                              BMD Analysis (Cmax)

                                 Iris Camacho
                                Paul Schlosser

Saillenfait et al. 2003, fetal body weights

                             Internal Dose, Cmax
                                    (mg/L)
                                   # litters
                                 Fetal BW (g)
                              Standard Deviation
                                       0
                                      24
                                     5.671
                                     0.37
                                     11.90
                                      20
                                     5.623
                                     0.358
                                     24.05
                                      19
                                     5.469
                                     0.252
                                     49.57
                                      25
                                     5.393
                                     0.446

                                  Model Type
                                   Risk Type
                                    P-Value
                                      AIC
                                 BMD (BMR= 5%)
                                BMDL (BMR= 5%)
                                      BMD
                                  (BMR= 10%)
                                     BMDL
                                  (BMR= 10%)
                                   Comments
                               Exponential (M2)
                                   Rel. Dev.
                                    0.9337
                                    -83.656
                                     47.8
                                     30.2
                                     98.3
                                     62.0

                               Exponential (M3)
                                   Rel. Dev.
                                    0.7594
                                    -81.699
                                     48.6
                                     30.3
                                     90.1
                                     51.3

                               Exponential (M4)
                                   Rel. Dev.
                                    0.8351
                                    -83.656
                                     47.8
                                     20.9
                                     98.3
                                     62.0
               Same best fit, but more fitted parameters than M2
                               Exponential (M5)
                                   Rel. Dev.
                                    0.9337
                                    -79.793
                                     47.8
                                     12.6
                                     error
                                     error
                    Model did not compute BMD for BMR = 10%
                                     Hill
                                   Rel. Dev.
                                      NA
                                    -79.793
                                     48.5
                                     13.1
                                     error
                                     error
                     Chi-square test for fit is not valid.
                    Model did not compute BMD for BMR = 10%
                                     Power
                                   Rel. Dev.
                                    0.7562
                                    -81.697
                                     48.6
                                     30.7
                                     88.9
                                     51.2

                                Polynomial 3°
                                   Rel. Dev.
                                      NA
                                    -79.793
                                     42.5
                                     19.7
                                     error
                                     error
                     Chi-square test for fit is not valid.
                    Model did not compute BMD for BMR = 10%
                                Polynomial 2°
                                   Rel. Dev.
                                    0.7367
                                    -81.680
                                     48.5
                                     19.7
                                     85.9
                                     57.6

                                    Linear
                                   Rel. Dev.
                                    0.9366
                                    -83.662
                                     47.9
                                     30.7
                                     95.8
                                     61.3

Among models with valid fits, the linear model has the lowest AIC and the BMDL values varied less than three fold.   Therefore the linear model is selected.

BMDL05=30.7 mg-hr/L was selected for the analysis.

Model output files for BMR=5%

====================================================================
   	  Exponential Model. (Version: 1.9;  Date: 01/29/2013)
 	  Input Data File: C:/Bmds/BMDS240/Data/exp_NMP_Saillenfait_BW_Cmax_Setting.(d)
  	  Gnuplot Plotting File:
 							Thu Sep 12 14:49:40 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   The form of the response function by Model:
      Model 2:     Y[dose] = a * exp{sign * b * dose}
      Model 3:     Y[dose] = a * exp{sign * (b * dose)^d}
      Model 4:     Y[dose] = a * [c-(c-1) * exp{-b * dose}]
      Model 5:     Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}]

    Note: Y[dose] is the median response for exposure = dose;
          sign = +1 for increasing trend in data;
          sign = -1 for decreasing trend.

      Model 2 is nested within Models 3 and 4.
      Model 3 is nested within Model 5.
      Model 4 is nested within Model 5.

   Dependent variable = Mean
   Independent variable = Dose
   Data are assumed to be distributed: normally
   Variance Model: exp(lnalpha +rho *ln(Y[dose]))
   The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho)

   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

   MLE solution provided: Exact
                                 Initial Parameter Values
     Variable          Model 2           Model 3           Model 4           Model 5
     --------          -------           -------           -------           -------
     lnalpha         -0.761471         -0.761471           -0.761471         -0.761471
         rho         -0.784145         -0.784145           -0.784145         -0.784145
           a           5.40995           5.40995             5.95455           5.95455
           b        0.00105023        0.00105023            0.026838          0.026838
           c                --                --               0.862566          0.862566
           d                --                 1                  --                 1

