5  Defining Intervention Effects

ITS analysis helps you pinpoint different ways a time series might be affected by an intervention.

Immediate Effect:

• Represents a sudden shift in the data the moment the intervention takes place. Imagine a new policy leading to an abrupt change in behavior.

• Did the intervention create an immediate spike or drop in the data?

Step Effect:

• Reflects a permanent change in the baseline level of the time series. Think of stepping onto a higher or lower platform after the intervention – the overall level has shifted.

• Did the intervention fundamentally alter the overall level of the time series?

Ramp Effect:

• Demonstrates a gradual increase or decrease following the intervention. Picture yourself walking up or down a slope after the event – the trend and trajectory of the time series are constantly changing.

• Did the intervention set in motion a gradual upward or downward trend?

ITS analysis isn’t just about single, isolated effects. The beauty of the method lies in its ability to capture a variety of ways the intervention might change the time series data:

• Shifts & Slopes:

  • You can identify combinations of both immediate level changes (“step” effects) and changes in the trend of the data (“ramp” effects):

    • Level Only: Did the intervention create a jump or drop that then persists at a new, stable level?

    • Trend Only: Did the slope of the series gradually change direction over time after the intervention?

    • Both: An immediate change in the level, combined with a new upward or downward trend.

• Delays:

  • In some cases, the full change caused by the intervention might not appear immediately. ITS can detect if an effect, whether a level shift or trend change, starts after a delay.

• Temporary Changes:

  • Interventions don’t always have everlasting effects. Sometimes there’s a momentary shock and then a return to previous levels, or a brief trend change that flattens out again.

Below is a graphical visualization of potential different effects you might consider when designing an ITS analysis.

library(ggplot2)
library(tidyverse)
library(lubridate)

# --- Parameters ----
outcome_baseline <- 50           
pre_intervention_slope <- 2          
interv_point <- 40        
n_timepoints <- 100    

# --- Simulation ----
set.seed(123) 
base_data <- tibble(
  time = 1:n_timepoints,
  outcome = outcome_baseline + pre_intervention_slope * time + rnorm(n_timepoints, 0, 50)
)


# --- Functions to add effects ---
level_change <- function(data, magnitude) {
  data$outcome[data$time >= interv_point] <- data$outcome[data$time >= interv_point] + magnitude
  return(data)
}

trend_change <- function(data, slope_change) {
  data$outcome[data$time >= interv_point] <- data$outcome[data$time >= interv_point] + 
    slope_change * (data$time[data$time >= interv_point] - interv_point)
  return(data)
}

delayed_effect <- function(data, magnitude, delay, type = "level") {
  if(type == "level") {
    data$outcome[data$time >= (interv_point + delay)] <- 
      data$outcome[data$time >= (interv_point + delay)] + magnitude
  } else {
    data$outcome[data$time >= (interv_point + delay)] <- 
      data$outcome[data$time >= (interv_point + delay)] + 
      slope_change * (data$time[data$time >= (interv_point + delay)] - (interv_point + delay))
  }
  return(data)
}

temporary_effect <- function(data, magnitude, duration, type = "level") {
  if (type == "level") {
    data$outcome[data$time >= interv_point & data$time < (interv_point + duration)] <- 
      data$outcome[data$time >= interv_point & data$time < (interv_point + duration)] + magnitude
  } else {
    start_trend <- interv_point
    end_trend <- interv_point + duration
    data$outcome[data$time >= start_trend & data$time < end_trend] <- 
      data$outcome[data$time >= start_trend & data$time < end_trend] + 
      magnitude * (data$time[data$time >= start_trend & data$time < end_trend] - start_trend)
  }
  return(data)
}

