Adaptive Multiple Regression

The adaptive multiple regression algorithm fits a linear model to a baseline of counts or percentages of length B, and forecasts a predicted value g + 1 days later (guard-band). This value is compared to the current observed value and divided by the standard error of prediction in the test-statistic. The model includes terms to account for linear trends and day-of-week effects. Note that this implementation does NOT account for federal holidays as in the Regression 1.2 algorithm in ESSENCE. An alert (red value) is signaled if the statistical test (student's t-test) applied to the test statistic yields a p-value less than 0.01. If the p-value is greater than or equal to 0.01 and strictly less than 0.05, a warning (yellow value) is signaled. Blue values are returned if an alert or warning does not occur. Grey values represent instances where anomaly detection did not apply (i.e., observations for which baseline data were unavailable).

alert_regression(df, t = date, y = count, B = 28, g = 2)

Arguments

df	A data frame, data frame extension (e.g. a tibble), or a lazy data frame.
t	Name of the column of type Date containing the dates
y	Name of the column of type Numeric containing counts or percentages
B	Baseline parameter. The baseline length is the number of days to which each liner model is fit (default is 28)
g	Guardband parameter. The guardband length is the number of days separating the baseline from the current date in consideration for alerting (default is 2)

Value

A data frame with test statistic, p.value, and alert indicator

References

• Statistical Methods for Biosurveillance, Fricker (2013)

• Developments in the Roles, Features, and Evaluation of Alerting Algorithms for Disease Outbreak Monitoring

Examples

# Example 1
df <- data.frame(
  date = seq.Date(as.Date("2020-01-01"), as.Date("2020-12-31"), by = 1),
  count = floor(runif(366, min = 0, max = 101))
)

head(df)

df_regression <- alert_regression(df)

head(df_regression)

df <- data.frame(
  Date = seq.Date(as.Date("2020-01-01"), as.Date("2020-12-31"), by = 1),
  percent = runif(366)
)

head(df)

df_regression <- alert_regression(df, t = Date, y = percent)

head(df_regression)

if (FALSE) {
# Example 3: Data from NSSP-ESSENCE
library(ggplot2)

myProfile <- create_profile()

url <- "https://essence2.syndromicsurveillance.org/nssp_essence/api/timeSeries?
endDate=20Nov20&ccddCategory=cli%20cc%20with%20cli%20dd%20and%20coronavirus%20dd%20v2
&percentParam=ccddCategory&geographySystem=hospitaldhhsregion&datasource=va_hospdreg
&detector=probrepswitch&startDate=22Aug20&timeResolution=daily&hasBeenE=1
&medicalGroupingSystem=essencesyndromes&userId=2362&aqtTarget=TimeSeries&stratVal=
&multiStratVal=geography&graphOnly=true&numSeries=0&graphOptions=multipleSmall
&seriesPerYear=false&nonZeroComposite=false&removeZeroSeries=true&startMonth=January
&stratVal=&multiStratVal=geography&graphOnly=true&numSeries=0&graphOptions=multipleSmall
&seriesPerYear=false&startMonth=January&nonZeroComposite=false"

url <- url %>% gsub("\n", "", .)

api_data <- get_api_data(url)

df <- api_data$timeSeriesData

df_regression <- df %>%
  group_by(hospitaldhhsregion_display) %>%
  alert_regression(t = date, y = dataCount)

# Visualize alert for HHS Region 4
df_regression_region <- df_regression %>%
  filter(hospitaldhhsregion_display == "Region 4")

df_regression_region %>%
  ggplot() +
  geom_line(aes(x = date, y = dataCount), color = "grey70") +
  geom_line(
    data = subset(df_regression_region, alert != "grey"),
    aes(x = date, y = dataCount), color = "navy"
  ) +
  geom_point(
    data = subset(df_regression_region, alert == "blue"),
    aes(x = date, y = dataCount), color = "navy"
  ) +
  geom_point(
    data = subset(df_regression_region, alert == "yellow"),
    aes(x = date, y = dataCount), color = "yellow"
  ) +
  geom_point(
    data = subset(df_regression_region, alert == "red"),
    aes(x = date, y = dataCount), color = "red"
  ) +
  theme_bw() +
  labs(
    x = "Date",
    y = "Count"
  )
}