Real World Evidence

Real-World Evidence Analysis in R

Overview

Methods for analyzing real-world data (RWD) to generate real-world evidence (RWE). Covers target trial emulation, comparative effectiveness research, propensity score methods for observational data, external control arms, bias quantification, and sensitivity analysis for unmeasured confounding.

Target Trial Emulation

Conceptual Framework

# Target trial emulation framework
# Specify the target trial protocol, then emulate using observational data

# Key elements to specify:
# 1. Eligibility criteria
# 2. Treatment strategies
# 3. Assignment procedures
# 4. Follow-up period
# 5. Outcome
# 6. Causal contrast (ITT, per-protocol, etc.)
# 7. Analysis plan

Using TrialEmulation Package

library(TrialEmulation)

# Prepare data for target trial emulation
# Data should be in long format with time-varying covariates

# Example: Clone-censor-weight approach
trial_data <- initiators(
  data = rwd,
  id = "patient_id",
  period = "period",
  treatment = "treatment",
  outcome = "outcome",
  eligible = "eligible",
  outcome_cov = ~ age + sex + comorbidity,
  model_var = "assigned_treatment",
  switch_d_cov = ~ time_since_start + lag_outcome,
  first_period = 1,
  last_period = 52,
  use_censor_weights = TRUE
)

# Fit the model
fit <- trial_msm(
  trial_data,
  outcome_cov = ~ assigned_treatment * poly(follow_up, 2),
  model_var = "assigned_treatment",
  include_followup_time = TRUE,
  include_trial_period = TRUE,
  use_sample_weights = TRUE,
  analysis_weights = "asis"
)

summary(fit)

Sequential Trial Emulation

# Emulate multiple trials starting at different time points
# Pool results across trials

# Step 1: Identify eligible patients at each time point
rwd_expanded <- rwd |>
  group_by(patient_id) |>
  mutate(
    # Check eligibility at each visit
    eligible = check_eligibility(age, lab_values, prior_treatment),
    # Time zero for each potential trial
    trial_start = if_else(eligible & treatment_initiated, visit_date, NA)
  ) |>
  ungroup()

# Step 2: Clone patients for each trial they're eligible for
# Step 3: Apply artificial censoring per assigned strategy
# Step 4: Weight for selection and artificial censoring
# Step 5: Pool and analyze

Propensity Score Methods for RWE

Propensity Score Estimation

library(MatchIt)
library(WeightIt)
library(cobalt)

# Estimate propensity scores
ps_model <- glm(
  treatment ~ age + sex + bmi + smoking + diabetes +
    prior_hosp + baseline_egfr + acei_use,
  family = binomial,
  data = rwd
)

rwd$ps <- predict(ps_model, type = "response")

# Check positivity (overlap)
ggplot(rwd, aes(x = ps, fill = factor(treatment))) +
  geom_density(alpha = 0.5) +
  labs(x = "Propensity Score", fill = "Treatment") +
  theme_bw()

Inverse Probability Weighting (IPW)

library(WeightIt)

# ATT weights (Average Treatment Effect on the Treated)
weights_att <- weightit(
  treatment ~ age + sex + bmi + smoking + diabetes +
    prior_hosp + baseline_egfr,
  data = rwd,
  method = "ps",
  estimand = "ATT"
)

# ATE weights (Average Treatment Effect)
weights_ate <- weightit(
  treatment ~ age + sex + bmi + smoking + diabetes,
  data = rwd,
  method = "ps",
  estimand = "ATE"
)

# Check balance
library(cobalt)
bal.tab(weights_att, stats = c("m", "v", "ks"))
love.plot(weights_att, threshold = 0.1)

# Weighted analysis
library(survey)
design <- svydesign(ids = ~1, weights = ~weights_att$weights, data = rwd)
fit_weighted <- svyglm(outcome ~ treatment, design = design, family = binomial)
summary(fit_weighted)

Overlap Weighting

library(PSweight)

# Overlap weights (target population with equipoise)
ow_result <- PSweight(
  ps.formula = treatment ~ age + sex + bmi + smoking + diabetes,
  data = rwd,
  yname = "outcome",
  weight = "overlap"
)

summary(ow_result)

Propensity Score Matching

library(MatchIt)

# 1:1 nearest neighbor matching
match_nn <- matchit(
  treatment ~ age + sex + bmi + smoking + diabetes + baseline_egfr,
  data = rwd,
  method = "nearest",
  distance = "glm",
  caliper = 0.2,
  ratio = 1,
  replace = FALSE
)

summary(match_nn)
plot(match_nn, type = "jitter")