                               Parameter Estimates by Model
     Variable          Model 2           Model 3           Model 4           Model 5
     --------          -------           -------           -------           -------
     lnalpha        10.4028           11.4716             10.4028           9.88712
         rho          -7.27186          -7.89679            -7.27186          -6.97149
           a           5.66815           5.65943             5.66815           5.65863
           b        0.00107208        0.00161294          0.00107208          0.034696
           c             --                --                      0          0.947571
           d             --           1.16651                  --           2.22275

            Table of Stats From Input Data
     Dose      N         Obs Mean     Obs Std Dev
     -----    ---       ----------   -------------
         0     24        5.671         0.37
      11.9     20        5.623        0.358
     24.05     19        5.469        0.252
     49.57     25        5.393        0.446

                      Estimated Values of Interest
      Model      Dose      Est Mean      Est Std     Scaled Residual
     -------    ------    ----------    ---------    ----------------
          2         0         5.668       0.3307          0.04223
                 11.9         5.596       0.3464           0.3447
                24.05         5.524       0.3632          -0.6585
                49.57         5.375       0.4012           0.2269
          3         0         5.659       0.3302           0.1716
                 11.9         5.603       0.3434           0.2543
                24.05         5.533        0.361          -0.7737
                49.57          5.37       0.4062           0.2832
          4         0         5.668       0.3307          0.04223
                 11.9         5.596       0.3464           0.3447
                24.05         5.524       0.3632          -0.6585
                49.57         5.375       0.4012           0.2269
          5         0         5.659       0.3336           0.1816
                 11.9          5.62       0.3417          0.04083
                24.05         5.514       0.3651          -0.5367
                49.57         5.372       0.3997           0.2565

   Other models for which likelihoods are calculated:

     Model A1:        Yij = Mu(i) + e(ij)
               Var{e(ij)} = Sigma^2

     Model A2:        Yij = Mu(i) + e(ij)
               Var{e(ij)} = Sigma(i)^2

     Model A3:        Yij = Mu(i) + e(ij)
               Var{e(ij)} = exp(lalpha + log(mean(i)) * rho)

     Model  R:        Yij = Mu + e(i)
               Var{e(ij)} = Sigma^2

                                Likelihoods of Interest
                     Model      Log(likelihood)      DF         AIC
                    -------    -----------------    ----   ------------
                        A1        45.53621            5     -81.07243
                        A2        48.82817            8     -81.65634
                        A3        45.89652            6     -79.79305
                         R        41.22097            2     -78.44193
                         2        45.82797            4     -83.65594
                         3        45.84964            5     -81.69927
                         4        45.82797            4     -83.65594
                         5        45.89652            6     -79.79305

   Additive constant for all log-likelihoods =     -80.87.  This constant added to the above values gives the log-likelihood including the term that does not depend on the model parameters.

                                 Explanation of Tests
   Test 1:  Does response and/or variances differ among Dose levels? (A2 vs. R)
   Test 2:  Are Variances Homogeneous? (A2 vs. A1)
   Test 3:  Are variances adequately modeled? (A2 vs. A3)
   Test 4:  Does Model 2 fit the data? (A3 vs. 2)

   Test 5a: Does Model 3 fit the data? (A3 vs 3)
   Test 5b: Is Model 3 better than Model 2? (3 vs. 2)

   Test 6a: Does Model 4 fit the data? (A3 vs 4)
   Test 6b: Is Model 4 better than Model 2? (4 vs. 2)

   Test 7a: Does Model 5 fit the data? (A3 vs 5)
   Test 7b: Is Model 5 better than Model 3? (5 vs. 3)
   Test 7c: Is Model 5 better than Model 4? (5 vs. 4)

                            Tests of Interest
     Test          -2*log(Likelihood Ratio)       D. F.         p-value
   --------        ------------------------      ------     --------------
     Test 1                         15.21           6             0.01865
     Test 2                         6.584           3             0.08641
     Test 3                         5.863           2             0.05331
     Test 4                        0.1371           2              0.9337
    Test 5a                       0.09377           1              0.7594
    Test 5b                       0.04333           1              0.8351
    Test 6a                        0.1371           2              0.9337
    Test 6b                     2.26e-012           0                 N/A
    Test 7a                   -2.127e-011           0                 N/A
    Test 7b                       0.09377           1              0.7594
    Test 7c                        0.1371           2              0.9337

     The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levels, it seems appropriate to model the data.

     The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate.

     The p-value for Test 3 is less than .1.  You may want to consider a different variance model.

     The p-value for Test 4 is greater than .1.  Model 2 seems to adequately describe the data.

     The p-value for Test 5a is greater than .1.  Model 3 seems to adequately describe the data.

     The p-value for Test 5b is greater than .05.  Model 3 does not seem to fit the data better than Model 2.

