(yc = y_c, nc = n_c, \n yt = y_t, nt = n_t, Study = Study)\n\nmx2 <- hmr(data = AD, # Published aggregate data\n two.by.two = FALSE, # \n dataIPD = IPD, # Data frame of the IPD \n re = \"sm\", # Random effects model: \"sm\" scale mixtures \n link = \"logit\", # Link function of the random effects\n sd.mu.1 = 1, # Scale parameter for the prior of mu.1\n sd.mu.2 = 1, # Scale parameter for the prior of mu.2 \n sd.mu.phi = 1, # Scale parameter for the prior of mu.phi \n sigma.1.upper = 5, # Upper bound of the prior of sigma.1 \n sigma.2.upper = 5, # Upper bound of the prior of sigma.2\n sigma.beta.upper = 5, # Upper bound of the prior of sigma.beta\n sd.Fisher.rho = 1.25, # Scale parameter for the prior of rho\n df.estimate = TRUE, # If TRUE the degrees of freedom are estimated\n df.lower = 3, # Lower bound of the df's prior\n df.upper = 10, # Upper bound of the df's prior\n nr.chains = 2, # Number of MCMC chains\n nr.iterations = 10000, # Total number of iterations\n nr.adapt = 1000, # Number of iteration for burnin \n nr.thin = 1) # Thinning rate\n\nWe start our analysis by visualizing the conflict of evidence between the different types of data and study types. The figure below depicts the posterior distribution of \\(\\mu_{\\phi}\\), which is the mean bias of the IPD-NRS compared to the AD-RCTs control groups. The posterior distribution has a substantial probability mass on the right of zero, which indicates that in average the IPD-NRS patients present a better prognoses than the AD-RCTs control groups. That means that taking the IPD-NRS results at face value would be misleading if we aim to combine them with a meta-analysis of AD-RCTs.\n\n\n\n\n\nConflict of evidence analysis. The left panel shows the prior to posterior sensitivity analysis of bias mean between the RCTs and the IPD-NRS. The right panel depicts the posterior distribution of the outliers detection weights.\n\n\n\n\nThe figure below presents the posterior distribution of the weights \\(w_{i}\\) for each study included in the HMR. These posteriors are summarized using a forest plot, where posterior intervals substantially greater than one indicate outliers. One important aspect of the HMR is that those outliers are automatically down-weighted in the analysis.\n\n\n\n\n\nPosterior distribution of the weights for each study included in the HMR" }, { "objectID": "chapter_12.html#introduction",

    Healing without amputation
    +(N=165)    		No healing without amputation
    +(N=95)    		 Overall
    (N=260)
    Age (years)
    Mean (SD)69.1 (10.9)68.5 (11.0) 68.9 (10.9)
    Median [Min, Max]70.0 [25.0, 90.0]69.0 [36.0, 91.0] 70.0 [25.0, 91.0]
    Diabetes duration (years)
    Mean (SD)15.9 (10.3)15.9 (11.2) 15.9 (10.6)
    Median [Min, Max]14.0 [1.00, 53.0]14.0 [0, 50.0] 14.0 [0, 53.0]
    Sex
    Female71 (43.0%)35 (36.8%) 106 (40.8%)
    Male94 (57.0%)60 (63.2%) 154 (59.2%)
    Ever smoker
    Yes97 (58.8%)57 (60.0%) 154 (59.2%)
    No68 (41.2%)38 (40.0%) 106 (40.8%)
    Diabetes type 2
    Yes150 (90.9%)79 (83.2%) 229 (88.1%)
    No15 (9.1%)16 (16.8%) 31 (11.9%)
    Peripheral arterial disease
    Yes82 (49.7%)66 (69.5%) 148 (56.9%)
    No83 (50.3%)29 (30.5%) 112 (43.1%)
    Neuropathy
    Yes144 (87.3%)80 (84.2%) 224 (86.2%)
    No21 (12.7%)15 (15.8%) 36 (13.8%)
    First ever lesion
    Yes70 (42.4%)44 (46.3%) 114 (43.8%)
    No95 (57.6%)51 (53.7%) 146 (56.2%)
    No continuous care
    Yes115 (69.7%)62 (65.3%) 177 (68.1%)
    No50 (30.3%)33 (34.7%) 83 (31.9%)
    Insulin dependent
    Yes109 (66.1%)65 (68.4%) 174 (66.9%)
    No56 (33.9%)30 (31.6%) 86 (33.1%)
    History of coronary events (CHD)
    Yes31 (18.8%)21 (22.1%) 52 (20.0%)
    No134 (81.2%)74 (77.9%) 208 (80.0%)
    History of stroke
    Yes36 (21.8%)19 (20.0%) 55 (21.2%)
    No129 (78.2%)76 (80.0%) 205 (78.8%)
    Charcot foot syndrome
    Yes28 (17.0%)24 (25.3%) 52 (20.0%)
    No137 (83.0%)71 (74.7%) 208 (80.0%)
    Dialysis
    Yes3 (1.8%)6 (6.3%) 9 (3.5%)
    No162 (98.2%)89 (93.7%) 251 (96.5%)
    DNOAP
    Yes19 (11.5%)10 (10.5%) 29 (11.2%)
    No146 (88.5%)85 (89.5%) 231 (88.8%)
    Wagner score
    1-2115 (69.7%)27 (28.4%) 142 (54.6%)
    3-4-550 (30.3%)68 (71.6%) 118 (45.4%)