Statistics in Clinical Cancer Research
Megan Othus1, Bart Barlogie3, Michael L. LeBlanc1, and John J. Crowley2
Cure models are a popular topic within statistical literature but are not as widely known in the clinical
literature. Many patients with cancer can be long-term survivors of their disease, and cure models can be a
useful tool to analyze and describe cancer survival data. The goal of this article is to review what a cure
model is, explain when cure models can be used, and use cure models to describe multiple myeloma
survival trends. Multiple myeloma is generally considered an incurable disease, and this article shows that
by using cure models, rather than the standard Cox proportional hazards model, we can evaluate whether
there is evidence that therapies at the University of Arkansas for Medical Sciences induce a proportion of
patients to be long-term survivors. Clin Cancer Res; 18(14); 3731–6. ?2012 AACR.
Progress in the treatment of cancer has led to a spate of
cancer survival data are based on overall survival or pro-
gression-free survival (PFS). No patient can be "cured" of
death, so in these situations cure models can be used to
model long-term survivors rather than cured patients.
Cure models can be used to investigate the heterogeneity
between patients with cancer who are long-term survivors
and those who are not. A straightforward way to identify
whether a particular data set might have a subset of long-
term survivors is to look at the survival curve. If the survival
be an appropriate and useful way to analyze the data.
is provided in Fig. 1, the PFS curve for patients treated on
the University of Arkansas for Medical Sciences (UAMS;
a tandem autotransplant approach for patients with mul-
tiple myeloma (1, 2). Here, PFS is defined from the time of
response to the first of death or progression, with patients
last known to be alive without progression censored at the
date of last contact. With the current amount of follow-up,
curve is that there are 2 groups of patients in this trial. One
group of patients are long-term survivors and will not fail
during the follow-up of the study, whereas the rest of the
patients will fail during the first 15 years of the study.
Cure models can be a useful alternative to the standard
Cox proportional hazards models (3) for data with
First, the assumption of proportional hazards can fail
when survival curves have plateaus at their tails. Second,
survival plots with long plateaus may indicate hetero-
geneity within a patient population that can be useful to
effects. For example, cure models can allow us to evaluate
whether a new therapy is associated with an increase or
decrease in the probability of being a long-term survivor
or an improvement or detriment in survival for those who
are not long-term survivors.
While cure models have been a popular component of
statistical literature for the past 20 years or more, they have
not been implemented in some areas of the clinical liter-
ature. The purpose of this article is to review cure models
with the hope that some researchers will find the models a
useful alternative to standard survival models when ana-
lyzing some types of cancer survival data. To this end, we
first describe in a fairly nontechnical manner what cure
models are and how they differ from more widely used
survival models. Then, we present a cure model analysis
of multiple myeloma data from the UAMS. Multiple mye-
loma is generally considered an incurable disease (4), but
researchers at UAMS have developed an approach called
Total Therapy that may allow some patients with multiple
myeloma to be long-term survivors. The analysis will high-
a cure model analysis beyond a standard Cox analysis.
There are 2 major classes of cure models, mixture and
nonmixture models. Mixture cure models, as the name
suggests, explicitly model survival as a mixture of 2 types
of patients: those who are cured and those who are not
Research And Biostatistics, Seattle, Washington; and3Myeloma Institute
for Research and Therapy, University of Arkansas for Medical Sciences,
Little Rock, Arkansas
Note: Supplementary data for this article are available at Clinical Cancer
Research Online (http://clincancerres.aacrjournals.org/).
Corresponding Author:Megan Othus,FredHutchinsonCancerResearch
Center 1100 Fairview Ave NW, M3-C102, Seattle, WA 98117. Phone: 206-
667-5749; Fax: 206-667-4408; E-mail: email@example.com
?2012 American Association for Cancer Research.
mixture cure models for grouped survival data. Stat Med 2004;23:
13. Liu H, Shen Y. A semiparametric regression cure model for interval-
censored data. J Am Stat Assoc 2009;104:1168–78.
14. Ma S. Cure model with current status data. Stat Sin 2009;19:233–49.
with long-term survivors. Biometrics 1982;38:1041–46.
16. Tsodikov AD, Asselain B, Fourque A, Hoang T, Yakovlev AY. Discrete
strategies of cancer post-treatment surveillance: Estimation and opti-
mization problems. Biometrics 1995;51:437–47.
with a surviving fraction. J Am Stat Assoc 1999;94:909–19.
18. Chen MH, Ibrahim JG, Sinha D. Bayesian inference for multivariate
survival data with a cure fraction. J Multivariate Anal 2002;80:
19. Tsodikov AD, Ibrahim JG, Yakovlev AY. Estimating cure rates from
survival data. J Am Stat Assoc 2003;98:1063–78.
20. Yin G, Ibrahim JG. A general class of Bayesian survival models with
zero and nonzero cure fractions. Biometrics 2005;61:403–12.
21. Yin G, Ibrahim JG. Cure rate models: a unified approach. Can J Stat
22. Zeng D, Yin G, Ibrahim J. Semiparametric transformation models for
survival data with a cure fraction. J Am Stat Assoc 2006;101:670–84.
23. Barlogie B, Tricot G, Anaissie E, Shaughnessy J, Rasmussen E, van
Rhee F, et al. Thalidomide and hematopoietic-cell transplantation for
multiple myeloma. N Engl J Med 2006;354:1021–30.
24. Barlogie B, Anaissie E, Van Rhee F, Haessler J, Hollmig K, Pineda-
Roman M, et al. Incorporating bortezomib into upfront treatment for
multiple myeloma: early results of Total Therapy 3. Br J Haematol
25. Nair B, van Rhee F, Shaughnessy JD Jr, Anaissie E, Szymonifka J,
Hoering A, et al. Superior results of Total Therapy 3 (2003-33) in gene
expression profiling-defined low-risk multiple myeloma confirmed in
subsequent Trial 2006-66 with VRD maintenance. Blood 2010;115:
26. Armitage JO.Bonemarrowtransplantationinthetreatment ofpatients
with lymphoma. Blood 1989;73:1749–58.
27. Psyrri A, Kwong M, DiStasio S, Lekakis L, Kassar M, Sasaki C, et al.
Cisplatin, fluorouracil, and leucovorin induction chemotherapy fol-
lowed by concurrent cisplatin chemoradiotherapy for organ preser-
term follow-up. J Clin Oncol 2004;22:3061–9.
28. Sargent D, Sobrero A, Grothey A, O'Connell MJ, Buyse M, Andre T,
et al. Evidence for cure by adjuvant therapy in colon cancer: observa-
tions based on individual patient data from 20,898 patients on 18
randomized trials. J Clin Oncol 2009;27:872–7.
first analysis of intergroup trial E1690/S9111/C9190. J Clin Oncol
30. Bennett JM, Andersen JW, Cassileth PA. Long term survival in acute
myeloid leukemia: The Eastern Cooperative Oncology Group (ECOG)
experience. Leukemia Res 1991;15:223–7.
31. Bloomfield CD, Lawrence D, Byrd JC, Carroll A, Pettenati MJ, Tan-
travahi R, et al. Frequency of prolonged remission duration after high-
dose cytarabine intensification in acute myeloid leukemia varies by
cytogenetic subtype. Cancer Res 1998;58:4173–9.
32. Wang ZY, Chen Z. Acute promyelocytic leukemia: from highly fatal to
highly curable. Blood 2008;111:2505–15.
model. Biometrics 1992;48:1223–34.
Othus et al.
Clin Cancer Res; 18(14) July 15, 2012Clinical Cancer Research