AMFIT Version 2.06 Mar 1997 May 14,
1997
Ganbarimashoo! 9:33:31
Copyright (C) HiroSoft International 1986-96
Written by Dale L. Preston and Donald A. Pierce
DOS version
Workspace size - 1500000
The data are read into AMFIT from the Report 12 cancer mortality data file using a script (r12canc.amf) supplied with the publically available data set (r12canc.dat). This cross-tabulation has one more high-dose category than the cross- tabulation used for the paper, but results are essentially the same. The dataset, detailed documentation and the input script can be downloaded from the Scientific Archives section of the RERF Home Page here
!------------------------------------------------------ ! EPICURE command file ! Created by AMFIT on September 13, 1996 at 13:17:22 ! from data in file: r12fdat2.bsf ! Number of variables: 53 !------------------------------------------------------ Names city sex k4gy agexcat agecat dcat tcat atrisk pyr subjects age agex tsx year gkerma nkerma gcolon ncolon d10 adf10 deaths cancer leuk nonleuk solid tongue pharynx digest esoph stomach colon rectum liver gallb pancre othdig resp nose larynx lung bone nmskin fbreast uterus cervix ovary prost urinary bladder kidney brain lympho myeloma @ Input r12canc.dat @ Input from R12CANC.DAT 16612 records read 16612 records used 0 records rejected Workspace for 90 variables. 55 are currently defined. Up to 35 new variables can be created
Define categorical variables, AGEXCAT and AGECAT define categories for age at exposure and attained age. The variable DCAT indicates dose categories. In the low-dose range ( < 2 Sv ) DCAT corresponds to the dose categories specified in the paper.
levels city sex k4gy agexcat agecat tcat DCAT @ CITY has 2 levels from 1 to 2 SEX has 2 levels from 1 to 2 K4GY has 2 levels from 1 to 2 AGEXCAT has 15 levels from 1 to 15 AGECAT has 20 levels from 1 to 20 TCAT has 10 levels from 1 to 10 DCAT has 14 levels from 1 to 14
Create some additional variables used in fitting the models of interest.
tran female = sex == 2 @ tran e30 = agex - 30 @
The background rates are stratified on sex, city, attained age and age at exposure categories. (This means the models include one parameter for each strata defined by the cross-classification of these factors)
strata sex city agecat agexcat @ Workspace for 81 variables. 59 are currently defined. Up to 22 new variables can be created The current model has 1200 strata
We first fit a model to all of the data with separate dose effects for each of the 14 dose categories in the data set. This model includes sex and age at exposure effects. These parameter estimates for these effects in this model are used in fitting the low dose model. The dose category effects and there asymptotic standard errors from this fit were use to make Figure 5 in the paper.
cases solid @
line 1 dcat @
logl 1 female e30 @
para 2=0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 552 strata
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.05602 Aliased
Linear term 1
2 DCAT_1 .................. 0 Fixed 2.316 0.021
3 DCAT_2 .................. 0.02470 0.02033 1.215 0.224
4 DCAT_3 .................. 0.05317 0.02852 1.864 0.062
5 DCAT_4 .................. 0.04141 0.03112 1.331 0.183
6 DCAT_5 .................. 0.06271 0.03538 1.772 0.076
7 DCAT_6 .................. 0.1185 0.04243 2.792 0.005
8 DCAT_7 .................. 0.1436 0.06321 2.272 0.023
9 DCAT_8 .................. 0.3106 0.1091 2.847 0.004
10 DCAT_9 .................. 0.4652 0.1362 3.415 < 0.001
11 DCAT_10 ................. 0.5932 0.1957 3.032 0.002
12 DCAT_11 ................. 0.4996 0.2268 2.203 0.028
13 DCAT_12 ................. 0.9215 0.3943 2.337 0.019
14 DCAT_13 ................. 0.3564 0.2771 1.286 0.198
15 DCAT_14 ................. 0.8252 0.3720 2.218 0.027
Log-linear term 1
16 FEMALE .................. 0.8775 0.2764 3.174 0.002
17 E30 ..................... -0.03911 0.008625 -4.534 < 0.001
Records used = 16612
Deviance = 6928.11 df = 16045
Pearson Chi2 = 38612.5
We note that the parameter estimates 3-7 here are the dose category excess relative risk (ERR) estimate's given in the paper on page 9. Dividing these estimates by the mean dose for the categories leads to the estimates of the ERR per Sv corresponding to those shown in the the table on that page. (The dose-category specific mean doses are given later.) Restrict the analyses to those people with doses less than 0.05 Sv. D10 is the weighted colon dose computed as the sum of the gamma dose and 10 times the neutron dose.