# Get matched data
matched_data <- match.data(match_nn)

# Analyze matched data
fit_matched <- glm(outcome ~ treatment,
                   family = binomial,
                   data = matched_data,
                   weights = weights)

Doubly Robust Estimation

library(AIPW)

# Doubly robust estimator
aipw_result <- AIPW$new(
  Y = rwd$outcome,
  A = rwd$treatment,
  W = rwd |> select(age, sex, bmi, smoking, diabetes, baseline_egfr),
  Q.SL.library = c("SL.glm", "SL.ranger", "SL.xgboost"),
  g.SL.library = c("SL.glm", "SL.ranger"),
  k_split = 5,
  verbose = FALSE
)

aipw_result$fit()$summary()

# Risk difference and risk ratio
aipw_result$summary()

External Control Arms

Historical Controls Integration

# Combine trial data with external controls

# Step 1: Identify comparable external controls
external_controls <- rwd |>
  filter(
    # Match eligibility criteria
    age >= 18 & age <= 75,
    egfr >= 30,
    no_prior_treatment == TRUE
  )

# Step 2: Propensity score matching/weighting
library(MatchIt)

combined <- bind_rows(
  trial_data |> mutate(source = "trial", treatment = treatment),
  external_controls |> mutate(source = "external", treatment = 0)
)

# Match external controls to trial control arm characteristics
match_ext <- matchit(
  (source == "trial" & treatment == 0) ~ age + sex + stage + biomarker,
  data = combined |> filter(treatment == 0 | source == "external"),
  method = "nearest",
  caliper = 0.2
)

# Step 3: Analysis with matched external controls
matched_combined <- match.data(match_ext)

Propensity Score Integration

library(WeightIt)

# Weight external controls to match trial population
weights_ext <- weightit(
  source == "trial" ~ age + sex + stage + biomarker + region,
  data = combined,
  method = "ebal",          # Entropy balancing
  estimand = "ATT"
)

# Check balance
bal.tab(weights_ext)

# Weighted analysis
library(survival)
fit_ext <- coxph(
  Surv(time, event) ~ treatment + source,
  data = combined,
  weights = weights_ext$weights
)

Inverse Probability of Censoring Weighting

# Handle informative censoring in RWD

library(ipw)

# Model censoring probability
cens_model <- glm(
  censored ~ time_period + treatment + age + prior_event,
  family = binomial,
  data = rwd_long
)

# Calculate IPCW
rwd_long <- rwd_long |>
  group_by(patient_id) |>
  mutate(
    p_uncensored = 1 - predict(cens_model, type = "response"),
    ipcw = cumprod(p_uncensored)
  ) |>
  ungroup()

# Stabilized weights
rwd_long <- rwd_long |>
  mutate(
    sw = ps_weight * ipcw / mean(ps_weight * ipcw, na.rm = TRUE)
  )

# Weighted analysis with stabilized weights
library(survey)
design_ipcw <- svydesign(ids = ~patient_id, weights = ~sw, data = rwd_long)

Time-Varying Confounding and MSMs

library(ipw)

# Marginal Structural Model for time-varying treatment

# Step 1: Estimate time-varying treatment weights
temp_weights <- ipwtm(
  exposure = treatment,
  family = "binomial",
  link = "logit",
  numerator = ~ 1,
  denominator = ~ age + cd4 + viral_load + prior_oi,
  id = patient_id,
  timevar = visit,
  type = "first",
  data = rwd_long
)

# Step 2: Estimate censoring weights
temp_cens <- ipwtm(
  exposure = censored,
  family = "binomial",
  link = "logit",
  numerator = ~ 1,
  denominator = ~ age + cd4 + viral_load + treatment,
  id = patient_id,
  timevar = visit,
  type = "first",
  data = rwd_long
)

# Step 3: Combine weights
rwd_long$msm_weight <- temp_weights$ipw.weights * temp_cens$ipw.weights

# Step 4: Truncate extreme weights
rwd_long$msm_weight_trunc <- pmin(rwd_long$msm_weight,
                                   quantile(rwd_long$msm_weight, 0.99))

# Step 5: Fit MSM
library(geepack)
msm_fit <- geeglm(
  outcome ~ treatment + time,
  id = patient_id,
  weights = msm_weight_trunc,
  corstr = "independence",
  family = binomial,
  data = rwd_long
)

Adjusted Survival Curves

library(adjustedCurves)

