Trend Analysis

Concept

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Theoretically, Trend Analysis is a quantitative analytical method used to identify, estimate and interpret systematic changes in a variable over time. It distinguishes long-term directional movement from short-term random variation and cyclical fluctuations, providing evidence for forecasting, monitoring and evaluating healthcare utilisation, expenditure, outcomes and epidemiological patterns. Trend analysis is founded on statistical time series analysis and regression theory and exists to quantify temporal change in observed data.

Mathematically, trend analysis represents the relationship between an outcome variable and time using statistical models. The simplest representation is a linear regression in which time serves as the explanatory variable, although polynomial regression, segmented regression, exponential models and other time series methods may also be employed where appropriate. The estimated trend quantifies the expected change in the outcome for each unit increase in time.

In practice, trend analysis is implemented using routinely collected longitudinal datasets such as healthcare expenditure, hospital admissions, mortality rates or disease incidence. Model parameters are estimated using recognised statistical methods, most commonly ordinary least squares regression for linear trends, and model fit is assessed using standard diagnostic measures before interpretation and forecasting.

Purpose

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Used to identify, quantify and forecast temporal changes in healthcare utilisation, costs, outcomes, disease burden, service performance and other longitudinal indicators used in health economic evaluation and health services research.

Mathematical Formulae

Primary Formula

Y? = ?? + ??t + �?

Supporting Formulae

?? = (X?X)??X?Y

R� = 1 ? RSS / TSS

Related Mathematical Methods

• Linear regression
• Time series analysis
• Polynomial regression
• Segmented regression
• Moving averages
• Exponential smoothing

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Example

Annual inpatient expenditure for a healthcare programme is recorded over six years. Linear regression estimates:

Expenditure = �82.4 million + (�3.1 million ? Year)

The estimated trend coefficient (??? = �3.1 million) indicates that expenditure increases by approximately �3.1 million per year, providing an evidence base for future budget planning and economic modelling.

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Excel Implementation

Function	Example Formula	Health Economics Application
SLOPE	=SLOPE(B2:B11,A2:A11)	Estimate the annual trend in healthcare expenditure or utilisation.
INTERCEPT	=INTERCEPT(B2:B11,A2:A11)	Estimate the baseline value at the start of the observation period.
TREND	=TREND(B2:B11,A2:A11,A12:A15)	Forecast future healthcare activity or costs.
LINEST	=LINEST(B2:B11,A2:A11,TRUE,TRUE)	Estimate regression coefficients and associated statistics.
RSQ	=RSQ(B2:B11,A2:A11)	Assess goodness of fit of the trend model.

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VBA (Optional)

Automate periodic trend estimation, forecasting and graphical reporting for healthcare activity, expenditure and outcome indicators across multiple datasets.

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Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
• NICE. Health Technology Evaluation Manual.
• ISPOR Task Force Reports on Good Research Practices.
• Montgomery DC, Jennings CL, Kulahci M. Introduction to Time Series Analysis and Forecasting.
• Box GEP, Jenkins GM, Reinsel GC, Ljung GM. Time Series Analysis: Forecasting and Control.