select d10 < 0.05 @ 4458 records to be used
Fix the sex (female) and age at exposure (e30) effects
para 16-17 fixed @
Replace the dose category indicators with the continuous weighted dose variable and fit the null (no dose effect) model
line 1 d10=0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 549 strata
Using D10 < 0.05
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.05602 Aliased
Linear term 1
2 D10 ..................... 0 Fixed 2.369 0.018
Log-linear term 1
3 FEMALE .................. 0.8775 Aliased
4 E30 ..................... -0.03911 Aliased
Records used = 4458
Deviance = 2429.10 df = 3909
Pearson Chi2 = 3135.84
Free the dose parameter and fit the full model
null @
para 2:0 3-4 fixed @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 549 strata
Using D10 < 0.05
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.07431 Aliased
Linear term 1
2 D10 ..................... 1.770 0.8070 2.194 0.028
Log-linear term 1
3 FEMALE .................. 0.8775 Fixed -0.2083 > 0.5
4 E30 ..................... -0.03911 Fixed -0.2094 > 0.5
Records used = 4458
Deviance = 2423.63 df = 3908
Pearson Chi2 = 3060.64
Compute the likelihood ratio test comparing the no-effect model to the dose response model. This is a two-sided test. The P-value for this test is given in the paper (p. 12). The one-sided P-value is half of that shown.
lrt LR statistic = 5.474 df = 1 P = 0.0193
The dose-category specific mean doses are shown in the following table:
select @ 16612 records to be used mean d10 ; by dcat weight subjects @ Using D10 < 0.05 Summary for D10 DCAT Mean Weight Std. Dev. 1 0.000247454 36459 0.91224E-04 2 0.00974613 16921 0.00060540 3 0.0326394 9390.0 0.0010540 4 0.0714166 6538.0 0.0014551 5 0.141989 5467.0 0.0037202 6 0.318358 6308.0 0.011479 7 0.613168 2080.0 0.017087 8 0.868478 1122.0 0.021372 9 1.22902 1115.0 0.036508 10 1.71644 493.00 0.064412 11 2.23218 261.00 0.056148 12 2.72353 149.00 0.10295 13 3.49363 133.00 0.21888 14 4.61256 136.00 0.30844
The next section of this analysis illustrates a better approach for
carrying out the low dose test that we developed after publication of the
Report 12. The new analysis differs from the old one in that it does not
fix the sex and age-at-exposure effects at values determined in a separate
analysis. Instead common sex and age-at-exposure effects are estimated for
the low and high dose portions of the dose response curve.
This is done by using an excess relative risk (ERR) model of the form
b_1 * dose * exp( g_1*female + g_2*agex) for dose < 50 mSv
ERR =
b_2 * dose * exp( g_1*female + g_2*agex) for dose >= 50 mSv
where b_1 and b_2 are separately estimated dose response slopes for low and
high dose ranges, and g_1 and g_2 are parameters associated with the sex
and age at exposure effects on the dose response. Interest centers on
testing the null hypothesis that the low dose slope (b_1) is 0.
Note that there are no constraints on the relationship between the two dose
response parameters in this model.
We use this method to test for effects on the range 0 - 50 mSv and 0 - 200 mSv.
First define (categorical) high dose indicator functions for the dose
ranges of interest.
tran d050 = d10 >= 0.05 ; d200 = d10 >= 0.20 @ levels d050 d200 @ D050 has 2 levels from 0 to 1 D200 has 2 levels from 0 to 1
The model presented above can be rewritten by defining separate dose variables for the low and high dose regions, becoming
ERR = (b_1 * lodose + b_2 * hidose) * exp( g_1*female + g_2*agex)
When the model is written in this form it can be fit using AMFIT where log-linear terms multiply linear terms. The following commands specify the ERR model described above. Because the D050 variable is categorical this model will include low and high dose effects are generated by the program.
linear 1 d050*adf10 @ loglinear 1 female e30 @
Fit a model in which there is no dose response over the low dose range.
para 2=0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 552 strata
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.1100 Aliased
Linear term 1
2 D050_0 * ADF10 .......... 0 Fixed 2.132 0.033
3 D050_1 * ADF10 .......... 0.3225 0.07724 4.176 < 0.001
Log-linear term 1
4 FEMALE .................. 0.8000 0.2729 2.932 0.003
5 E30 ..................... -0.03673 0.008579 -4.281 < 0.001
Records used = 16612
Deviance = 6939.74 df = 16057
Pearson Chi2 = 37025.0
Now free the low dose parameter and carry out the likelihood ratio test for the low dose effect.
