Subgroup Analyses: Can We Smooth' out the Rough Edges

1
Subgroup Analyses  Can We Smooth' out the Rough
Edges?

• Daniel Sargent, PhD
• Mayo Clinic
• Sept 28, 2006

2
Outline

• Motivation
• Subgroups ARE medicine (especially its future)
• Examples
• Good and bad conduct
• Strategies
• Hierarchical models
• Smoothing approaches
• Conclusion

3
Subgroups analysis My Definition My Bias

• Definition An effort to draw inference on an
  effect of an intervention in a set of patients
  smaller than the entire experimental cohort
• Bias Such inferences will be more robust when
  based on a model using all patients than an
  analysis restricted to just the cohort of interest

4
Subgroups are medicine

• If all patients were the same, wouldnt need
  physicians
• Human Genome Project massively expanding
  knowledge base
• Technology, biology, chemistry, etc. allowing
  manufacture of highly specific, targeted
  compounds
• Patients seek tailored treatment
  recommendations

5
Example Colon Cancer Model-Derived Estimates
of 5 year DFS () with Surgery plus Adjuvant
Therapy
Gill, JCO 2004 http//www.mayoclinic.com/calcs
6
Example Breast Cancer

• Most common cancer in women in the US
• The HER-2 gene is overexpressed in 25-30 of
  breast cancers associated with worse prognosis.
• Trastuzumab, a humanized monoclonal antibody
  targets the HER-2 receptor previous trials have
  demonstrated activity in the treatment of HER-2
  overexpressing late stage breast cancer.
• Performed a clinical trial testing trastuzumab in
  subset of HER-2 positive women with early stage
  breast cancer

7
Disease-Free Survival
Survival
AC?TH ?H 62 events
AC?TH ?H 134 events
AC?T 92 events
94
AC?T 261 events
91
87
92
85
87
75
HR0.48, 2P3x10-12
HR0.67, 2P0.015
67
Years
Years
Romond et al, NEJM 2005
8
Avoiding subgroup analysis Targeted Phase
II/III Trials

• Patient Selection for targeted therapies
• Test the recommended dose on patients who are
  most likely to respond based on their molecular
  expression levels
• May result in a large savings of patients (Simon
  Maitournam, Clinical Cancer Research 2004)

9
Trials in targeted populations

• Gains in efficiency depend on marker prevalence
  and relative efficacy in marker and marker
  patients
• Details Session 13 tomorrow

(Simon Maitournam, CCR 2004)
10
Case Study Stage II colon cancer

• Colon cancer Prognosis defined by stage
• Prior trials generally enrolled patients with
  both stage II and III disease
• Previous randomized trials uniformly demonstrate
  benefit of chemotherapy in stage III patients
  (node positive)
• Previous trials pooled analyses mixed regarding
  benefit in stage II patients
• No single trial powered for modest effect seen in
  stage II ( ? 2-3 in 5 year survival)

11
Meta-analysis Stage II Adjuvant Therapy
N2,732 RR0.88 P0.08
Benson et al. J Clin Oncol. 2004
12
American Society of Clinical Oncology Guidelines
2004

• Direct evidence from randomized trials does not
  support routine use of chemotherapy for patients
  with stage II colon cancer.
• Those who accept the relative benefit in stage
  III disease as adequate indirect evidence of
  benefit for stage II disease are justified in
  considering chemotherapy, particularly for
  patients with high-risk stage II disease.
• Ultimate clinical decision should be based on
  discussions with the patient.