# G-computation adjusted survival curves
adj_surv <- adjustedsurv(
  data = rwd,
  variable = "treatment",
  ev_time = "time",
  event = "event",
  method = "direct",
  outcome_model = coxph(Surv(time, event) ~ treatment + age + sex + stage,
                        data = rwd, x = TRUE),
  conf_int = TRUE,
  bootstrap = TRUE,
  n_boot = 500
)

# Plot
plot(adj_surv) +
  labs(x = "Time (months)", y = "Survival Probability",
       title = "Adjusted Survival Curves")

# IPTW-adjusted survival
adj_surv_iptw <- adjustedsurv(
  data = rwd,
  variable = "treatment",
  ev_time = "time",
  event = "event",
  method = "iptw_km",
  treatment_model = glm(treatment ~ age + sex + stage, family = binomial,
                        data = rwd),
  conf_int = TRUE
)

Sensitivity Analysis for Unmeasured Confounding

E-values

library(EValue)

# E-value for point estimate and confidence interval
evalue_result <- evalues.RR(
  est = 1.8,           # Observed risk ratio
  lo = 1.3,            # Lower CI bound
  hi = 2.5             # Upper CI bound
)

print(evalue_result)

# Interpretation: An unmeasured confounder would need to be
# associated with both treatment and outcome by RR of [E-value]
# to explain away the observed association

# Visualize
bias_plot(evalue_result)

Tip Analysis

library(tipr)

# Tipping point analysis
tip_result <- tip_coef(
  effect_observed = log(1.8),     # Observed log(RR)
  exposure_confounder_effect = seq(1, 3, 0.1),
  confounder_outcome_effect = seq(1, 3, 0.1),
  verbose = TRUE
)

# Visualize tipping points
plot(tip_result)

# Identify combinations that would tip result
tip_result |>
  filter(adjusted_effect < 0)  # Where effect becomes null/protective

Quantitative Bias Analysis

library(episensr)

# Probabilistic bias analysis for unmeasured confounding
set.seed(123)

# Observed data
obs_table <- matrix(c(100, 50, 80, 120), nrow = 2)

# Bias parameters (distributions)
pba_result <- probsens.conf(
  obs_table,
  reps = 10000,
  seca.parms = list("trapezoidal", c(0.7, 0.8, 0.9, 0.95)),  # Sensitivity
  spca.parms = list("trapezoidal", c(0.8, 0.85, 0.95, 1.0))  # Specificity
)

summary(pba_result)

Data Quality Assessment

# RWD quality checks

# 1. Completeness
completeness <- rwd |>
  summarise(across(everything(), ~mean(!is.na(.)) * 100)) |>
  pivot_longer(everything(), names_to = "variable", values_to = "pct_complete")

# 2. Plausibility
plausibility_checks <- rwd |>
  summarise(
    age_range_ok = all(age >= 0 & age <= 120),
    dates_consistent = all(discharge_date >= admission_date, na.rm = TRUE),
    lab_in_range = all(egfr >= 0 & egfr <= 200, na.rm = TRUE)
  )

# 3. Temporal patterns
rwd |>
  count(year = year(index_date)) |>
  ggplot(aes(year, n)) +
  geom_col() +
  labs(title = "Patient Enrollment Over Time")

# 4. Treatment patterns
rwd |>
  group_by(treatment) |>
  summarise(
    n = n(),
    mean_age = mean(age),
    pct_male = mean(sex == "male") * 100,
    mean_followup = mean(followup_time)
  )

Reporting RWE Studies

# Create Table 1 for RWE study
library(tableone)

# Unweighted baseline characteristics
vars <- c("age", "sex", "bmi", "smoking", "diabetes", "egfr", "stage")
cat_vars <- c("sex", "smoking", "diabetes", "stage")

tab1_unweighted <- CreateTableOne(
  vars = vars,
  strata = "treatment",
  data = rwd,
  factorVars = cat_vars,
  test = FALSE
)

# Weighted baseline characteristics (after PS weighting)
tab1_weighted <- svyCreateTableOne(
  vars = vars,
  strata = "treatment",
  data = design_weighted,
  factorVars = cat_vars,
  test = FALSE
)

# Print with SMD
print(tab1_unweighted, smd = TRUE)
print(tab1_weighted, smd = TRUE)

Key Packages Summary

Best Practices

1. Protocol first: Define target trial before touching data
2. Eligibility: Apply strict, transparent eligibility criteria
3. Time zero: Align treatment initiation with follow-up start
4. Immortal time: Avoid immortal time bias in study design
5. Balance: Check and report covariate balance (SMD < 0.1)
6. Positivity: Assess overlap and address violations
7. Sensitivity: Quantify impact of unmeasured confounding
8. Reporting: Follow RECORD/STROBE-RWE guidelines