Readme file
SERIES C
 Applied Statistics
Attribution of tumor lethality and estimation of the time to
onset of occult tumours in the absence of cause-of-death information, by H. Ahn, H. Moon and R. L. Kodell,
Journal of the Royal Statistical Society Series C, Applied Statistics, Volume 49
(2000), Part 2.
1) Description of the Calorie Restriction (PCR) data
Data from the Project on Calorie Restriction (PCR) conducted at the National Center for
Toxicological Research (NCTR) are used in the corresponding paper for illustration. The
PCR study was conducted for investigation of the effects of calorie restriction on
tumorigenicity and longevity in Fischer 344 rats. For each sex, the study included both ad
libitum (AL) and calorie restricted (CR) groups of animals. The two tumors of primary
interest in the study were mononuclear cell leukemia (MCL) and pituitary adenoma/carcinoma
(PIT). The study involved up to six scheduled sacrifices. A detailed description of
interval sacrifices is provided in Section 2 of the paper. These two tumor types have high
spontaneous incidence in Fischer rats fed ad libitum.
* The data file contains the following counts for each group.
int.: interval id
a1+d: number of deaths with tumor
(a1: #deaths with incidental tumor, d: #deaths with fatal tumor)
b1: number of deaths without tumor
a2: number of sacrifices with tumor
b2: number of sacrifices without tumor
2) Estimation Program (ANSI C for UNIX and PC)
This program works for any standard C (ANSI: American National Standards Institute)
interactive compilers for UNIX4.*, Solaris 5.6 and PC.
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***** Last updated: July 29, 1999 ****
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* Estimation using Mixture likelihood includes:
1. Generate K set of initial pts. for each pi2[INTERVAL][K],
p[INTERVAL][K], q[INTERVAL][K].
2. Check if the selected pts. satisfy the constraints.
0 <= pi2(i) <= 1 0 <= p(i) <= 1
0 <= q(i) <= 1 pi2(i)*p(i) <= pi2(i-1).
3. Maximization:
3-1. Evaluate objective function value at each K point.
and the point which has the lowest function value is replaced to a new point with BOX
recommended.
Make sure if a new point meets constraints.
3-2. If a point repeats in giving the lowest function values in consecutive trials, it
moves to the centroid of the remaining points: change all pi2(i),p(i),q(i)
3-3. New point is checked against the constraints and is replaced like in step2 if the
constraints are violated.
3-4. Check convergence criterion: objective function values at each point are within beta
units for gamma consecutive iterations and also consider parameter convergence.
4. Estimate d_hat and a1_hat.
5. perform Complex algorithm by checking convergence criterion.
Note: The random number generator, Unif(0,1), is based on L'Ecuyer's random number
generator with Bays-Durham shuffle (L'Ecuyer, P. 1988, Communications of the ACM, vol. 31,
pp. 742-774).
* Input data:
The data file should contain the following counts for each group.
gp int. a1+d b1 a2 b2
----- -------- ----- ----- --------- ---------
group interval death death sacrifice sacrifice
ID with w/o with without
tumor tumor tumor tumor
For the PCR (Project on Calorie Restriction) data,
Mononuclear cell leukemia (MCL), Male and Ad Libitum (AL) group in the corresponding
paper, each input should be in the following format:
gp int. a1+d b1 a2 b2
1 1 0 0 0 12 <- counts in the 1st interval
1 2 4 8 0 12 <- counts in the 2nd interval
1 3 37 45 6 6 <- counts in the 3rd interval
1 4 38 17 5 4 <- counts in the 4th interval
Note: If you want to input two or more groups in one data set, the number of intervals in
each group should be the same. (i.e., The input data should have the same number of
intervals in each group.)
Otherwise, please separate each group.
* The source code is in "lethal.c" and "lethal.h."
Suppose the executable file name is "Lethal."
To run the program with data, type
> Lethal input_file output_file
Then follow the command
For example, MCL Male AL group,
> Lethal mcl_m_al.dat mcl_m_al.out
> Type initial seed with any negative number
> -5
> Enter No. of sacrifice intervals
> 4
> Enter No. of groups
> 1
* Output consists of the following: at jth interval
group ID (gp)
interval (int.)
Number of natural deaths with tumor (a1+d)
Number of imputed fatal tumor death (d_hat)
Number of imputed incidental tumor death (a1_hat)
MLE's of parameters (pi2, p and q)
The following is the output for the above input data.
gp int. a1+d d_hat a1_hat pi2 p q
-- --- ----- ------ ------- ------ ------ ------
1 1 0 0.0000 0.0000 1.0000 1.0000 1.0000
1 2 4 3.8245 0.1755 1.0000 0.9770 0.9541
1 3 37 16.8149 20.1851 0.5553 0.7825 0.5383
1 4 38 18.8817 19.1183 0.3076 0.2767 0.1995
* If you have any question, please contact:
Hongshik Ahn (hahn@ams.sunysb.edu)
Hojin Moon (hojin@ams.sunysb.edu)
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