#Julia package for survival analysis (under development)# This module aims to provide support for most of up-to-date staistical analytic approaches used in survival analysis. It will include functions through basic layout of survival data from survival analysis to complex survival models. ##Update## 01/27/2016 Function for Kaplan-Meier analysis Calculate Nelson-Aalen estimator ##Usage## ####Create a survival data object for further use#### To carry out some non-parametric survival analysis, we usually collect data of time-to-event and censoring information. This module allows to create a survival object for further use by running SurvObject(time, event). Where time is a vector of time-to-event data and event is a vector of corresponding indicators, where 0 denotes being censored, 1 denotes having events.

#####Example 1.1#####

In a study of remission of poststroke depression in weeks for two groups of stroke patients, with 10 patients in each group. Group 1 was the treatment group with mood treatment and group2 was the control, the study went on for 9 weeks. At the end of study, 5 patients had remissions in the intervention arm, 5 were censored during the trial. The time-to-remission data for group 1 was also collected: 1, 2, 5, 5, 5+, 7+, 8+, 8, 9+, 9+, where '+' denotes censoring.

In general survival analysis, we should obtain two vectors for this, time=[1, 2, 5, 5, 5, 7, 8, 8, 9, 9] and event=[1, 1, 1, 1, 0, 0, 0, 1, 0, 0]. Therefore we could create the object first, survobj = SurvObject(time, event),

####Alternative Data Layout for Kaplan-Meier Curves####

Alternative data layout is required for Kaplan-Meier(K-M) curves. K-M estimator is calculated from the product limit of survival probabilities. With the data object we instantiated above, a K-M data object for data layout and K-M curve is returned from kmobject = KMEst(survobj).

To get the Kaplan-Meier estimator from the returned data object, retrieve the attribute surv_func in the K-M object, kmobject.surv_func, in the same Example 1.1, the K-M estimators of survival probability at each time points are returned in a vector.

To get the Kaplan-Meier estimator from the returned data object,

kmobject.surv_func

7-element Array{Float64,1}:
1.0
0.9
0.8
0.6
0.6
0.45
0.45

To transform the returned object into a DataFrame object in Julia, DataFrame needs to be installed. Using SurvLayout(kmobject) performs the transformation, a dataframe for the alternative survival data layout is then returned.

7x6 DataFrames.DataFrame
| Row | Time | Total | Censored | Event | Death_Prob | Survival |
|-----|------|-------|----------|-------|------------|----------|
| 1   | 0.0  | 10    | 0        | 0     | 1.0        | 1.0      |
| 2   | 1.0  | 10    | 0        | 1     | 0.9        | 0.9      |
| 3   | 2.0  | 9     | 0        | 1     | 0.888889   | 0.8      |
| 4   | 5.0  | 8     | 1        | 2     | 0.75       | 0.6      |
| 5   | 7.0  | 5     | 1        | 0     | 1.0        | 0.6      |
| 6   | 8.0  | 4     | 1        | 1     | 0.75       | 0.45     |
| 7   | 9.0  | 2     | 2        | 0     | 1.0        | 0.45     |

####Kaplan-Meier Curve#### To plot the survival data using K-M curves, SurvPlot(kmobject)

Specify a color of the curve, SurvPlot(km_object1, color="red", xlim=(0, 10))

To plot multiple curves in a same figure,SurvPlot(km_object1, km_object2...)

####Nelson-Aalen Estimator#### To get the Nelson-Aalen (N-A) estimator, run naobject = NAEst(surv_obj1), the returned object could also be transformed into a DataFrame, by running SurvLayout(naobject).

6x6 DataFrames.DataFrame
| Row | Time | Total | Censored | Event | Death_Prob | Cumulative_Hazard |
|-----|------|-------|----------|-------|------------|-------------------|
| 1   | 1.0  | 10    | 0        | 1     | 0.9        | 0.9               |
| 2   | 2.0  | 9     | 0        | 1     | 0.888889   | 1.78889           |
| 3   | 5.0  | 8     | 1        | 2     | 0.75       | 2.53889           |
| 4   | 7.0  | 5     | 1        | 0     | 1.0        | 3.53889           |
| 5   | 8.0  | 4     | 1        | 1     | 0.75       | 4.28889           |
| 6   | 9.0  | 2     | 2        | 0     | 1.0        | 5.28889           |

####Mean Residual Life for Censored Data#### Based on the Kaplan-Meier estimates, mean residual life could be calculated for censored data. Run meanresidobject(kmobject) to get a mean residual life estimates for all the censored data in the input survival data. Similarly, SurvLayout(meanresidobject) could transform the returned data into a dataframe.

4x2 DataFrames.DataFrame
| Row | Time | Mean_Residual_Life |
|-----|------|--------------------|
| 1   | 5.0  | 2.25               |
| 2   | 7.0  | 1.05               |
| 3   | 8.0  | 0.45               |
| 4   | 9.0  | 0.0                |