Test whether the reporting-delay distribution drifts over time

Runs an autocorrelation-robust monotonic-trend test on the per-period, count-weighted delay summaries, to answer "do delays drift over time?" in a way that respects the fact that a delay series is correlated with itself.

Usage

diagnose_drift(
  x,
  ...,
  stat = c("median", "spread"),
  method = c("hamed-rao", "yue-pilon", "block-bootstrap"),
  by_strata = FALSE,
  strata = NULL,
  mature_only = TRUE,
  level = 0.95,
  alpha = 0.05,
  axis = c("report", "validation")
)

Arguments

x: A tbl_now object.
...: Passed to the underlying modifiedmk function (e.g. nsim for "block-bootstrap").
stat: Which delay summaries to test: any of "median", "mean", "iqr" (q75 - q25) and "spread" (q90 - q10). Defaults to median + spread, i.e. one location and one dispersion statistic.
method: Trend test: "hamed-rao" (default; Hamed-Rao variance correction, modifiedmk::mmkh()), "yue-pilon" (Yue-Pilon, modifiedmk::mmky()) or "block-bootstrap" (block-bootstrap MK, modifiedmk::bbsmk()). See the Choosing a method section.
by_strata: Logical (default FALSE). When TRUE, the test is run separately per stratum.
strata: Character vector of columns to group on when by_strata = TRUE. NULL (default) uses the object's strata.
mature_only: Logical (default TRUE). Drop event dates after the level incompleteness cutoff before testing.
level: Completeness level for the maturity cutoff (default 0.95).
alpha: Significance level for the drift verdict column (default 0.05).
axis: Which time axis the delay is measured to: "report" (default) or "validation". Both are measured from the event, so the two are directly comparable – run each in turn and the gap between them is the time the laboratory adds. (This is not the same quantity as the .validation_delay column, which is the laboratory's own turnaround, measured from the report.) Needs a validation process (see add_validation_date()); cases still "pending" are left out.

Value

A tibble with one row per requested stat per stratum, and the following columns:

strata: character. The stratum the row refers to. When by_strata = FALSE (the default) there is a single stratum labelled "all"; otherwise one level per observed combination of strata.
stat: character. Which delay summary was tested — one of "median", "mean", "iqr" or "spread". "median"/"mean" are location statistics (are delays getting longer?); "iqr"/"spread" are dispersion statistics (are delays getting more erratic?).
n: integer. Length of the tested series, i.e. the number of event dates contributing a non-missing value after the mature_only filter. This is a count of periods, not a count of cases. Series with n < 10 (or with zero variance) are not tested and return NA for every test column.
tau: numeric in [-1, 1]. Kendall's rank correlation between the statistic and time — the effect size. Positive means delays are growing, negative means they are shrinking. Roughly, |tau| below 0.1 is a negligible trend even when p_value is small.
sens_slope: numeric. Sen's slope: the median pairwise rate of change, expressed in delay units per period — so for weekly data with delays measured in weeks, "weeks of delay gained per week elapsed". Multiply by n for the total drift implied across the series. Unlike an OLS slope this is robust to outlying periods.
statistic: numeric. The autocorrelation-corrected Mann-Kendall Z score. Under the null it is standard normal, so |Z| > 1.96 corresponds to p_value < 0.05.
p_value: numeric. Two-sided p-value for the null hypothesis of no monotonic trend, after the serial-correlation correction implied by method. NA when the series was too short or constant.
method: character. The method actually used, echoed back so the result is self-documenting when several runs are bound together.
drift: logical. The verdict: TRUE when p_value < alpha. NA p-values give FALSE, so a FALSE means "no drift detected" and not necessarily "no drift".

Details

For each requested stat (and each stratum) it builds the per-event-date series of that statistic and tests it for a monotonic trend with the modifiedmk package, which corrects the Mann-Kendall variance for serial autocorrelation. A plain Mann-Kendall (or an OLS slope) would be anti-conservative here, because positive autocorrelation shrinks the effective sample size.

By default the test uses only mature event dates (those on or before the level incompleteness cutoff), because the recent, not-yet-fully-reported dates would otherwise inject a spurious downward trend.

Interpreting the result

Read tau and sens_slope before p_value. On long surveillance series a tiny, operationally irrelevant trend will still be highly significant, so drift = TRUE on its own is not a reason to act. The question to ask is whether sens_slope * n — the total drift implied over the observed window — is large relative to the delays themselves.

The location and dispersion statistics answer different questions and can disagree, which is informative rather than contradictory:

median drifting up, spread flat: reporting is uniformly slower.
median flat, spread drifting up: the typical case is unaffected but the tail is getting worse — often a subset of reporting sites degrading.
both drifting up: broad deterioration in reporting timeliness.

A detected drift means a nowcasting model fitted on a fixed delay distribution will be biased, because it is averaging over delay regimes that are not exchangeable. Consider a model with a time-varying delay, or fitting only to the recent, homogeneous stretch of data.

Because this is a trend test it will not find an abrupt one-off shift; a step change can even cancel out to a non-significant monotonic trend. Pair it with diagnose_changepoint(), which is built for exactly that case.

Choosing a method

All three options are Mann-Kendall tests that correct for the serial correlation of a delay series; they differ in what they assume about that correlation, and in cost.

"hamed-rao" (default): Inflates the Mann-Kendall variance using all significant autocorrelation lags of the detrended ranks. It makes no AR(1) assumption, is deterministic, and is effectively instantaneous, so it is the sensible default for a routine diagnostic. Its variance correction is known to be unstable on short series — treat results with n below roughly 30 as indicative only.
"yue-pilon": Trend-free pre-whitening, which effectively assumes the series is AR(1). That assumption is a poor fit for daily reporting delays, which carry strong day-of-week periodicity, and pre-whitening is known to remove part of the very trend being tested. Offered for comparability with the hydrology literature; rarely the right choice here.
"block-bootstrap": Resamples contiguous blocks, so it accommodates arbitrary dependence within a block — including weekly periodicity, if the block length covers it. Statistically the most defensible for daily data, and the best cross-check when a hamed-rao result is borderline. Two caveats: it is stochastic, so call set.seed() first for a reproducible p-value, and it is thousands of times slower — it scales at roughly the square of the series length, so a multi-year daily series can take many minutes per statistic. Reduce nsim (passed through ...) or restrict to a shorter window before reaching for it.

When a decision matters, run the default first and confirm a borderline result with method = "block-bootstrap" on a restricted window.

Examples

data(denguedat)
dengue <- tbl_now(denguedat,
  event_date = "onset_week", report_date = "report_week", verbose = FALSE
)
diagnose_drift(dengue)
#> Warning: ! `diagnose_drift()` is experimental: results are not guaranteed and the
#>   interface may change.
#> ℹ Interpret a significant result as a potential trend change, not a confirmed
#>   one.
#> This warning is displayed once every 8 hours.
#> # A tibble: 2 × 9
#>   strata stat       n      tau sens_slope statistic p_value method    drift
#>   <chr>  <chr>  <int>    <dbl>      <dbl>     <dbl>   <dbl> <chr>     <lgl>
#> 1 all    median  1090 -0.00918          0    -0.243  0.808  hamed-rao FALSE
#> 2 all    spread  1090 -0.178            0    -2.32   0.0203 hamed-rao TRUE