# --- Scenarios ------

# 1. Level change only
df_level <- level_change(base_data, magnitude = 4)

# 2. Slope change only
df_trend <- trend_change(base_data , slope_change = 0.5)

# 3. Level and Slope change
df_both <- level_change(df_trend, magnitude = 4)

# 4. Delays
slope_change = 0.3
df_delayed_level <- delayed_effect(base_data,  magnitude = 4, delay = 25)
df_delayed_trend <- delayed_effect(base_data,  magnitude = 0.5, delay = 25, "trend")
df_delayed_both <- delayed_effect(df_delayed_trend,  magnitude = 4, delay = 25)

# 5. Temporary changes
df_temp_level <- temporary_effect(base_data , magnitude = 4, duration = 25)
df_temp_trend <- temporary_effect(base_data , magnitude = 0.5, duration = 25, type="trend")
df_temp_both <- temporary_effect(df_temp_trend , magnitude = 4, duration = 25)


df_effects <- 
  dplyr::bind_rows(
    dplyr::mutate(df_level,effects = "Level Change", order = 1),
    dplyr::mutate(df_trend,effects = "Trend Change", order = 2),
    dplyr::mutate(df_both,effects = "Level and Trend", order = 3),
    dplyr::mutate(df_delayed_level,effects = "Delayed (level)", order = 4),
    dplyr::mutate(df_delayed_trend,effects = "Delayed (trend)", order = 5),
    dplyr::mutate(df_delayed_both,effects = "Delayed (level and trend)", order = 6),
    dplyr::mutate(df_temp_level,effects = "Temporary (level)", order = 7),
    dplyr::mutate(df_temp_trend,effects = "Temporary (trend)", order = 8),
    dplyr::mutate(df_temp_both,effects = "Temporary (level and trend)", order = 9)
  )


# --- Plotting  -----
ggplot(df_effects, aes(x = time, y = outcome, 
                       color = fct_reorder(effects, order), 
                       group = fct_reorder(effects, order), 
                       fill = fct_reorder(effects, order))) +
  geom_line() + 
  geom_vline(xintercept = interv_point, linetype = "dashed") + 
  facet_wrap(vars(fct_reorder(effects, order)), nrow = 3)  + 
  theme_bw() +
  theme(
    # White background areas
    panel.background = element_rect(fill = "white"),
    plot.background = element_rect(fill = "white"),
    plot.margin = unit(c(0.5, 0.5, 0.5, 0.5), "inches"),
    # Plot margins
    plot.title =  element_text(
      size = 12,
      face = "bold",
      color = "black"
    ),
    axis.title.y = element_text(
      size = 12,
      face = "bold",
      color = "black",
      vjust = 7
    ),
    axis.title.x = element_text(
      size = 12,
      face = "bold",
      color = "black",
      vjust = -7
    ),
    axis.text.y = element_text(
      face = "bold",
      size = 12,
      color = "black"
    ),
    axis.text.x = element_text(
      face = "bold",
      color = "black",
      size = 12,
      angle = 0,
      vjust = 1
    ),
    
    # Remove axis ticks
    axis.ticks = element_blank(),
    legend.position = "none"
    ) + 
  ggtitle("Examples of Possible ITS Effects")  +
  ylab("Outcome") +
  scale_y_continuous(expand = c(0, 0),breaks = scales::pretty_breaks()) +
  scale_x_continuous(expand = c(0, 0),breaks = scales::pretty_breaks()) +
  xlab("Time") + 
    scale_color_manual(values= c("#203864", "#3086c3", "#4754eb", "#5fb4cc" ,"#985b9a", "#ee6c9b", "#42ae65", "#ef9c33", "#c23a2e", "#b06d18"),aesthetics = "colour") + 
  scale_color_manual(values= c("#203864", "#3086c3", "#4754eb", "#5fb4cc" ,"#985b9a", "#ee6c9b", "#42ae65", "#ef9c33", "#c23a2e", "#b06d18"),aesthetics = "fill") 

Understanding these combined effects gives you a richer picture of the intervention’s impact:

• Magnitude: What was the combined influence on the overall level of your outcome?

• Timing: Was the bulk of the impact immediate, delayed, or gradual?

• Duration: Was the effect permanent or fleeting?