chapter_11.qmd

---
title: "Individual Participant Data Meta-analysis of clinical trials and real-world data"
authors:   
  - name: Pablo Verde
    affiliations:
      - ref: umcdusseldorf
  - name: Thomas Debray
    orcid: 0000-0002-1790-2719
    affiliations:
      - ref: smartdas
affiliations:
  - id: smartdas
    name: Smart Data Analysis and Statistics B.V.
    city: Utrecht
  - id: umcdusseldorf
    name: Universitätsklinikum Düsseldorf
    city: Düsseldorf
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'
---


```{r}
#| include: false
#| echo: false
#| message: false
#| warning: false

# List of required packages
required_packages <- c("ggplot2", "dplyr", "gridExtra", "mcmcplots", 
                       "grid", "table1", "jarbes", 
                       "gridExtra", "GGally")

# Install required packages
for (pkg in required_packages) {
    if (!requireNamespace(pkg, quietly = TRUE)) {
        install.packages(pkg)
    }
}
library(kableExtra)
library(table1)
library(ggplot2)
```

## Introduction


## Hierarchical Meta-Regression
We illustrate the implementation of hierarchical meta-regression using an example that involves the following data sources:

* Aggregate data from 35 randomized trials investigating the efficacy of adjunctive treatments in managing diabetic foot problems compared with routine care
* Individual participant data from a prospective cohort study investigating patient and limb survival in patients with diabetic foot ulcers 

### Aggregate data
We first retrieve the randomized evidence and summarize the treatment effect estimates using a random effects meta-analysis:

```{r}
#| warning: false
#| message: false
#| results: hide
library(dplyr)
library(jarbes)
library(meta)

data("healing")

results.ADJ <- metabin(event.c = y_c, n.c = n_c,
                       event.e = y_t, n.e = n_t,
                       studlab = Study, data = healing,
                       sm = "OR", 
                       prediction = TRUE)
```

The corresponding forest plot is depicted below. The endpoint is healing without amputations within a period less than or equal to 1 year.

```{r}
#| echo: false
#| fig-width: 10
#| fig-height: 10
meta::forest(results.ADJ, leftcols = c("studlab", "n.e", "event.e", "n.c", "event.c"), rightcols = "effect.ci")
```

The random effects meta-analysis yielded a pooled odds ratio of `r sprintf("%.2f", exp(results.ADJ$TE.random))`. However, substantial between-study heterogeneity was found, with $\tau$ = `r sprintf("%.2f", results.ADJ$tau)`.

### Individual participant data
Subsequently, we retrieve the individual participant data:

```{r}
#| warning: false
data("healingipd")
IPD <- healingipd %>% dplyr::select(healing.without.amp, PAD, neuropathy,
                                    first.ever.lesion, no.continuous.care, 
                                    male, diab.typ2, insulin, HOCHD, 
                                    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_long-term_2012]. The baseline characteristics of the study population are summarized below:

```{r}
#| echo: false

wagner.groups <- table(IPD$wagner.class)
IPD.and.wagner <- table(IPD$PAD, IPD$wagner.class)


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")),
                        gender = ifelse(male == 1, "Male", "Female"),
                        diab.typ2 = factor(diab.typ2, levels = c(1,0), labels = c("Yes", "No")),
                        insulin = factor(insulin, levels = c(1,0), labels = c("Yes", "No")),
                        HOCHD = factor(HOCHD, levels = c(1,0), labels = c("Yes", "No")),
                        HOS = factor(HOS, levels = c(1,0), labels = c("Yes", "No")),
                        CRF = factor(CRF, levels = c(1,0), labels = c("Yes", "No")),
                        dialysis = factor(dialysis, levels = c(1,0), labels = c("Yes", "No")),
                        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"
label(dstbl$first.ever.lesion) <- "First ever lesion"
label(dstbl$no.continuous.care) <- "No continuous care"
label(dstbl$gender) <- "Sex"
label(dstbl$diab.typ2) <- "Diabetes type 2"
label(dstbl$insulin) <- "Insulin dependent"
label(dstbl$HOCHD) <- "History of coronary events (CHD)"
label(dstbl$HOS) <- "History of stroke"
label(dstbl$CRF) <- "Charcot foot syndrome"
label(dstbl$dialysis) <- "Dialysis"
label(dstbl$DNOAP) <- "DNOAP"
label(dstbl$smoking.ever) <- "Ever smoker"
label(dstbl$diabdur) <- "Diabetes duration"
label(dstbl$wagner.class) <- "Wagner score"

units(dstbl$age) <- "years"
units(dstbl$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 | 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 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}
#| message: false
#| warning: false
#| results: hide
set.seed(2022)

