Analyze Disease-Free Survival with Confidence Bands

Explore disease-free survival after bone marrow transplantation using confidence bands and hypothesis testing

The following data record times to relapse, death, or the end of follow-up for 38 individuals with acute lymphoblastic leukemia who received bone marrow transplants. Use these observations to model disease-free survival and assess survival probability over time.

Enter the disease-free survival times, using pairs of the form {t, ∞} to represent right-censored observations:

In[1]:=

data={{2081,∞},{1602,∞},{1496,∞},{1462,∞},{1433,∞},{1377,∞},{1330,∞},{996,∞},{226,∞},{1199,∞},{1111,∞},{530,∞},{1182,∞},{1167,∞},418,383,276,104,609,172,487,662,194,230,526,122,129,74,122,86,466,192,109,55,1,107,110,332};

Fit a survival model and restrict the confidence-band calculations to the interval from 100 to 600 days:

In[2]:=

model=SurvivalModelFit[data,ConfidenceRange{100,600}]

Out[2]=

SurvivalModel

Time: 1 to 2081

Data points: 38



Compare the fitted survival function with different types of confidence bands over the selected time interval:

In[3]:=

Plot[{model[x],model["HallWellnerBands"][x],model["EqualPrecisionBands"][x],model["PointwiseBands"][x]},{x,100,600},ExclusionsNone,PlotLegends{"Model","Hall-Wellner Bands","Equal Precision Bands","Pointwise Bands"},Filling{3{1},2{1},4{1}}]

Out[3]=

	Model
	Hall-Wellner Bands
	Equal Precision Bands
	Pointwise Bands

Define a helper function that tests whether a hypothesized survival probability lies within the pointwise confidence interval at a given time:

In[4]:=

survProbTest[h0_,t_,lev_]:=IntervalMemberQ[Interval[model["PointwiseBands",ConfidenceLevel1-lev][400]],h0]/.{TrueRow[{"Do not reject at the ",100lev,"% level"}],FalseRow[{"Reject at the ",100lev,"% level"}]}

Evaluate the estimated disease-free survival probability at 400 days:

In[5]:=

model[400]

Out[5]=

0.521739

Test whether the disease-free survival probability at 400 days differs significantly from 0.5 at the 5% level:

In[6]:=

survProbTest[0.5,400,.05]

Out[6]=

Do not reject at the 5.% level

The estimated disease-free survival probability at 400 days is close to 0.5, and the pointwise confidence interval indicates that this value is not significantly different from 0.5 at the 5% level.

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Analyze Disease-Free Survival with Confidence Bands

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Analyze Disease-Free Survival with Confidence Bands

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