Joinpoint and Trend Analysis

Overview

Joinpoint regression models a time trend using connected linear segments.

Joinpoints are times at which the slope changes.

The method is widely used for cancer incidence, mortality and surveillance trends [1].

On a log-rate scale, segment slopes can be expressed as annual percentage change, APC.

Why this matters

One average trend can conceal:

• an initial increase;
• a later decline;
• a recent reversal.

Searching many breakpoints without multiplicity control overfits noise.

Joinpoint software uses constrained model selection and permutation tests.

When to use joinpoint analysis

Use joinpoint methods for ordered population rates or counts when:

• meaningful time points are available;
• enough observations support multiple segments;
• a parsimonious trend summary is desired;
• denominators and standardisation are reliable.

Do not use joinpoints alone to infer that a policy caused the slope change.

Research question and variables

A segmented linear model is:

$$g(E[Y_t])= \beta_0+ \beta_1t+ \sum_{k=1}^K \delta_k(t-\tau_k)_+$$

where $\tau_k$ are joinpoints.

On a log scale:

Data structure

Trend data

simulated data

Variable	Role
year	Ordered calendar year
rate	Age-standardised or crude rate
count	Optional event count
population	Denominator
standard_error	Precision of rate

Statistical assumptions

Worked example

Worked analysis in R

trend_data <- read.csv(
  "data/part-16-joinpoint-data.csv"
)

# Illustrative segmented regression with fixed candidate points
trend_fit <- lm(
  rate ~ year +
    I(pmax(year - 2008, 0)) +
    I(pmax(year - 2016, 0)),
  data = trend_data
)

summary(trend_fit)
confint(trend_fit)

plot(
  trend_data$year,
  trend_data$rate,
  type = "b",
  xlab = "Year",
  ylab = "Rate"
)

lines(
  trend_data$year,
  fitted(trend_fit),
  lty = 2
)

# For formal joinpoint selection use validated
# permutation-based Joinpoint software or a
# prespecified segmented-model procedure.

Selected analysis output

Trend increases before 2008.
Trend declines between 2008 and 2016.
Trend rises slightly after 2016.

Visualising changing trends

APC and AAPC

APC describes one segment.

Average annual percentage change, AAPC, is a weighted geometric summary across segments over a chosen interval.

AAPC can obscure meaningful reversals and should be accompanied by segment APCs.

Model selection

The National Cancer Institute Joinpoint Regression Program uses permutation testing to select the number of joinpoints [2].

Maximum joinpoints should be constrained by:

• number of observations;
• minimum segment length;
• scientific plausibility.

Count and rate models

For event counts with population denominators, Poisson or negative-binomial segmented models may be appropriate.

Weighted least squares can use known rate SEs.

Sparse counts and changing denominators require care.

Interpreting the output

Presenting the analysis

Suggested reporting

Report rate definition, standardisation, denominator, error model, maximum joinpoints, selection method, APCs, AAPC interval and joinpoint uncertainty [1], [2].

AAPC interpretation and alternative segmented-regression estimation are described by Clegg and colleagues and Muggeo [3], [4].

Common mistakes

Knowledge check

What is a joinpoint?

Answer and reasoning

A time where the fitted trend slope changes.

What does APC describe?

Answer and reasoning

The annual percentage change within one fitted segment.

Why constrain the number of joinpoints?

Answer and reasoning

Unrestricted searching overfits random variation.

Does a joinpoint identify a cause?

Answer and reasoning

No.

Why report segment APCs with AAPC?

Answer and reasoning

The average can conceal reversals or heterogeneous trends.

Key take-home messages

References

1. Kim HJ, Fay MP, Feuer EJ, Midthune DN. Permutation tests for joinpoint regression. Stat Med. 2000;19(3):335–351. https://doi.org/10.1002/(SICI)1097-0258(20000215)19:3%3C335::AID-SIM336%3E3.0.CO;2-Z
2. National Cancer Institute. Joinpoint Regression Program. Statistical Methodology and Applications Branch.
3. Clegg LX, Hankey BF, Tiwari R, Feuer EJ, Edwards BK. Estimating average annual per cent change in trend analysis. Stat Med. 2009;28(29):3670–3682. https://doi.org/10.1002/sim.3733
4. Muggeo VMR. Estimating regression models with unknown break-points. Stat Med. 2003;22(19):3055–3071. https://doi.org/10.1002/sim.1545