Term2 Integration Methods: Performance Comparison

# Load and prepare example data
data_with_lags <- SensIAT_example_data |>
  group_by(Subject_ID) |>
  mutate(
    ..prev_outcome.. = lag(Outcome, default = NA_real_, order_by = Time),
    ..prev_time.. = lag(Time, default = 0, order_by = Time),
    ..delta_time.. = Time - lag(Time, default = NA_real_, order_by = Time)
  ) |>
  ungroup()

cat("Data summary:\n")
cat("  Patients:", n_distinct(data_with_lags$Subject_ID), "\n")
cat("  Total observations:", nrow(data_with_lags), "\n")

# Fit outcome model (single-index with splines)
outcome.model <- fit_SensIAT_single_index_fixed_coef_model(
  Outcome ~ splines::ns(..prev_outcome.., df = 3) + ..delta_time.. - 1,
  id = Subject_ID,
  data = data_with_lags |> filter(Time > 0)
)

# Imputation function for extrapolation
impute_fn <- function(t, df) {
  extrapolate_from_last_observation(
    t, df, "Time",
    slopes = c("..delta_time.." = 1)
  )
}

# Marginal mean spline knots
knots <- c(60, 260, 460)

# Run isolated term2 benchmark
benchmark_results <- benchmark_term2_methods(
  data = data_with_lags,
  id = Subject_ID,
  time = data_with_lags$Time,
  outcome.model = outcome.model,
  knots = knots,
  alpha = c(-0.05, 0, 0.05),
  impute_data = impute_fn,
  link = "identity",
  methods = c("fast", "original", "fixed_grid", "seeded_adaptive"),
  grid_sizes = c(50, 100, 200),
  n_patients = 20,
  n_iterations = 5,
  reference_method = "fast"
)

# Benchmark with varying grid sizes
grid_benchmark <- benchmark_term2_methods(
  data = data_with_lags,
  id = Subject_ID,
  time = data_with_lags$Time,
  outcome.model = outcome.model,
  knots = knots,
  alpha = 0,
  impute_data = impute_fn,
  link = "identity",
  methods = c("fast", "fixed_grid"),
  grid_sizes = c(25, 50, 75, 100, 150, 200),
  n_patients = 15,
  n_iterations = 3,
  reference_method = "fast"
)

# Extract grid-specific results
grid_accuracy <- grid_benchmark$accuracy |>
  filter(grepl("fixed_grid", method)) |>
  mutate(
    grid_n = as.numeric(gsub("fixed_grid_", "", method))
  )

grid_timing <- grid_benchmark$timing |>
  filter(grepl("fixed_grid", method)) |>
  mutate(
    grid_n = as.numeric(gsub("fixed_grid_", "", method))
  )

# Combine for plotting
grid_combined <- left_join(grid_accuracy, grid_timing, by = c("method", "grid_n"))

ggplot(grid_combined, aes(x = grid_n)) +
  geom_line(aes(y = rmse), color = "steelblue", linewidth = 1) +
  geom_point(aes(y = rmse), color = "steelblue", size = 3) +
  scale_y_log10() +
  labs(
    title = "Fixed-Grid Accuracy vs Grid Density",
    x = "Number of Grid Points",
    y = "RMSE from Reference (log scale)"
  ) +
  theme_minimal()

ggplot(grid_combined, aes(x = mean_time, y = rmse, label = grid_n)) +
  geom_point(size = 4, color = "steelblue") +
  geom_text(vjust = -1, hjust = 0.5) +
  scale_y_log10() +
  labs(
    title = "Speed-Accuracy Tradeoff for Fixed-Grid Method",
    subtitle = "Labels show number of grid points",
    x = "Computation Time (seconds)",
    y = "RMSE from Reference (log scale)"
  ) +
  theme_minimal()

sessionInfo()
#> R version 4.6.0 (2026-04-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] ggplot2_4.0.3      dplyr_1.2.1        SensIAT_0.3.0.9000 rmarkdown_2.31    
#> 
#> loaded via a namespace (and not attached):
#>  [1] Matrix_1.7-5                gtable_0.3.6               
#>  [3] jsonlite_2.0.0              compiler_4.6.0             
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#> [15] R6_2.6.1                    labeling_0.4.3             
#> [17] generics_0.1.4              knitr_1.51                 
#> [19] MASS_7.3-65                 tibble_3.3.1               
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#> [25] rlang_1.2.0                 cachem_1.1.0               
#> [27] xfun_0.57                   S7_0.2.2                   
#> [29] sass_0.4.10                 sys_3.4.3                  
#> [31] cli_3.6.6                   withr_3.0.2                
#> [33] magrittr_2.0.5              orthogonalsplinebasis_0.1.7
#> [35] digest_0.6.39               grid_4.6.0                 
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#> [39] KernSmooth_2.23-26          pracma_2.4.6               
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