Simulated Treatment Comparison (STC)

Author

Xiaoge Zhang

Published

June 5, 2026

Predicting Outcomes Across Disconnected Networks via Regression

1 Executive Summary: The Predictive Approach

When attempting an indirect comparison between Trial A and Trial B, differing patient populations can introduce severe bias if there are Effect Modifiers (covariates that change the treatment effect) that are imbalanced between the trials.

If we have full Individual Patient Data (IPD) for both trials, we can simply run an IPD Network Meta-Analysis (IPD-NMA) to adjust for these differences. However, the standard reality in HEOR is that we only have IPD for our own Trial A, and only published Aggregate Data (AgD) for the competitor’s Trial B. This creates a severe population mismatch that prevents a fair “apples-to-apples” comparison.

While MAIC resolves this mismatch by re-weighting the IPD of Trial A to match Trial B’s baseline, Simulated Treatment Comparison (STC) approaches it by predicting outcomes. STC builds a regression model using Trial A’s IPD to understand the relationship between baseline characteristics and the clinical outcome. It then plugs Trial B’s aggregate baseline characteristics into this model to predict what Trial A’s outcome would have been if its patients had the same average baseline as Trial B.

  • Pros: STC does not reduce the Effective Sample Size (ESS) like MAIC does, and it can handle scenarios where covariate overlap is poor.
  • Cons: STC suffers from severe ecological bias when the outcome model is non-linear (e.g., Logistic regression for binary endpoints, Cox PH for survival). Plugging aggregate means into a non-linear function is mathematically flawed (\(f(E[X]) \neq E[f(X)]\)).

2 The Minimal Mock Case: Continuous Outcome

To demonstrate STC without the distraction of complex clinical datasets, we will simulate a minimal scenario:

  • Drug A (Index Trial): We have full IPD for 200 patients. The continuous outcome \(y\) is highly dependent on age.
  • Drug B (Target Trial): We only have published aggregate data. The mean age is 65, and the published mean outcome is 3.0.
View the code 
set.seed(42)

# ---------------------------------------------------------
# 1. Simulate Mock Data
# ---------------------------------------------------------
N_A <- 200
# Drug A (IPD): Mean age = 55, SD = 8
age_A <- rnorm(N_A, mean = 55, sd = 8)
# True outcome for Drug A (True effect = 10, minus 0.5 per year of age)
y_A <- rnorm(N_A, mean = 10 - 0.5 * (age_A - 55), sd = 2)
df_A <- data.frame(id = 1:N_A, age = age_A, y = y_A)

# Drug B (AgD published data)
mean_age_B <- 65.0
mean_y_B_published <- 3.0

# Naive comparison (Unadjusted)
mean_y_A_naive <- mean(df_A$y)

3 Custom R Implementation: STC from Scratch

The STC workflow consists of two simple mathematical steps:

  1. Fit a multivariable regression model on the IPD from Trial A. For a continuous outcome, we estimate the regression coefficients \(\hat{\beta}_0\) (intercept) and \(\hat{\beta}_1\) (effect of covariate \(X\)) using Trial A’s data: \[ y_{Ai} = \beta_0 + \beta_1 X_{Ai} + \epsilon_i \]

  2. Predict the outcome using the aggregate covariate values from Trial B. We take the published mean of the covariate from Trial B (\(\bar{X}_B\)) and plug it into our fitted model. This gives us the simulated, adjusted mean outcome for Drug A: \[ \hat{Y}_{A|B} = \hat{\beta}_0 + \hat{\beta}_1 \bar{X}_B \]

View the code 
# ---------------------------------------------------------
# 2. STC Implementation
# ---------------------------------------------------------

# Step 1: Fit the regression model on Trial A IPD
stc_model <- lm(y ~ age, data = df_A)

# Step 2: Create a synthetic data frame representing Trial B's average patient
target_profile <- data.frame(age = mean_age_B)

# Step 3: Predict the outcome for Drug A at Trial B's baseline
# This is \hat{Y}_{A|B}
mean_y_A_stc <- predict(stc_model, newdata = target_profile)

cat("Naive Mean Outcome (Drug A): ", round(mean_y_A_naive, 2), "\n")
Naive Mean Outcome (Drug A):  10.13
View the code 
cat("STC Predicted Outcome (Drug A adjusted to B's baseline): ", round(mean_y_A_stc, 2), "\n")
STC Predicted Outcome (Drug A adjusted to B's baseline):  4.82

4 Industry Standard Packages for STC

In the previous chapter on MAIC, we used the maicplus package because calculating weights requires a dedicated non-linear optimization routine.

