Incorporating Historical Control Data when Comparing Tumor Incidence

Rates in Rodent Cancer Bioassay

Shyamal D. PeddadaBiostatistics Branch

National Inst. Environmental Health Sciences (NIH)

Research Triangle Park, NC

Outline of the talkOutline of the talk

The National Toxicology Program (NTP). NTP’s 2-year rodent cancer bioassay.

– Study design.– A motivating example.– Questions of interest.

Brief review of some existing methods and the current practice.

Proposed methodology. Illustration. Concluding remarks.

The National Toxicology Program The National Toxicology Program (NTP)(NTP)

Established in 1978 (became permanent in 1981)

One of the responsibilities of NTP is to provide information about potentially toxic chemicals.

Humans are exposed to a large collection of chemicals some of which can cause cancer.

So far NTP has evaluated nearly 550 chemicals.

Study design (NTP)Study design (NTP)

Species: Rats and Mice Sex: Males and Females Number of dose groups for a given chemical:

– Control, Low, Medium and High

Number of animals per dose group: 50 Duration of study: 2 years Variable of interest: Tumor incidence in

various organs

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular Male Mice. Hepatocellular

CarcinomaCarcinoma

Dose(ppm)

0 62.5 125 250

Number of animals with tumors

10 11 16 21

Route of exposure to the chemical: Inhalation.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular CarcinomaMale Mice. Hepatocellular Carcinoma

The P-value using NTP’s trend test: 0.002.

Question: Does this suggest a dose-related trend in the incidence of hepetaocellular carcinoma?

Question: Is the chemical potentially carcinogenic?

NTP’s decision

NTP not only relies on the p-value from the current data, but also uses other information in making decisions.

– E.g.

Any pre-cursors to the given tumor? Tumor incidence in the other sex and species? Mechanism/mode of action? Historically how often was the specific tumor

seen? Other tumors?

Etc.

Historical control data

NTP maintains a database of control animals from each study by sex and species.

(Statistical) problem

How to incorporate historical control (HC) data in evaluating the current experimental data for a given tumor?

– Should HC be used at all? If so, what are the conditions/circumstances?

– How to use the information?

Historical control data – heterogeneity among control groups

Potential genetic drift over time. Differences among pathologists over time. Differences between sexes and species. Route of exposure to a chemical

Inhalation Feed Water Subcutaneous Dermal

Diet used (NIH-07, NTP 2000) Etc.

NTP’s general strategy

Select suitable controls from the HC database.

Match the HC data with the current data by – sex and species– route of chemical exposure (i.e. feed study or

inhalation study etc.)– study period (most recent to the current study – 5

year sliding window).

Obtain the range of tumor incidence in the selected control groups. – This range is used by the NTP for making decisions.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular CarcinomaMale Mice. Hepatocellular Carcinoma

Observed relative frequency of tumors:

10/50, 11/50, 16/50, 21/50

NTP’s trend test: P = 0.002

Historical range: 11% to 48% (mean = 25.7%, sd = 10.4%)

The current data are within the historical range ! - Therefore NTP classified this neoplasm under

“uncertain finding”.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Forestomach squamous Forestomach squamous

cell papillomas (Male mice)cell papillomas (Male mice) Tumor rates: 1/50, 1/50, 2/50, 2/50 P-value > 0.05 - Not significant. Historical range: 0% to 2% (mean = 0.5%, sd

= 0.9%)

Female mice: 0/50, 1/50, 2/50, 5/50 P –value for trend = 0.008.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm)(0, 62.5, 125, 250 ppm)

Notes:

1. This is a rare tumor according to the HC database.

2. Although it is rare, 5/150 dosed male mice had this tumor.

3. A significant trend is seen in female mice.

NTP classified this tumor as an “uncertain finding”.

QuestionQuestion

Can a formal statistical procedure be developed to

incorporate historical control data when analyzing

“current data”?

Tarone (1982)Tarone (1982)Beta-binomial modelBeta-binomial model

Data from “current” study

Dose . . .

Number of animals with tumors

. . .

01 d 2d pd

1cY 2cY cpY

cnNumber of animals per dose group = The subscript c stands for “current” study.

Tarone (1982)Tarone (1982)

= Number of historical control groups

= Number of tumors in the j-th historical controlgroup

are assumed to be binomial random variables with

binomial probability are assumed to i.i.d. beta distributed. This is in attempt allow for extra binomial variation between studies.

k

hjY

hjY

hj

hj

The hypotheses

versus

Here denotes the tumor “rate” in dose group i in the current study (denoted by c).

