1 Event History Analysis

Event History Analysis for the Julia Language

using EventHistory

1.1 Event class

1.1.1 Right-censored event times

stop   = [2,3,3];
status = [false,true,true];
e1 = Event(stop,status)

3-element Array{EventHistory.Surv,1}:
 2+
 3 
 3

Time(e1)

3-element Array{Int64,1}:
 2
 3
 3

Status(e1)

3-element Array{Bool,1}:
 false
  true
  true

1.1.2 Right-censored+left truncation

start  = [0,1,2];
e2 = Event(start,stop,status)

3-element Array{EventHistory.SurvTrunc,1}:
 (0;2+]
 (1;3] 
 (2;3]

Entry(e2)

3-element Array{Int64,1}:
 0
 1
 2

1.1.3 Competing risks data

cause = [0,2,1];
e3 = Event(start,stop,cause)

3-element Array{EventHistory.CompRisk,1}:
 (0;2:+]
 (1;3:2]
 (2;3:1]

Status(e3)

3-element Array{Bool,1}:
 false
  true
  true

Cause(e3)

3-element Array{Int64,1}:
 0
 2
 1

1.1.4 Interval censoring

right  =  [2,3,Inf];
left =  [1,-Inf,1];
e4=Event(left,right,"interval")

3-element Array{EventHistory.SurvInt,1}:
 [1.0;2.0]              
 (-Inf;3.0]             
 [EventHistory.Time;Inf)

1.1.5 Formula syntax (see also examples below)

using DataFrames
d = DataFrame(start=start,stop=stop,status=status);
Event([:stop,:status],d)

3-element Array{EventHistory.Surv,1}:
 2+
 3 
 3

Event([:start,:stop,:status],d)

3-element Array{EventHistory.SurvTrunc,1}:
 (0;2+]
 (1;3] 
 (2;3]

1.2 Cox regression

1.2.1 Examples

1.2.1.1 Cox regression

Ovarian cancer example (randomized trial)

using RDatasets
using EventHistory
ovarian = dataset("survival", "ovarian");
ovarian[:Group] = ovarian[:Rx].-1;
ovarian[:S] = Event([:FUTime,:FUStat],ovarian);

mm = phreg(@formula(S~Age+Group),ovarian)

Model: Cox; Formula: S ~ Age + Group

n=26, events=12

        Estimate       S.E naive S.E.    P-value
Age     0.147327 0.0488846   0.046147 0.00258032
Group  -0.803973  0.633937   0.632049   0.204718

1.2.1.2 Prediction

Predictions:

## Prediction
predict(mm,surv=false,X=[0 0]); ## Baseline
s56 = predict(mm,X=[56 1],order=true); ## Survival probabilities age 40, group 1
predict(mm,X=[56 0],time=[100,400,600]); ## ... at time 100,400,600
predict(mm,X=[56 1; 56 0],time=[600,100,400]) ## ... both groups

3×3 Array{Real,2}:
 600.0  0.618402  0.341676
 100.0  0.983831  0.964233
 400.0  0.834936  0.668255

s = predict(mm,X=[56 1; 56 0], order=true);
pr = DataFrame(Time=[s[:,1];s[:,1]], S=[s[:,2];s[:,3]], 
		 Group=Compat.repeat(["Group1","Group2"], inner=size(s,1)));

using Gadfly
p = plot(pr, x="Time", y="S",color="Group",
         Geom.step, Geom.point,
         Guide.ylabel("Survival probability"), Guide.title("Age 56"))
draw(PNG("surv.png",7inch,7inch),p)

1.2.1.3 Cox regression, Left truncation+right censoring

Simple example from the `survival` R-package

d = DataFrame(start=[1,2,5,2,1,7,3,4,8,8],
                stop=[2,3,6,7,8,9,9,9,14,17],
                event=[1,1,1,1,1,1,1,0,0,0],
                x=[1,0,0,1,0,1,1,1,0,0]);
d[:S] = Event([:start,:stop,:event], d);

e = phreg(@formula(S~x), d)

Model: Cox; Formula: S ~ x

n=10, events=7

       Estimate      S.E naive S.E.  P-value
x    -0.0211052 0.838301   0.795177 0.979914

1.3 Installation

Get it from https://github.com/kkholst/EventHistory.jl

1.4 Roadmap

• Additive models
• Stratified analysis
• Handle ties (Efron)
• Frailty models (Copula)
• Residuals
• …