     The p-value for Test 6a is greater than .1.  Model 4 seems to adequately describe the data.

     Degrees of freedom for Test 6b are less than or equal to 0.  The Chi-Square test for fit is not valid.

     Degrees of freedom for Test 7a are less than or equal to 0.  The Chi-Square test for fit is not valid.

     The p-value for Test 7b is greater than .05.  Model 5 does not seem to fit the data better than Model 3.

     The p-value for Test 7c is greater than .05.  Model 5 does not seem to fit the data better than Model 4.

   Benchmark Dose Computations:
     Specified Effect = 0.050000
            Risk Type = Relative deviation
     Confidence Level = 0.950000
                BMD and BMDL by Model
      Model             BMD                BMDL
     -------        ------------        ----------
        2             47.8448            30.1693
        3             48.5931            30.2615
        4             47.8448            20.9141
        5             47.7531            12.5535

====================================================================
   	  Hill Model. (Version: 2.17;  Date: 01/28/2013)
  	  Input Data File: C:/Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW_Cmax_Opt.(d)
  	  Gnuplot Plotting File:  C:/Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW_Cmax_Opt.plt
 							Thu Sep 12 15:07:41 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   The form of the response function is:
 	  Y[dose] = intercept + v*dose^n/(k^n + dose^n)
   Dependent variable = Mean
   Independent variable = Dose
   Power parameter restricted to be greater than 1
   The variance is to be modeled as Var(i) = exp(lalpha  + rho * ln(mean(i)))

   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values
                         lalpha =     -1.98839
                            rho =            0
                      intercept =        5.671
                              v =       -0.278
                              n =      3.77069
                              k =      19.0795

           Asymptotic Correlation Matrix of Parameter Estimates
                 lalpha          rho    intercept            v            n            k
    lalpha            1           -1        -0.35        -0.24        -0.19         0.43
       rho           -1            1         0.36         0.24         0.19        -0.43
 intercept        -0.35         0.36            1        -0.31        -0.34       -0.017
         v        -0.24         0.24        -0.31            1         0.94        -0.92
         n        -0.19         0.19        -0.34         0.94            1        -0.85
         k         0.43        -0.43       -0.017        -0.92        -0.85            1

                                 Parameter Estimates
                                                         95.0% Wald Confidence Interval
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit
         lalpha          9.88715          14.1954            -17.9352             37.7096
            rho         -6.97151          8.29351            -23.2265             9.28347
      intercept          5.65863         0.071347              5.5188             5.79847
              v        -0.358204         0.474051            -1.28733            0.570918
              n          2.44477          4.67247             -6.7131             11.6026
              k          28.2007          40.5975            -51.3689              107.77

     Table of Data and Estimated Values of Interest
 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev   Scaled Res.
------     ---   --------     --------   -----------  -----------   ----------
    0    24       5.67         5.66         0.37        0.334          0.182
 11.9    20       5.62         5.62        0.358        0.342         0.0408
24.05    19       5.47         5.51        0.252        0.365         -0.537
49.57    25       5.39         5.37        0.446          0.4          0.257

 Warning: Likelihood for fitted model larger than the Likelihood for model A3.

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = exp(lalpha + rho*ln(Mu(i)))
Model A3 uses any fixed variance parameters that
were specified by the user

 Model  R:         Yi = Mu + e(i)
            Var{e(i)} = Sigma^2

                       Likelihoods of Interest
            Model      Log(likelihood)   # Param's      AIC
             A1           45.536214            5     -81.072428
             A2           48.828168            8     -81.656336
             A3           45.896524            6     -79.793047
         fitted           45.896524            6     -79.793047
              R           41.220967            2     -78.441934

                   Explanation of Tests
 Test 1:  Do responses and/or variances differ among Dose levels?
          (A2 vs. R)
 Test 2:  Are Variances Homogeneous? (A1 vs A2)
 Test 3:  Are variances adequately modeled? (A2 vs. A3)
 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)
 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest
   Test    -2*log(Likelihood Ratio)  Test df        p-value
   Test 1              15.2144          6         0.01865
   Test 2              6.58391          3         0.08641
   Test 3              5.86329          2         0.05331
   Test 4        -5.35465e-011          0              NA

The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levels. It seems appropriate to model the data

The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate

The p-value for Test 3 is less than .1.  You may want to consider a different variance model

NA - Degrees of freedom for Test 4 are less than or equal to 0.  The Chi-Square test for fit is not valid

