Hockey stick phenomenon

Hockey stick phenomenon or hockey stick curves has been used mostly in describing the climate change. it says that the tempeature variation over centuries are relatively unchanged until after 1900. The temperature rose sharply due to the human activities. Since 1998 Nature article by Mann, Bradley, and Hughes, the hockey stick curve (phenomenon) has stirred quite some debates / contraversies in climate research fields.

Hockey stick curves have also been used in described any change with a normal trend (trajectory), then with a different change or a interruption in the trend.  For example, the hockey stick curve may be used to describe the disease progression with gradual progression, then sudden deterioation. In clinical trials, one could observe that patients have initial rebound in the measured parameters (endpoints), then gradually decrease. In clinical trials for Alzheimer disease, the purpose is to prevent the paitent from further deterioation, rather than improvement or cure. If a rebound during the initial phase of the trial, it could be described as 'hockey stick".

During my PhD study, I analyzed the EPA whole effluent toxicity testing data and noticed the non-linear dose response and the phenomenon of 'hormesis' which says that exposure to low or very low dose of toxicants could have benefit effects. The hormesis or low dose response could be described as J-shaped or Hockey stick.

Way before the hockey stick model was used to describe the temperature data, the method was proposed to analyze the data in environmental health data. In 1979, Yanagimoto and Yamamoto published their paper in Environmental Health Perspectives titled "Estimation of Safety Doses: Critical Review of Hockey Stick Regression Method".

From data analysis standpoint, if the data presents with hockey stick phenomenon, the typical linear regression can not be used. Hockey stick regression can be considered as segmented linear regression with just one knot. In a paper by Simpson et al "excess risk thresholds in ultrasound safety studies: statistical method for data on occurrence an dsize of lesions", they used a piecewise linear model. A link from UGA had some discussions about using SAS procedures to model the data with hockey stick:

One thing for sure is that hockey stick could always be contraversial. Additional data may be needed to verify if the hockey stick phenomenon is true or is the data issue or is the data collection issue.