14  Trend Analysis

This chapter analyzes temporal trends in consultation volume and the “Consultation Rate” (percentage of total pathology cases that require consultation). Long-term trends in anatomic pathology workload have shown consistent increases in case complexity and volume (Bonert et al. 2021), and digital pathology implementations have been associated with measurable changes in efficiency and consultation patterns (Hanna et al. 2019). Interrupted time series (ITS) analysis is increasingly recognized as the strongest quasi-experimental design for evaluating quality improvement interventions in healthcare, though a systematic review found that 72.5% of published ITS studies had high or very high risk of bias, highlighting the importance of methodological rigor (Hategeka et al. 2020).

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14.1 Consultation Rate Over Time

The “Consultation Rate” is defined as the number of internal consultations divided by the total number of pathology cases for the same month.

Consultation Rates (Last 12 Months)
Month Total Cases Consultations Rate (%)
2025-07 6298 188 2.99
2025-06 5136 141 2.75
2025-05 6593 177 2.68
2025-04 6082 144 2.37
2025-03 5494 180 3.28
2025-02 5690 170 2.99
2025-01 6129 210 3.43
2024-12 6005 140 2.33
2024-11 6113 97 1.59
2024-10 5611 146 2.60
2024-09 5567 105 1.89
2024-08 5892 110 1.87

14.1.1 Monthly Consultation Rate Trend

14.2 Volume Comparison

Visualizing the relationship between absolute case volume and consultation requests.

14.5 Interrupted Time Series Analysis

The preceding trend analyses describe what happened over time. However, a simple trend line cannot tell us whether a specific event (such as a staffing change, new scanner deployment, or workflow reorganisation) caused a meaningful shift in consultation behaviour. Interrupted Time Series (ITS) analysis with segmented regression is considered one of the strongest quasi-experimental designs for evaluating pre/post intervention effects in observational data (Penfold and Zhang 2013; Bernal, Cummins, and Gasparrini 2017). It decomposes the time series into four components:

Coefficient Interpretation
B0 (intercept) Baseline level at the start of the study
B1 (time) Pre-intervention trend (slope per month)
B2 (intervention) Immediate level change at the intervention point
B3 (time after) Change in slope after the intervention
NoteWhat does ITS add beyond simple trend analysis?

Simple linear or LOESS trends assume a single, smooth trajectory. ITS explicitly tests whether a particular time point marks a structural break — an abrupt shift in level (B2) and/or a change in the rate of change (B3). This separates observed differences from pre-existing trends and generally supports stronger quasi-experimental inference than a naive before/after comparison.

14.5.1 Data-Driven Changepoint Detection

Because we do not have a single, externally defined intervention date, we adopt a data-driven strategy: we identify the month at which the largest absolute shift in the 3-month rolling average of consultation volume occurs, and treat that as the primary intervention point.

Detected changepoint: **January 2025** (month 30 of 40).
Pre-intervention: 29 months. Post-intervention: 11 months.

14.5.2 ITS Model: Consultation Volume

ITS Segmented Regression: Monthly Consultation Volume (Changepoint: January 2025)
Term Estimate Std. Error 95% CI Lower 95% CI Upper P-value
(Intercept) Intercept (B0) 60.815 9.635 41.274 80.356 <0.001
time Pre-trend (B1) 1.909 0.561 0.771 3.047 0.0016
intervention Level change (B2) 54.646 17.208 19.747 89.544 0.0031
time_after Slope change (B3) -1.563 2.474 -6.582 3.455 0.5315
Note:
P-values are conditional on the data-driven changepoint and are likely overstated (see warning below).
WarningP-values are conditional on the data-driven changepoint

The changepoint was selected as the month with the largest absolute shift in the 3-month rolling average — i.e., the data were searched for the most extreme change. Consequently, the p-values for B2 (level change) are overstated because standard OLS inference does not account for this selection process. A formal structural break test (e.g., Andrews’ sup-F test) would provide valid p-values, but was not applied here. The B2 and B3 coefficients should be interpreted as descriptive effect estimates rather than formal hypothesis tests.

Interpretation. B1 captures the monthly trend in volume before the detected changepoint. B2 estimates the immediate jump (or drop) in volume at the changepoint. B3 indicates whether the monthly trend changed after the changepoint compared to the pre-intervention slope. A significant B2 suggests a sudden structural shift; a significant B3 suggests a sustained change in trajectory.