AD <- healing %>% dplyr::select(yc = y_c, nc = n_c, 
                                yt = y_t, nt = n_t, Study = Study)

mx2 <- hmr(data = AD,               # Published aggregate data
           two.by.two = FALSE,      # 
           dataIPD = IPD,           # Data frame of the IPD 
           re = "sm",               # Random effects model: "sm" scale mixtures 
           link = "logit",          # Link function of the random effects
           sd.mu.1 = 1,             # Scale parameter for the prior of mu.1
           sd.mu.2 = 1,             # Scale parameter for the prior of mu.2 
           sd.mu.phi = 1,           # Scale parameter for the prior of mu.phi 
           sigma.1.upper = 5,       # Upper bound of the prior of sigma.1  
           sigma.2.upper = 5,       # Upper bound of the prior of sigma.2
           sigma.beta.upper = 5,    # Upper bound of the prior of sigma.beta
           sd.Fisher.rho = 1.25,    # Scale parameter for the prior of rho
           df.estimate = TRUE,      # If TRUE the degrees of freedom are estimated
           df.lower = 3,            # Lower bound of the df's prior
           df.upper = 10,           # Upper bound of the df's prior
           nr.chains = 2,           # Number of MCMC chains
           nr.iterations = 10000,   # Total number of iterations
           nr.adapt = 1000,         # Number of iteration for burnin 
           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 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}
#| fig.cap: 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.
#| echo: false
#| message: false
#| warning: false
#| results: hide
#| fig.width: 11
#| fig.height: 10

# Diagnostic plot
mu.phi <- mx2$BUGSoutput$sims.list$mu.phi
mean.mu.phi <- mx2$prior$mean.mu.phi
sd.mu.phi <- mx2$prior$sd.mu.phi
df.mu.phi <- data.frame(x = mu.phi, dist = "Posterior")

ggplot(df.mu.phi, aes(x = x, colour = "Posterior")) + 
  geom_density() + 
  geom_histogram(aes(y = after_stat(density)), fill = "gray", alpha = 0.3, bins = 60) + 
  geom_vline(xintercept = mean.mu.phi, linewidth = 0.5, lty = 2) + 
  #geom_vline(xintercept = mean(mu.phi), aes(col = 'Posterior'), size = 1, lty = 2) + 
  stat_function(fun = dlogis, n = 101, 
                args = list(location = mean.mu.phi, scale = sd.mu.phi), size = 0.5, aes(color='Prior')) + 
  labs(x = expression(mu[phi]), y = "Density", color = "Density") +
  scale_color_manual(name='',
                   breaks=c('Prior', 'Posterior'),
                   values=c('Prior'='black', 'Posterior'='gray')) + 
 guides(color = guide_legend(override.aes = list(fill = NA))) +
  xlim(c(-10, 10)) + theme_bw() +
theme(
  legend.position = "bottom"  # Move the legend to the bottom
)
```


The 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.
```{r}
#| fig.cap: Posterior distribution of the weights for each study included in the HMR
#| echo: false
#| message: false
#| results: hide
#| fig.width: 11
#| fig.height: 10

w <- mx2$BUGSoutput$sims.list$w
w.s <- apply(w, 2, median)
w.u <- apply(w, 2, quantile, prob = 0.75)
w.l <- apply(w, 2, quantile, prob = 0.25)
n.studies <- length(w.s)
w.col <- ifelse(w.s < 1.5, "grey", "red")
w.col[length(w.s)] <- "black"
study.names = c(as.character(mx2$data$Study), "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") +
        theme_bw()  +
  scale_y_log10()
```


## Version info {.unnumbered}
This chapter was rendered using the following version of R and its packages:

```{r}
#| echo: false
#| message: false
#| warning: false
sessionInfo()
```

## References {.unnumbered}