In cmu-delphi/epiprocess: Tools for basic signal processing in epidemiology

source("_common.R")

This vignette describes functionality for detecting and correcting outliers in signals in the detect_outlr() and correct_outlr() functions provided in the epiprocess package. These functions are designed to be modular and extendable, so that you can define your own outlier detection and correction routines and apply them to epi_df objects. We'll demonstrate this using state-level daily reported COVID-19 case counts from FL and NJ.

The dataset has 730 rows and 3 columns.

library(epiprocess)
library(dplyr)
library(tidyr)

x <- covid_incidence_outliers

library(ggplot2)

ggplot(x, aes(x = time_value, y = cases)) +
  geom_line() +
  geom_hline(yintercept = 0, linetype = 3) +
  facet_wrap(vars(geo_value), scales = "free_y", ncol = 1) +
  scale_x_date(minor_breaks = "month", date_labels = "%b %y") +
  labs(x = "Date", y = "Reported COVID-19 counts")

There are multiple outliers in these data that a modeler may want to detect and correct. We'll discuss those two tasks in turn.

Outlier detection

The detect_outlr() function allows us to run multiple outlier detection methods on a given signal, and then (optionally) combine the results from those methods. Here, we'll investigate outlier detection results from the following methods.

Detection based on a rolling median, using detect_outlr_rm(), which computes a rolling median on with a default window size of n time points centered at the time point under consideration, and then computes thresholds based on a multiplier times a rolling IQR computed on the residuals.
Detection based on a seasonal-trend decomposition using LOESS (STL), using detect_outlr_stl(), which is similar to the rolling median method but replaces the rolling median with fitted values from STL.
Detection based on an STL decomposition, but subtracting out the seasonality term from its predictions, which may result in the extrema of large seasonal variations being considered as outliers.

The outlier detection methods are specified using a tibble that is passed to detect_outlr(), with one row per method, and whose columms specify the outlier detection function, any input arguments (only nondefault values need to be supplied), and an abbreviated name for the method used in tracking results. Abbreviations "rm" and "stl" can be used for the built-in detection functions detect_outlr_rm() and detect_outlr_stl(), respectively.

detection_methods <- bind_rows(
  tibble(
    method = "rm",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5
    )),
    abbr = "rm"
  ),
  tibble(
    method = "stl",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5,
      seasonal_period = 7
    )),
    abbr = "stl_seasonal"
  ),
  tibble(
    method = "stl",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5,
      seasonal_period = 7,
      seasonal_as_residual = TRUE
    )),
    abbr = "stl_reseasonal"
  )
)

detection_methods

Additionally, we'll form combined lower and upper thresholds, calculated as the median of the lower and upper thresholds from the methods at each time point. Note that using this combined median threshold is equivalent to using a majority vote across the base methods to determine whether a value is an outlier.

x <- x %>%
  group_by(geo_value) %>%
  mutate(
    outlier_info = detect_outlr(
      x = time_value,
      y = cases,
      methods = detection_methods,
      combiner = "median"
    )
  ) %>%
  ungroup() %>%
  unnest(outlier_info)

head(x)

To visualize the results, we first define a convenience function for plotting.

# Plot outlier detection bands and/or points identified as outliers
plot_outlr <- function(x, signal, method_abbr, bands = TRUE, points = TRUE,
                       facet_vars = vars(.data$geo_value), nrow = NULL, ncol = NULL,
                       scales = "fixed") {
  # Convert outlier detection results to long format
  signal <- rlang::enquo(signal)
  x_long <- x %>%
    pivot_longer(
      cols = starts_with(method_abbr),
      names_to = c("method", ".value"),
      names_pattern = "(.+)_(.+)"
    )

  # Start of plot with observed data
  p <- ggplot() +
    geom_line(data = x, mapping = aes(x = .data$time_value, y = !!signal))

  # If requested, add bands
  if (bands) {
    p <- p + geom_ribbon(
      data = x_long,
      aes(
        x = .data$time_value, ymin = .data$lower, ymax = .data$upper,
        color = .data$method
      ), fill = NA
    )
  }

  # If requested, add points
  if (points) {
    x_detected <- x_long %>% filter((!!signal < .data$lower) | (!!signal > .data$upper))
    p <- p + geom_point(
      data = x_detected,
      aes(
        x = .data$time_value, y = !!signal, color = .data$method,
        shape = .data$method
      )
    )
  }

  # If requested, add faceting
  if (!is.null(facet_vars)) {
    p <- p + facet_wrap(facet_vars, nrow = nrow, ncol = ncol, scales = scales)
  }

  return(p)
}

Now we produce plots for each state at a time, faceting by the detection method.

method_abbr <- c(detection_methods$abbr, "combined")

plot_outlr(x %>% filter(geo_value == "fl"), cases, method_abbr,
  facet_vars = vars(method), scales = "free_y", ncol = 1
) +
  scale_x_date(minor_breaks = "month", date_labels = "%b %y") +
  labs(
    x = "Date", y = "Reported COVID-19 counts", color = "Method",
    shape = "Method"
  )

plot_outlr(x %>% filter(geo_value == "nj"), cases, method_abbr,
  facet_vars = vars(method), scales = "free_y", ncol = 1
) +
  scale_x_date(minor_breaks = "month", date_labels = "%b %y") +
  labs(
    x = "Date", y = "Reported COVID-19 counts", color = "Method",
    shape = "Method"
  )

Outlier correction

Finally, in order to correct outliers, we can use the posited replacement values returned by each outlier detection method. Below we use the replacement value from the combined method, which is defined by the median of replacement values from the base methods at each time point.

y <- x %>%
  mutate(cases_corrected = combined_replacement) %>%
  select(geo_value, time_value, cases, cases_corrected)

y %>% filter(cases != cases_corrected)

ggplot(y, aes(x = time_value)) +
  geom_line(aes(y = cases), linetype = 2) +
  geom_line(aes(y = cases_corrected), col = 2) +
  geom_hline(yintercept = 0, linetype = 3) +
  facet_wrap(vars(geo_value), scales = "free_y", ncol = 1) +
  scale_x_date(minor_breaks = "month", date_labels = "%b %y") +
  labs(x = "Date", y = "Reported COVID-19 counts")