14.5.3 ITS Model: Median Turnaround Time

ITS Segmented Regression: Median Monthly TAT (Changepoint: January 2025)
Term Estimate Std. Error 95% CI Lower 95% CI Upper P-value
(Intercept) Intercept (B0) 9.006 0.810 7.363 10.648 <0.001
time Pre-trend (B1) -0.269 0.047 -0.364 -0.173 <0.001
intervention Level change (B2) 1.156 1.446 -1.777 4.090 0.4292
time_after Slope change (B3) 0.334 0.208 -0.088 0.756 0.117
Note:
P-values are conditional on the data-driven changepoint and are likely overstated (see warning above).

14.5.4 ITS Residual Diagnostics

Before interpreting the ITS models, we verify key regression assumptions: normality and homoscedasticity of residuals.

ITS Model Diagnostic Tests and Effect Sizes
Diagnostic Statistic P-value / Magnitude Interpretation
Residual normality: Volume (Shapiro-Wilk) 0.9651 0.248 Residuals approximately normal
Residual normality: TAT (Shapiro-Wilk) 0.8420 5.8e-05 Non-normal residuals (interpret CIs with caution)
Heteroscedasticity: Volume (Breusch-Pagan) 4.0500 0.256 No heteroscedasticity
Heteroscedasticity: TAT (Breusch-Pagan) 17.1420 0.000661 Heteroscedasticity present
Intervention effect size: Volume (Cohen's f2) 0.3377 medium R2 change from adding intervention terms: 8.8pp
Intervention effect size: TAT (Cohen's f2) 0.1931 medium R2 change from adding intervention terms: 8.7pp
NoteCohen’s f2 for ITS

Cohen’s f2 quantifies the incremental explanatory power of the intervention terms (level change B2 and slope change B3) beyond the baseline time trend (B1). Benchmarks: f2 < 0.02 negligible, 0.02–0.15 small, 0.15–0.35 medium, > 0.35 large (Cohen, 1988).

14.5.5 Autocorrelation Diagnostics

A key assumption of ordinary least squares regression is that residuals are independent. Time series data often violate this assumption because consecutive months tend to be correlated (autocorrelation). The Durbin-Watson test formally checks for first-order autocorrelation in the residuals.

Durbin-Watson Test for Autocorrelation in ITS Residuals
Outcome DW Statistic P-value Interpretation
Consultation Volume 1.418 0.0080 Significant autocorrelation detected
Median TAT 1.686 0.0656 No significant autocorrelation

Autocorrelation detected in at least one model. Refitting with generalised least squares (GLS) using an AR(1) correlation structure to obtain corrected standard errors.

GLS-Corrected ITS: Monthly Consultation Volume (AR(1) Correlation)
Term Estimate Std. Error P-value
(Intercept) Intercept (B0) 57.309 15.067 <0.001
time Pre-trend (B1) 2.043 0.863 0.0234
intervention Level change (B2) 55.498 22.567 0.0189
time_after Slope change (B3) -1.264 3.489 0.7191

Estimated AR(1) autocorrelation coefficient (phi): 0.409

14.5.6 ITS Model Summary

ITS Model Fit and Pre/Post Comparison Summary
Metric Consultation Volume Median TAT (Hours)
R-squared 0.739 0.551
Adjusted R-squared 0.717 0.513
Mean (Pre) 89.4 5
Mean (Post) 174.5 2.4
Change (%) +95% -51.3%

The ITS analysis provides a rigorous framework for assessing whether the observed changes around January 2025 represent a genuine structural break or are merely a continuation of pre-existing trends. Unlike simple before/after comparisons, which confound the intervention effect with underlying temporal dynamics, the segmented regression model explicitly separates the pre-existing trend (B1) from the immediate level shift (B2) and the post-intervention trend change (B3). This decomposition strengthens the basis for causal inference, though — as with all observational designs — unmeasured confounders (such as concurrent staffing changes or case-mix shifts) cannot be entirely ruled out (Penfold and Zhang 2013).

WarningLimitations of Data-Driven Changepoint Selection

The changepoint was selected by the data itself (the month with the largest shift in rolling average), rather than being specified a priori based on a known intervention. This approach is exploratory rather than confirmatory: the statistical significance of B2 and B3 may be inflated because the changepoint was chosen to maximise the observed shift. The ITS results should therefore be interpreted as hypothesis-generating rather than hypothesis-confirming. If a specific known intervention date exists (e.g., scanner deployment, staffing change), the analysis should be re-run with that date fixed a priori to obtain valid inferential statistics.