For STC, however, there is no universally dominant dedicated R package. Why? Because the core methodology of STC is simply standard regression modeling. In pharmaceutical industry submissions, STC is almost exclusively performed using base R functions like lm() (for continuous outcomes), glm() (for binary), or survival::coxph() (for time-to-event). The model is fit, and predict() is called.

Recently, newer packages like outstandR have been developed to provide a unified framework for Population-Adjusted Indirect Comparisons (PAIC), but writing the regression equations explicitly in base R remains the most transparent and widely accepted practice by HTA reviewers.

5 Outcome Analysis: The Final Comparison

Just like in MAIC, once we have the adjusted outcome for Drug A, we perform the indirect comparison against Drug B.

5.1 Point Estimate of the Treatment Effect

The comparative treatment effect (\(\Delta\)) is the difference between the STC-predicted outcome of Drug A and the published outcome of Drug B.

View the code 
# Point Estimate
treatment_effect_stc <- mean_y_A_stc - mean_y_B_published
cat("Point Estimate of Treatment Effect (A vs B): ", round(treatment_effect_stc, 2), "\n")
Point Estimate of Treatment Effect (A vs B):  1.82

5.2 Quantifying Uncertainty

Unlike MAIC (which heavily relies on Bootstrapping because the weights are complex non-linear functions), the standard error for an STC prediction using linear regression can be extracted analytically directly from the model object.

View the code 
# Extract standard error of the prediction directly from the lm object
pred_obj <- predict(stc_model, newdata = target_profile, se.fit = TRUE)
se_stc <- pred_obj$se.fit

ci_lower_stc <- mean_y_A_stc - 1.96 * se_stc - mean_y_B_published
ci_upper_stc <- mean_y_A_stc + 1.96 * se_stc - mean_y_B_published

cat("STC Standard Error: ", round(se_stc, 3), "\n")
STC Standard Error:  0.221

5.3 Final Results

With the point estimate and the standard error, we can present the complete STC indirect comparison results:

Metric Estimate 95% CI Lower 95% CI Upper
Naive Difference 7.13 N/A N/A
STC Adjusted Difference 1.82 1.39 2.26

6 The Fatal Flaw: Ecological Bias in Non-Linear Models

If STC is so simple and preserves the full sample size (unlike MAIC), why is it considered highly flawed by HTA bodies like NICE?

The answer is Ecological Bias. In oncology and many other fields, outcomes are rarely continuous. They are typically binary (Logistic regression) or time-to-event (Cox Proportional Hazards). These models use non-linear link functions (e.g., logit, log).

A fundamental rule of mathematics (Jensen’s Inequality) states that for a non-linear function \(f\):

\[ f(E[X]) \neq E[f(X)] \]

If you fit a logistic regression model on Trial A, and then plug in the mean age of Trial B (\(\bar{X}_B = 65\)), you are calculating \(f(E[X])\). This predicts the probability of an event for a single hypothetical patient who is exactly 65 years old.

However, what you actually want is the average probability of the event across the entire Trial B population, which is \(E[f(X)]\).

Because STC plugs aggregate means into non-linear equations, it produces systematically biased population-level estimates. Quantifying this bias is impossible within the STC framework because it requires knowing the full distribution (variance and covariance) of the baseline characteristics in Trial B, which are not reported in the aggregate data. This mathematical inevitability is the exact reason why Multilevel Network Meta-Regression (ML-NMR) was invented—to perform numerical integration over simulated patient distributions to correctly calculate \(E[f(X)]\) without ecological bias.

7 Why STC is Still Alive

Given the severe criticism regarding Ecological Bias in non-linear models (which are the norm in oncology), one might wonder why STC is still widely used in HTA submissions. There are two primary reasons why STC remains a valid choice or even the only choice in certain scenarios:

7.1 1. Valid Linear Scenarios

There are many disease areas where the primary clinical endpoint is continuous and modeled via standard OLS linear regression. In these cases, the link function is linear, Jensen’s Inequality does not trigger, and STC is mathematically perfectly valid (yielding unbiased estimates). Examples include:

  • Diabetes: Mean reduction in HbA1c.
  • Obesity: Mean weight loss (kg).
  • Rheumatology/Psychiatry: Mean change in continuous symptom scores (e.g., PASI, HAQ-DI, MADRS).

7.2 2. The “Desperation” Scenario (Poor Overlap)

When Trial A and Trial B have very little covariate overlap (e.g., matching a very young cohort to a very old cohort), MAIC will drop the Effective Sample Size (ESS) to near zero, destroying statistical power and making the analysis dominated by a few outlier patients. STC, being a predictive regression model, does not rely on weighting and therefore does not suffer from ESS reduction. In these “desperate” cases with poor overlap, sponsors often submit STC even for non-linear outcomes, arguing that the resulting ecological bias is the “lesser evil” compared to a MAIC analysis with an ESS of 2.