null @
para 2:0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 552 strata
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.1236 Aliased
Linear term 1
2 D050_0 * ADF10 .......... 1.617 0.8688 1.861 0.063
3 D050_1 * ADF10 .......... 0.3439 0.08097 4.247 < 0.001
Log-linear term 1
4 FEMALE .................. 0.7989 0.2697 2.962 0.003
5 E30 ..................... -0.03838 0.008631 -4.447 < 0.001
Records used = 16612
Deviance = 6935.30 df = 16056
Pearson Chi2 = 36931.4
lrt
LR statistic = 4.445 df = 1
P = 0.0350
The above results shows that there is a statistically significant response over the range 0 - 50 mSv in the LSS data even when the sex and age-at-exposure effects are estimated. As noted in the Report 12, the statistical significance of the low dose slope over the 0 to 50 mSv dose range may be the result of a small, subtle bias that increases the apparent slope in the lowest dose categories. Because of this one should not put too much emphasis on the 0 - 50 mSv slope estimate. However, the effect of the hypothesized bias decreases as the dose range is extended. As the following analysis indicates, teh LSS cancer mortality data exhigbit a statictally significant dose response on the 0 - 200 mSv range. In our view estimates of the magnitiude of the low dose slope. The following analyses shows the results of testing for a dose-response on the 0 - 200 mSv range. The analysis also includes likelihood-based 95 confidence intervals for the low- and high-dose dose response slopes. There is no evidence that these slopes differ (P > 0.5 test not shown).
line 1 d200*adf10 @
para 2=0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 552 strata
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.1604 Aliased
Linear term 1
2 D200_0 * ADF10 .......... 0 Fixed 2.170 0.030
3 D200_1 * ADF10 .......... 0.3340 0.07688 4.344 < 0.001
Log-linear term 1
4 FEMALE .................. 0.7070 0.2659 2.659 0.008
5 E30 ..................... -0.03735 0.008627 -4.329 < 0.001
Records used = 16612
Deviance = 6942.52 df = 16057
Pearson Chi2 = 37328.5
null @
para 2:0 @
fit @
Piece-wise exponential regression model
Product additive excess model {T0*(1 + T1 + T2 + ...)}
Stratification on SEX CITY AGECAT AGEXCAT
with 552 strata
SOLID is used for cases
PYR is used for person years
Parameter Summary Table
# Name Estimate Std.Err. Test Stat. P value
-- ----------------------- ------------ ---------- ----------- -------
Log-linear term 0
1 CON .................... -0.1742 Aliased
Linear term 1
2 D200_0 * ADF10 .......... 0.4598 0.2361 1.947 0.051
3 D200_1 * ADF10 .......... 0.3235 0.07833 4.130 < 0.001
Log-linear term 1
4 FEMALE .................. 0.8328 0.2750 3.028 0.002
5 E30 ..................... -0.03714 0.008588 -4.325 < 0.001
Records used = 16612
Deviance = 6937.64 df = 16056
Pearson Chi2 = 36944.4
lrt
LR statistic = 4.877 df = 1
P = 0.0272
The following results present likelihood-based 95 confidence intervals for the low- and high- dose slopes.
bound 2 @ Likelihood bound for parameter 2 D200_0 * ADF10 MLE 0.4598 97.50 lower bound 0.53238E-01 97.50 upper bound 0.98378 bound 3 @ Likelihood bound for parameter 3 D200_1 * ADF10 MLE 0.3235 97.50 lower bound 0.17871 97.50 upper bound 0.48807
The following AMFIT commands were used to reproduce the Report 12 analysis.
< r12canc.amf levels dcat @ tran female = sex == 2 @ tran e30 = agex - 30 @ strata sex city agecat agexcat @ cases solid @ linear 1 dcat @ loglinear 1 female e30 @ parameter 2=0 @ fit @ select d10 < 0.05 @ parameter 16-17 fixed @ linear 1 d10=0 @ fit @ null @ parameter 2:0 3-4 fixed @ fit @ lrt select @ mean d10 ; by dcat weight subjects @
The commands below were used for the revised method for testing for low dose effects
! A more direct test of the low dose effect for d < 50 mSv tran d050 = d10 >= 0.05 ; d200 = d10 >= 0.20 @ leve d050 d200 @ select @ line 1 d050*adf10 @ logl 1 female e30 @ para 2=0 @ fit @ null @ para 2:0 @ fit @ lrt ! A more direct test of the low dose effect for d < 200 mSv line 1 d200*adf10 @ para 2=0 @ fit @ null @ para 2:0 @ fit @ lrt bound 2 @ bound 3 @(end)