Assess the Efficacy of Cancer Treatments

Use survival modeling to compare the effectiveness of 6-mercaptopurine and a placebo in a leukemia clinical trial

Leukemia patients in remission were treated with either 6-mercaptopurine or a placebo in a clinical trial. Fit survival models for the two groups, compare their estimated survival characteristics, and test whether the treatment is associated with longer remission.

Introduce the remission times for the 6-mercaptopurine group together with censoring indicators, and the remission times for the placebo group:

In[1]:=

sixmp={10,7,32,23,22,6,16,34,32,25,11,20,19,6,17,35,6,13,9,6,10};ci={0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,0,1,1,1};placebo={1,22,3,12,8,17,2,11,8,12,2,5,4,15,8,23,5,11,4,1,8};

Fit survival models for the treatment and placebo groups:

In[2]:=

treatment=SurvivalModelFit[EventData[sixmp,ci]];control=SurvivalModelFit[placebo];

Compare the estimated median survival times for the two groups:

In[3]:=

groups={"6-mercaptopurine","placebo"};models={treatment,control};TableForm[Transpose[{groups,(#["MedianSurvival"]&/@models)}],TableHeadings{None,{"Group","Median survival"}}]

Out[3]//TableForm=

Group	Median survival
6-mercaptopurine	19
placebo	11

Evaluate the estimated survival probabilities at selected follow-up times:

In[4]:=

times={5,10,15,20};TableForm[({#,treatment[#],control[#]}&/@times),TableHeadings{None,{"Time","6-mercaptopurine","placebo"}}]

Out[4]//TableForm=

Time	6-mercaptopurine	placebo
5	1	0.571429
10	0.752941	0.380952
15	0.690196	0.142857
20	0.627451	0.0952381

Plot the estimated survival functions for the two groups:

In[5]:=

Plot[{treatment[x],control[x]},{x,0,40},ExclusionsNone,PlotLegends{"6-mercaptopurine","placebo"},AxesLabel{"Time","Survival probability"},PlotLabel"Estimated survival functions"]

Out[5]=

	6-mercaptopurine
	placebo

Test whether the two groups have different survival distributions using a log-rank test with Tarone-Ware weights:

In[6]:=

LogRankTest[{treatment["EventData"],control["EventData"]},"TaroneWare","TestDataTable"]

Out[6]=

	Statistic	P-Value
Log-Rank	15.1236	0.000100698

The 6-mercaptopurine group has a larger estimated median survival and higher estimated survival probabilities over the follow-up period. The log-rank test supports a difference between the two survival distributions.

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Assess the Efficacy of Cancer Treatments

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Assess the Efficacy of Cancer Treatments

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