Benson et al. J Clin Oncol. 2004
13
New therapy FOLFOX
FOLFOX4 LV5FU2 oxaliplatin 85 mg/m²
N2246 Stage II 40 Stage III 60
LV5FU2

• Primary end-point disease-free survival (DFS)

de Gramont et al., ASCO 2005
14
Disease-free Survival (ITT)
1.0
0.9
0.8
6.6
0.7
0.6
Events FOLFOX4 279/1123 (24.8) LV5FU2
345/1123 (30.7) HR 95 CI 0.77 0.65
0.90
DFS probability
0.5
0.4
0.3
plt0.001
0.2
0.1
0.0
0
66
6
12
18
24
30
36
42
48
54
60
Months
de Gramont et al., ASCO 2005
15
Disease-free Survival (ITT) Stage II and Stage
III Patients
1.0
0.9
3.5
0.8
0.7
8.6
0.6
DFS probability
0.5
0.4
0.3
FOLFOX4 451 Stage II LV5FU2 448 Stage
II FOLFOX4 672 Stage III LV5FU2 675 Stage
III
HR 95 CI 0.82 0.60 1.13 Stage II 0.75
0.62 0.89 Stage III
0.2
0.1
0.0
0
66
6
12
18
24
30
36
42
48
54
60
Months
Data cut-off January 16, 2005
de Gramont et al., ASCO 2005
16

DFS in high-risk stage II patients
1.0
0.9
5.4
0.8
Probability
0.7
HR 0.76
FOLFOX4 286 HRStage II LV5FU2 290 HR Stage
II
0.6
0 6 12 18 24 30 36 42 48
DFS (months)
T4 and/or bowel obstruction and/or tumor
perforation and/or poorly differentiated tumor
and/or venous invasion and/or lt10 examined
LNs Data cut-off January 16, 2005
de Gramont et al., ASCO 2005
17
FDA Action

• Approval of FOLFOX therapy only in stage III
  patients, even though trial designed for stage II
  and III patients
• Possible rationale
• Standard chemotherapy vs control not shown
  beneficial in stage II patients
• This trial not significant for experimental vs
  standard chemotherapy

18
Stage II trial QUASAR
R A N D O M I Z E
Observation (n 1617)

• Colon or rectal cancer
• Stage I-III
• Complete resection with no evidence of residual
  disease

No clear indicationfor chemotherapy (n 3239)
Chemotherapy (n 1622)
Gray et al. ASCO 2004. Abstract 3501. At
http//www.asco.org/ac/1,1003,_12-002511-00_18-002
6-00_19-0010698,00.asp. Accessed November 2004.
19
QUASAR Overall Survival
100
Observation (n1622)
Chemotherapy (n1617)
80
60
of Patients
40
P .02 5-year OS, Observation 77.4 vs
Chemotherapy 80.3 Relative risk 0.83 (95
CI, 0.71-0.97)
20
0
0
1
2
3
4
5
6
7
8
9
10
Years
Gray et al. ASCO 2004. Abstract 3501. At
http//www.asco.org/ac/1,1003,_12-002511-00_18-002
6-00_19-0010698,00.asp.Accessed November 2004.
20
Implication Stage II patients

• Compared to control, 5-FU provides 2-3 ? in OS,
  statistically significant in a single trial
• Debate over clinical relevance
• In a large trial, FOLFOX provides 3-4 ? in DFS
  compared to 5-FU, not statistically significant
  for stage II alone
• No hint of interaction between rx and stage, p
  0.77
• On its own, debatable benefit compared to 5-FU
• Cross trial comparison FOLFOX may result in 5-7
  improvement vs control, but not approved
• No debate about clinical relevance

Grothey Sargent, JCO 2005
21
Stage II Colon Cancer Lessons Learned

• Decisions based on subgroups may seem rational at
  the time, but lead to unintended consequences
• Results may make further trials impossible
  (FOLFOX vs control)
• Need better approaches to analyze subgroups using
  modeling (or meta-analyses), not individual trial
  results

22
Potential solution for prospectively defined
subgroups Hierarchical models

• Goal Test a treatment in a number of
  populations
• Hypothesis Effect may depend vary between
  populations
• Example Targeted cancer therapy
• Mechanism of action based therapy
• Multiple tumor types express target, to varying
  degrees

23
Basic statistical formulation

• Suppose N subgroups, with mean response mi,
  i1,...N
• Assume mi N(m,s2)
• If Bayesian, put a prior on s2
• Depending on estimate of s2, allows heterogeneity
  between subgroups
• Easily extends to non-normal models

