---
title: "Full Emulation Pipeline"
format:
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execute:
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---

## Goal

This notebook puts the entire target trial emulation pipeline together in one place:

1. Simulate the observational data.
2. Define eligibility at time zero.
3. Clone eligible patients into treatment arms.
4. Apply censoring rules at the 2-hour mark.
5. Compute IPTW + IPCW weights.
6. Estimate the per-protocol effect.

Then we compare all four methods we have learned so far.

## Setup

```{r}
suppressPackageStartupMessages({
  library(dplyr)
  library(gt)
  library(tibble)
  library(tidyr)
})

source("../R/simulate_icu_cohort.R")
source("../R/simulate_icu_cohort_longitudinal.R")
source("../R/estimate_naive_vasopressor_mortality_effect.R")
source("../R/estimate_standardized_vasopressor_mortality_effect.R")
source("../R/estimate_iptw_vasopressor_mortality_effect.R")
source("../R/clone_trial_arms.R")
source("../R/estimate_iptw_and_ipcw_effect.R")
```

## Step 1: Simulate Data

We generate both the cross-sectional and longitudinal datasets using the same seed.

```{r}
icu_data <- simulate_icu_cohort(n_patients = 1000, seed = 20260531)
longitudinal_data <- simulate_icu_cohort_longitudinal(n_patients = 1000, seed = 20260531)
```

## Step 2: Cross-Sectional Estimates

### Naive comparison

```{r}
naive_analysis <- estimate_naive_vasopressor_mortality_effect(icu_data)
```

### Outcome regression standardization

```{r}
standardized_analysis <- estimate_standardized_vasopressor_mortality_effect(icu_data)
```

### Cross-sectional IPTW

```{r}
iptw_analysis <- estimate_iptw_vasopressor_mortality_effect(icu_data)
```

## Step 3: Longitudinal Emulation

### Clone and censor

```{r}
clones <- clone_trial_arms(longitudinal_data)
```

### Compute IPTW + IPCW weights and estimate effect

```{r}
longitudinal_analysis <- estimate_iptw_and_ipcw_effect(clones$clone_baseline)
```

## Four-Way Comparison

We now extract the risk difference and risk ratio from each method and place them in one table.

```{r}
# Naive
naive_rd <- naive_analysis$mortality_effect_estimates |>
  filter(estimate == "Naive risk difference") |>
  pull(value)

naive_rr <- naive_analysis$mortality_effect_estimates |>
  filter(estimate == "Naive risk ratio") |>
  pull(value)

# Standardized
std_rd <- standardized_analysis$standardized_mortality_effect_estimates |>
  filter(estimate == "Standardized risk difference") |>
  pull(value)

std_rr <- standardized_analysis$standardized_mortality_effect_estimates |>
  filter(estimate == "Standardized risk ratio") |>
  pull(value)

# Cross-sectional IPTW
iptw_rd <- iptw_analysis$iptw_mortality_effect_estimates |>
  filter(estimate == "IPTW risk difference") |>
  pull(value)

iptw_rr <- iptw_analysis$iptw_mortality_effect_estimates |>
  filter(estimate == "IPTW risk ratio") |>
  pull(value)

# Longitudinal IPTW + IPCW
long_rd <- longitudinal_analysis$weighted_effect_estimates |>
  filter(estimate == "IPTW + IPCW risk difference") |>
  pull(value)

long_rr <- longitudinal_analysis$weighted_effect_estimates |>
  filter(estimate == "IPTW + IPCW risk ratio") |>
  pull(value)

four_way <- tibble(
  method = c(
    "1. Naive observed comparison",
    "2. Outcome regression standardization",
    "3. Cross-sectional IPTW",
    "4. Longitudinal IPTW + IPCW (per-protocol)"
  ),
  risk_difference = c(naive_rd, std_rd, iptw_rd, long_rd),
  risk_ratio = c(naive_rr, std_rr, iptw_rr, long_rr)
)

four_way |>
  gt() |>
  tab_header(title = "Four-Way Comparison of Effect Estimation Methods") |>
  cols_label(
    method = "Method",
    risk_difference = "Risk difference",
    risk_ratio = "Risk ratio"
  ) |>
  fmt_number(columns = c(risk_difference, risk_ratio), decimals = 3)
```

## Interpretation

### What each method answers

| Method | Question it answers |
|--------|-------------------|
| **Naive** | "What was the mortality difference between patients who did and did not receive early vasopressors?" |
| **Standardization** | "What would the mortality risk be if everyone followed each strategy, holding the eligible population fixed?" |
| **Cross-sectional IPTW** | "What is the effect of receiving early vasopressors versus not, reweighted to balance confounders?" |
| **Longitudinal IPTW + IPCW** | "What is the per-protocol effect of the early vasopressor strategy versus the no early strategy, respecting the grace period and accounting for censoring?" |

### What to notice in the simulated data

In the data-generating process, early vasopressors have a modest **protective** effect.

1. The **naive** estimate shows **harm** (positive risk difference, risk ratio > 1). This is because sicker patients are more likely to receive early vasopressors and more likely to die — confounding by indication.

2. **Standardization** and **cross-sectional IPTW** both move the estimate toward a **protective** direction, correcting for baseline confounding.

3. The **longitudinal IPTW + IPCW** estimate may differ slightly from cross-sectional IPTW because it:
   - Restricts to the per-protocol population (patients who could adhere through the 2-hour window)
   - Re-weights for informative censoring (patients censored due to protocol deviation or early death)
   - Respects the grace period as a longitudinal treatment assignment window

None of the methods perfectly recover the true effect in a single finite sample, but the longitudinal method most closely emulates the target trial design.

## Assumption Checklist

Every method above relies on assumptions. A quick checklist:

| Assumption | Naive | Standardized | IPTW | IPTW + IPCW |
|------------|-------|-------------|------|-------------|
| No unmeasured confounding | ❌ | ✅ | ✅ | ✅ |
| Positivity (every patient has some probability of each treatment) | ❌ | ✅ | ✅ | ✅ |
| Correct model specification | N/A | ✅ | ✅ | ✅ |
| No informative censoring | N/A | N/A | N/A | ✅ |

- **No unmeasured confounding**: We must have measured all variables that affect both treatment assignment and mortality. In a real study, this is never fully testable.
- **Positivity**: Every patient must have a non-zero probability of receiving each treatment. Extreme propensity scores cause unstable weights.
- **Correct model specification**: The logistic regression models must capture the true relationships between confounders, treatment, and outcome.
- **No informative censoring (for IPCW)**: Censoring must be independent of the outcome given measured confounders. In practice, we use baseline-only IPCW here; a full analysis would include time-varying covariates.

## Next Steps

From here, the tutorial can extend into several directions:

1. **Time-varying confounders**: Include `map_current` and `lactate_current` in the censoring model to handle post-baseline severity changes.
2. **Survival analysis**: Model time-to-death rather than 28-day binary mortality, using Kaplan-Meier or Cox models with IPCW.
3. **Sensitivity analysis**: Test how sensitive the results are to unmeasured confounding (e.g., E-values).
4. **`targets` pipeline**: Convert the analysis into a reproducible pipeline with dependency tracking.

These topics move the project from a teaching scaffold toward a production-ready target trial emulation workflow.