43210 : ccccH

4321: ccccaH

ci

An important feature of the dataAn important feature of the data

Not all animals survive until the end of the study.

Consequently, the binomial parameter is not a suitable parameter to study.

– This parameter represents life time risk of developing tumors and not tumor incidence!

An exampleAn example

Control : All n = 50 survive until the end of the study (i.e. 2 years) and Y = 5 develop tumors.

High dose: 30 animals die within the first 6 months. Of the remaining 20, Y = 2 develop tumors.

– Should we compare 5/50 vs 2/50 Or is it 5/50 vs 2/20?

Other methodsOther methods The following take a more direct approach by

studying tumor incidence rather than life-time risk of developing tumors:

– Ibrahim and Ryan (1996). Applicable if a tumor is known to be instantly lethal.

– Ibrahim et al (1998). Applicable if a tumor is known to be non-lethal.

– Dinse and Dunson (2001). A general Bayesian approach. Not very convenient to apply in practice.

NTP Board of Scientific Councilors recommendation (2005)

None of the existing methods are endorsed by the NTP and in the 2005 meeting of the NTP Board of Scientific Councilors they recommended the development of a formal statistical procedure to incorporate historical control data.

– http://ntp.niehs.nih.gov/files/TRRSMins0905.pdf (page 10)

Some notations and background: Some notations and background: Analysis of “current” dataAnalysis of “current” data

Poly-3 methodology(Bailer and Portier, 1988)

Estimation of tumor incidence requires more data, e.g. interim animal sacrifice, or more assumptions.

– Interim sacrifices are expensive.

NTP developed tests based on hypothesis regarding life time tumor rates but adjust estimates to account for

animal survival.

– The resulting test procedure seems to perform well even for testing hypothesis on the tumor incidence.

Notations

Bailer and Portier (1988, Biometrics):

: Length of the study (current study)

: Number of days the j-th animal survived.

if the j-th animal in the i-th dose in the current study has a tumor. It is 0

otherwise.

sact

cijxsaccij tx 0

1cijY

Sample size correction for survival data

if tumor present before death or .

otherwise:

Then effective sample size for the i-th group is:

1ij

3

sac

ijij t

x

sacij tx

cn

jijcin

1

*

NTP’s Poly-3 test

Poly-3 survival adjust tumor rate for the i-th dose group in the current study is given by:

Using these estimates the NTP constructed the well-known Cochran-Armitage trend test. This is the Poly-3 test.

**ˆ

ci

cici n

Y

New test for trend (in “current” data): Basic idea

1. The classical Cochran-Armitage (CA) trend test is ideal for linear trend in dose-response.

2. The order-restricted inference based procedures work well for monotone responses that are not necessarily linear.

3. The trend test proposed in Peddada et al. (2005, 2006) is the maximum of tests 1 and 2. Thus this procedure works well for linear as well as non-linear, but monotonic responses.

Notations

Let

jcijcicij

ici

ijcij

cijcijij

cicij

c rrwn

Y

YrkN

rr

S , ,

)(

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cici n

nw

2*

Modified Cochran-Armitage trend test for NTP data

2/1

1

2

11

2

1 11

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}/)({

/)ˆ)((ˆ

p

ici

p

iici

p

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p

i

p

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p

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p

iiciciici

c

wdwdwS

wwdwdwT

Williams’ type test for NTP data

Let

cpcc

kc

wwS

W11

~~

1

1

.1 ,

ˆ

maxmin~*

**

pin

n

t

sjcj

t

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Test for trend in the current data

Peddada, et al. (2005, 2006)

– As good as Cochran-Armitage trend test for linear response.

– Maintains good power for non-linear but monotone response.

),max( ccc WTV

Analysis of “current” data making Analysis of “current” data making use of historical control datause of historical control data

Data

Number of historical controls = k

Number of animals in the m-th historical

control group:

Tumor status of the j-th animal in the

control group:

hmn

hmjY

thm

Data

Number of animals with tumors in the

control group:

Total number of animals with tumor among all historical controls

thm

hmn

jhmjhm YY

1

k

mhmh YY

1

Basic ideas

The current and all historical controls are random realizations from a population of control animals.

