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The Cox proportional-hazards model is also called Cox regression analysis. A regression analysis is performed using the Cox proportional-hazards model.
Regression analysis
We created a correlation diagram for strength training and incremental skeletal muscle volume (Figure 1) and drew a straight line passing through the middle of the scatter diagram.
[Figure 1] Correlation diagram for strength training and incremental skeletal muscle volume (straight line)
Figure 1 shows a relationship between strength training and incremental skeletal muscle volume, which can be inferred by fitting an appropriate straight line.
In some cases, the curve fits well, as shown in Figure 2.
[Figure 2] Correlation diagram for strength training and incremental skeletal muscle volume (curve)
Fitting a straight line or curve in this way is called “fitting a relational equation.” The statistical method of fitting a functional formula is called “regression analysis.”
The method of fitting a straight line, as shown in Figure 1, is called a “single-regression analysis” (linear regression analysis). In this case, the relational equation is “y = ax + b” (single regression equation).
The method of fitting a curve, as shown in Figure 2, is called a “curvilinear regression analysis.”
Many relational equations exist; however, in this case, the relational equation is “y = ax2 + bx + c.” Estimate a, b, and c that best fit the data.
These methods are called the regression analyses, and the relational equations are called “models.”
What kind of a model is the Cox proportional-hazards model (Cox regression model)?
The Cox proportional-hazards model is used to determine the survival rate from death/censored data, considering the temporal element of the survival rate and creating a relational equation (model) with variables affecting the survival rate.
The objective variable (outcome) of the relational equation was binary data of 1s and 0s, not limited to “death/censored” but also referring to various situations, such as “death/survival,” “recurrence/no recurrence,” and “remission/no remission.”
Explanatory variables included treatment methods affecting survival rates and background factors, such as sex, age, and body mass index.
The Cox proportional-hazards model was used to calculate the hazard ratios for each explanatory variable. Hazard refers to danger; therefore, it is a measure of the death risk. It is the mortality rate at a point in time, which changes over time. The unit is “person/unit time.”
The Cox proportional-hazards model is a “model with hazards as data.”
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