USING TANGENT LINE SEGMENTS TO DETERMINE STATISTICAL DIFFERENCES BETWEEN SURVIVAL CURVES AT A SINGLE POINT IN TIME
Author(s)
Wasser T1, Kern DM2, Eisenberg D1
1HealthCore Inc., Wilmington, DE, USA, 2HealthCore Inc, Wilmington, DE, USA
Presentation Documents
OBJECTIVES: Typical survival analysis examines differences in curves across the entire spectrum of time. Often the research question relates to differences in survival at a single point in time without considering other aspects of the survival curve. METHODS: This research used data from the United States Surveillance, Epidemiology and End Results Program (US-SEER), comparing cervical and ovarian cancer 5-year survival rates from 2007-2011. The steps in this analysis are: 1. Calculate Kaplan-Meier curve (or any survival curve) using standard methods, 2. Calculate the quadratic curve for the survival measure and record the formula. 3. Using the point of interest (in this example 12 months) calculate the tangent line for that point, using the derivative power method. These two slope values are tested against each other using standard slope comparisons. 4. Use the standard error of the model for the quadratic equation for significance testing. 5. Test the difference between slopes for significance using standard statistical methods for slope comparisons. RESULTS: Quadratic formulas were determined for both ovarian and cervical cancer survival curves and the tangent lines were calculated using the derivative for the equation from the curve. This resulted in two slope values at 12 months (cervical 4.116 and ovarian 7.151). Using the standard errors for the cervix and ovarian groups (2.268 and 3.854 respectively), the Z-value=0.6787 and p=0.497, indicating the trajectory of survival for cervical and ovarian cancer are not statistically different from each other even though the point estimates of survival (88.4% for cervical; 75.4% for ovarian) are statistically different from each other at that point. CONCLUSIONS: The strengths of this method is that a single point difference test can be conducted for a single point in time based on the trajectory of the line. This method does not pool the data across all points. Several other examples will be presented graphically.
Conference/Value in Health Info
2015-11, ISPOR Europe 2015, Milan, Italy
Value in Health, Vol. 18, No. 7 (November 2015)
Code
PRM207
Topic
Methodological & Statistical Research
Topic Subcategory
Confounding, Selection Bias Correction, Causal Inference
Disease
Multiple Diseases