If no animals die before the end of the study then we assume:

hmhmhmhmhm nnYVnYE /)1()/( ,)/( 2

Basic ideas

The proposed test statistic has two components:

– As in Peddada et al. (2005, 2006) compare the dose groups from the current study with the current control group by computing:

– Similarly, compare the dose groups from the current study with the historical control group by computing:

),max( ccc WTV

),max( hhh WTV

Basic ideas

The two terms are analogous to

respectively, except that they

account for the “between controls” variability term, i.e.,

cc WT ,

2

hh WT ,

Proposed test

Thus the proposed test statistic is then given by:

Approximate null distribution of the above statistic can be derived very easily as follows:

),,,max( hhcc WTWTV

Null distributionNull distribution

Let

Similarly are isotonized values of

,,...,3,2,0,ˆ piU i

.,...,1,1

minmaxˆ pist

Z

Z

t

sjj

itisi

.,...,1,0),1,0( piN~Ziid

i

....,2,1, ,/00 piZUkZU ii

.,...,3,2,0, piU i

Null distributionNull distribution

Then the null distribution of the proposed test

is approximated by the distribution of

),,,max( hhcc WTWTV

2

ˆˆ,

)(

)(

,2

ˆˆ,

)(

)(max 0

1,0

2

1,01

1

2

1UU

dd

ZddZZ

dd

ZddV p

p

iii

p

iiii

p

p

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p

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null

Back to the NTP examplesBack to the NTP examples

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Male Mice. Hepatocellular CarcinomaMale Mice. Hepatocellular Carcinoma

Observed relative frequency of tumors:

10/50, 11/50, 16/50, 21/50

NTP’s trend test: P = 0.002

Historical range: 11% to 48% (mean = 25.7%, sd = 10.4%)

The current data are within the historical range ! - Therefore NTP classified this neoplasm under

“uncertain finding”.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): Forestomach squamous Forestomach squamous

cell papillomas (Male mice)cell papillomas (Male mice) Tumor rates: 1/50, 1/50, 2/50, 2/50 P-value > 0.05 - Not significant. Historical range: 0% to 2% (mean = 0.5%, sd

= 0.9%)

Female mice: 0/50, 1/50, 2/50, 5/50 P –value for trend = 0.008.

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm)(0, 62.5, 125, 250 ppm)

Hepatocellular Carcinoma

P-value based on the new historical control test: 0.0024

Forestomach squamous cell papillomas

P-value based on the new historical control test: 0.003

2-Butoxyethanol (TR-484): 2-Butoxyethanol (TR-484): (0, 62.5, 125, 250 ppm)(0, 62.5, 125, 250 ppm)

NTP:

“There was some evidence of carcinogenic activity of 2-Butoxyethanol in male B6C3F1 mice… based on Hemangiosarcoma of liver … A marginal increase in the forestomach squamous cell papilloma and an increase in the incidence of hepatocellular carcinoma may have been exposure related.”

Simulation study

Simulation experimentSimulation experiment

As usually done, we generated independent Weibull random variables for (a) Tumor incidence and (b) Mortality.

Weibull parameters were chosen so that the data “resemble” some of the commonly seen patterns in NTP studies.

– Dose effect on mortality: None, Moderate.– Background tumor rate: .001 (rare tumor), .01, .05, .15, .30

(common tumor)– Heterogeneity of historical control groups: Low, Medium and

High.– Tumor incidence shape parameter: 1.5, 3 and 6– Tumor incidence ratio patterns: 5 different non-null patterns and

1 null pattern.

– Total number of non-null patterns = 450. – Total number of null patterns = 90.– Each simulation was based on 10000 samples.

Some research questionsSome research questions

Is there a better approach to this problem? Perhaps an empirical Bayes approach.

How do we adjust for co-variables such as the body weight of the animal?

– Note that the changes in body weight and animal survival and carcinogenicity are common response to changes in dose of a chemical.

How do we perform simultaneous analyses of multiple tumors?

Concluding remarksConcluding remarks

The new historical control test procedure:

(a) Operates at the desired level of significance.

(b) Gains in power over NTP’s Poly-3 trend test.

(c) Computationally simple to implement (a user friendly JAVA-based multiplatform computer software package is available).

(d) Unlike other existing statistical procedures, it is non-parametric. No complicated modeling/distributional assumptions are made.

AcknowledgementsAcknowledgements

Gregg Dinse, NIEHS Grace Kissling, NIEHS Shawn Harris, Constella group Kevin McGowan, Constella group