We wanted to explore the association between survival time and the independent variables.
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1. Numeric variable information list
2. Categorical variable information list
Histogram: to roughly show the probability distribution of a variable by depicting the frequencies of observations occurring in certain ranges of values.
Density plot: to show the distribution of a variable
Histogram
When the number of bins is 0, plot will use the default number of bins
Density plot
Kaplan–Meier estimator, also known as the product-limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data.
The log-rank test is a hypothesis test to compare the survival distributions of two samples. It compares estimates of the hazard functions of the two groups at each observed event time.
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Kaplan-Meier survival probability by group
This implements the G-rho family of Harrington and Fleming (1982), with weights on each death of S(t)rho, where S is the Kaplan-Meier estimate of survival.
Log-rank Test Result
In this example, we could not find the statistical difference between 2 laser groups (p=0.8). Also from the Kaplan-Meier plot, we could found that the survival curves from 2 laser group intersect with each other.
This implements the G-rho family of Harrington and Fleming (1982), with weights on each death of S(t)rho, where S is the Kaplan-Meier estimate of survival.
Pairwise Log-rank Test P Value Table
Cox Regression, also known as Cox proportional hazard regression, assumes that if the proportional hazards assumption holds (or, is assumed to hold), then it is possible to estimate the effect parameter(s) without any consideration of the hazard function. Cox regression assumes that the effects of the predictor variables upon survival are constant over time and are additive in one scale.
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Fitting values and residuals from the existed data
Model selection suggested by AIC
The adjusted survival curves from Cox regression
Explanations
Martingale residuals against continuous independent variable is a common approach used to detect nonlinearity. For a given continuous covariate, patterns in the plot may suggest that the variable is not properly fit. Martingale residuals may present any value in the range (-INF, +1):The residuals can be found in Data Fitting tab.
Red points are those who 'died soon'; black points are whose who 'lived long'
1. Martingale residuals plot against continuous independent variable
2. Deviance residuals plot by observational id
3. Cox-Snell residuals plot
Brier score is used to evaluate the accuracy of a predicted survival function at given time series. It represents the average squared distances between the observed survival status and the predicted survival probability and is always a number between 0 and 1, with 0 being the best possible value.
The Integrated Brier Score (IBS) provides an overall calculation of the model performance at all available times.
The default setting give time series 1,2,...10
Brier score at given time
Explanations
AUC here is time-dependent AUC, which gives AUC at given time series.Time dependent AUC at given time
Accelerated failure time (AFT) model is a parametric model that assumes that the effect of a covariate is to accelerate or decelerate the life course of a disease by some constant.
Check full data in Data tab
Fitting values and residuals from the existed data
Model selection suggested by AIC
Explanations
Martingale residuals against continuous independent variable is a common approach used to detect nonlinearity. For a given continuous covariate, patterns in the plot may suggest that the variable is not properly fit. Martingale residuals may present any value in the range (-INF, +1):The residuals can be found in Data Fitting tab.
Red points are those who 'died soon'; black points are whose who 'lived long'
1. Martingale residuals plot against continuous independent variable
2. Deviance residuals plot by observational id
3. Cox-Snell residuals plot
The predicted survival probability of N'th observation