24
Hierarchical Model Example

• Phase II clinical trial of a new agent
  specifically targeted at patients with a
  methylated MGMT promoter
• Prevalence from 10 to 60 across various cancer
  types
• High prevalence seen in Head and Neck,
  Esophageal, Colorectal, and Non Small-Cell Lung
  Cancer
• Goal Determine if overall efficacy gt 10, but
  efficacy may depend on tumor type

25
Logistic regression Example

• Hierarchical logistic model for tumor response
• Stopping rules for each tumor site
• P ( Response ratei gt 10) lt 10 OR
• P (Response ratei gt 10) lt 25 P
  (Response rateOverall gt 10) lt 10
• Simulation for operating characteristics
• Benefits
• Single trial (opposed to 4)
• Use all data formally but flexibly

26
Survival Example

• Survival following chemotherapy for colon cancer
• Pooled analysis of 5 trials, suggestion of a
  study-specific treatment effect (a different type
  of subgroup)
• Fit a random effect Cox model
• l(t x) l0i(t) exp (xmi)
• mi N(m,s2)
• Can either model l0 parametrically, or use Cox
  model

27
Model Results
Prior mean for precision (1/s2) 50, posterior
mean 106, Little evidence of heterogeneity
Sargent et al, 2000
28
Another approach Modeling Interactions using
Shrinkage

• Subgroup analyses are fundamentally looking at
  interactions
• In multi-factor experiment, the number of
  interactions can explode
• Well known that shrinkage (or model averaging)
  provides much better performance than all or
  nothing approach (stepwise)
• Idea Include interactions in model, but shrink
  them away if they are not strongly supported by
  the data

29
Another approach Modeling Interactions using
shrinkage

• Dental Experiment
• Dentures are often made with a soft liner between
  the gums and the hard denture base
• Polishing the liner can cause a gap between the
  liner and the base
• Such gaps harbor pathogens like Candida
• The experiment
• Main interest new vs. standard soft liner
  material
• Factor M 2 materials
• Factor P 4 polishing methods
• Factor F 8 finishing methods
• Fully crossed design, no replication
• Outcome measure gap btwn liner base, in log10
  mm

Pesun, Hodges Lai (2002) J. Prosthetic Dentistry
30
Smoothing interactions Smoothed ANOVA

• Fit full ANOVA model (include all interactions)
• y X Q e
• y is 64 x 1, contains log10 gap
• e is 64 x 1, normal mean 0, precision h0I64
• X is 64 x 64
• Q is 64 x 1 we will smooth/shrink its elements
• 12 main effects, 52 interactions
• Model interactions
• qk N (0,1/ fk) , k13, , 64
• Large fk implies qk shrunk toward 0

31
Smoothed ANOVA The model/prior for the fk

• How to model the interactions
• Each interaction smoothed by its own fk
• Each effect's fk are all the same, feffect
• All two-way interactions are smoothed by a single
  f
• Mix the above options
• Use priors on fk to specify desired operating
  characteristics for interactions

32
Use Degrees of Freedom to set priors for the fk

• Hodges Sargent (2001 Biometrika) extended
  methods for computing DF in standard ANOVA to
  linear hierarchical models
• Hodges et al (Technometrics, 2006) present
  methodology to use DF to set priors
• Example I want the 51 2-way interactions to
  share 5 degrees of freedom
• See references for technical details
• Ongoing work extending to non-linear (Cox)
  models

33
Summary Smoothed ANOVA

• Subgroup analyses are fundamentally looking at
  interactions
• A priori have low probability of a significant
  interaction, but dont want to exclude the
  possibility
• Idea Include interactions in model, but shrink
  them

34
Summary

• Subgroup analysis is essential to clinical
  research
• People usually perform such analyses with best of
  intentions
• Up-front thought can allow us to
• Carefully define population under study
• Pre-specify sub-populations to be examined
• Hierarchical/Shrinkage models offer attractive
  possibilities for addressing subgroups, if
  defined prospectively

35
Thank You

• Acknowledgements
• Smoothed ANOVA Jim Hodges
• Colon Cancer Axel Grothey, Aimery deGramont,
  Sharlene Gill