Drawing a Forest Plot for Coxph with Subject IDs in R

Introduction

In this article, we will explore how to draw a forest plot for a Cox proportional hazards model (Coxph) that includes subject IDs as a variable. We’ll use the ggforest package from the ggplot2 family of packages to create these plots.

The Coxph model is used in survival analysis to estimate the hazard rate, which represents the probability of an event occurring within a given time period for subjects at risk. When working with clustered data (e.g., patients with multiple measurements over time), it’s essential to account for the clustering using a cluster-robust standard error.

Background

The ggforest package is part of the ggplot2 family of packages that provide high-level interfaces for plotting data in R, including various types of forest plots. The Coxph model provides hazard ratios and p-values for variables included in the model.

When using ggforest, the default behavior includes all predictor variables as fixed effects in the model. In our case, we want to exclude the subject ID (Id) from the plot because it doesn’t represent a variable that affects survival time but rather is an identifier used by R’s survival package for clustering.

The Problem with Subject IDs

In the provided example code, ggforest attempts to include both variables (QS and Age) in the forest plot. The issue lies in how these models are defined in practice when using clustered data:

# Define the Cox model
model <- coxph(Surv(start, end, Event) ~ QS + Age
           + cluster(Id), data = data, id=Id)

In this example, QS and Age have been modeled as predictors but without their interaction. However, these variables aren’t truly independent because the Id variable is nested within data. This structure makes sense in that patients only have one measurement per cluster (Id), so there isn’t an individual-level effect of Id.

However, when using Coxph with clustered data, we need to ensure that the clustering variable (Id) appears as a term in the model. This allows R to estimate the robust standard error correctly.

The ggforest function, by default, doesn’t provide the interaction between variables and cluster (in our case, Id) because it needs to be specified manually when generating a Coxph model with clustered data.

Solution

Step 1: Adjusting for Cluster

To get an accurate picture that only includes your predictor variable of interest (QS or Age), you will need to create a new term in your coxph model that captures cluster by including the interaction between the variable and the clustering variable.

However, since our goal is not to adjust the model but rather draw it without Id, we can modify the code used with ggforest. The issue here lies in how we structure the Coxph model.

Step 2: Specifying Variables for Forest Plot

To avoid including the subject ID (Id) and still utilize its clustering feature when calculating standard errors, you need to adjust your model so that it includes the interaction between your variable of interest (QS or Age) and the cluster term. Here’s how you might approach this:

# Create a new variable representing the cluster
data$cluster <- factor(data$Id)

# Define the Cox model
model <- coxph(Surv(start, end, Event) ~ QS + Age*cluster,
              data = data)

In our example above, QS and Age are modeled as main effects but without their interaction. We manually define a new term (Age*cluster) that captures the clustering effect.

Step 3: Generating Forest Plot

Now that we have adjusted our model to include an interaction with the cluster term, we can generate the forest plot using ggforest. However, we need to remove the unnecessary variable from the plot because it’s not what we want represented:

# Generate the forest plot
model <- coxph(Surv(start, end, Event) ~ QS + Age*cluster,
              data = data)

ggforest(model, data = data, effect = "odds ratio")

In this example, we generate a forest plot but specify effect = "odds ratio", which will ensure that the variable included in our model (QS) appears as an odds ratio in the forest plot rather than hazard ratios or other effects.

Additional Notes

• The most accurate representation of your desired forest plot may require additional steps depending on how you wish to present these results. For instance, if Age is a covariate that has been treated like a fixed effect for no reason (i.e., when accounting for cluster), then we can remove this term.
• You should verify whether the model assumptions hold by checking residuals against the fitted survival curves and plotting them to see if there’s any clear pattern of deviations.
• Always ensure that the model output is clearly understandable by interpreting all coefficients, p-values, and confidence intervals accordingly.

Example Usage

Let’s combine these steps into a fully functional R script that draws the desired forest plot without subject IDs:

# Load necessary libraries
library(ggplot2)
library(survival)

# Create sample data
data <- read.table(header = TRUE, text="
  Id   start end     QS   Age Event 
  01     0     70     1    25   1
  01    70     78     2    25   1
  01    78     85     3    25   1
  02     0     92     4    23   1
  02    92     98     5    23   1
  02    98     105    6    23   1
  02   105     106    7    23   0
")

# Define the Cox model and create a new term for cluster
data$cluster <- factor(data$Id)
model <- coxph(Surv(start, end, Event) ~ QS + Age*cluster,
              data = data)

# Generate forest plot without subject Id but with clustering effect
ggforest(model, data = data, effect = "odds ratio")

Conclusion

In this article, we’ve explored how to generate a forest plot for Coxph models that includes variables like QS and Age while excluding unnecessary variables like the subject ID (Id). We’ve walked through an example model specification and adjusted it where necessary.

Last modified on 2024-04-25