        Benchmark Dose Computation
Specified effect =          0.05
Risk Type        =     Relative deviation
Confidence level =           0.95
             BMD =        48.4703
            BMDL =       13.0919

 ====================================================================
   	  Power Model. (Version: 2.17;  Date: 01/28/2013)
	  Input Data File: C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW_Cmax_Opt.(d)
  	  Gnuplot Plotting File:  C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW_Cmax_Opt.plt
 							Thu Sep 12 15:14:26 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   The form of the response function is:
   Y[dose] = control + slope * dose^power
   Dependent variable = Mean
   Independent variable = Dose
   The power is restricted to be greater than or equal to 1
   The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho)
   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values
                         lalpha =     -1.98839
                            rho =            0
                        control =        5.671
                          slope =     -129.432
                          power =     -1.57384
           Asymptotic Correlation Matrix of Parameter Estimates
                 lalpha          rho      control        slope        power
    lalpha            1           -1        -0.41         0.43          0.4
       rho           -1            1         0.41        -0.43         -0.4
   control        -0.41         0.41            1        -0.69        -0.64
     slope         0.43        -0.43        -0.69            1         0.99
     power          0.4         -0.4        -0.64         0.99            1

                                 Parameter Estimates
                                                         95.0% Wald Confidence Interval
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit
         lalpha          11.4954          13.3254            -14.6218             37.6126
            rho         -7.91072          7.78441            -23.1679             7.34643
        control          5.65941        0.0692366              5.5237             5.79511
          slope      -0.00326494        0.0114188          -0.0256454           0.0191155
          power          1.14888         0.868344           -0.553038             2.85081

     Table of Data and Estimated Values of Interest
 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev   Scaled Res.
------     ---   --------     --------   -----------  -----------   ----------
    0    24       5.67         5.66         0.37         0.33          0.172
 11.9    20       5.62          5.6        0.358        0.343          0.257
24.05    19       5.47         5.53        0.252        0.361         -0.777
49.57    25       5.39         5.37        0.446        0.406          0.283
 Model Descriptions for likelihoods calculated
 Model A1:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma^2
 Model A2:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma(i)^2
 Model A3:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = exp(lalpha + rho*ln(Mu(i)))
     Model A3 uses any fixed variance parameters that were specified by the user
 Model R:         Yi = Mu + e(i)
            Var{e(i)} = Sigma^2

                       Likelihoods of Interest
            Model      Log(likelihood)   # Param's      AIC
             A1           45.536214            5     -81.072428
             A2           48.828168            8     -81.656336
             A3           45.896524            6     -79.793047
         fitted           45.848341            5     -81.696681
              R           41.220967            2     -78.441934

                   Explanation of Tests
 Test 1:  Do responses and/or variances differ among Dose levels?
          (A2 vs. R)
 Test 2:  Are Variances Homogeneous? (A1 vs A2)
 Test 3:  Are variances adequately modeled? (A2 vs. A3)
 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)
 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest
   Test    -2*log(Likelihood Ratio)  Test df        p-value
   Test 1              15.2144          6         0.01865
   Test 2              6.58391          3         0.08641
   Test 3              5.86329          2         0.05331
   Test 4             0.096366          1          0.7562

The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levels.  It seems appropriate to model the data

The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate

The p-value for Test 3 is less than .1.  You may want to consider a different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems to adequately describe the data

               Benchmark Dose Computation
Specified effect =          0.05
Risk Type        =     Relative deviation
Confidence level =          0.95
             BMD = 48.6112
            BMDL = 30.7309

====================================================================
   	   Polynomial Model  -  3[rd] degree. (Version: 2.17;  Date: 01/28/2013)

  	  Input Data File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.(d)
  	  Gnuplot Plotting File:  C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.plt
 							Thu Sep 12 15:20:55 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   The form of the response function is:
	   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...
   Dependent variable = Mean
   Independent variable = Dose
   Signs of the polynomial coefficients are not restricted
   The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho)

   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values
                         lalpha =     -1.98839
                            rho =            0
                         beta_0 =        5.671
                         beta_1 =   0.00380278
                         beta_2 = -0.000806573
                         beta_3 = 1.24414e-005

           Asymptotic Correlation Matrix of Parameter Estimates
                 lalpha          rho       beta_0       beta_1       beta_2       beta_3
    lalpha            1           -1        -0.17        -0.18         0.35        -0.41
       rho           -1            1         0.17         0.18        -0.35         0.41
    beta_0        -0.17         0.17            1        -0.44         0.23        -0.16
    beta_1        -0.18         0.18        -0.44            1        -0.95         0.91
    beta_2         0.35        -0.35         0.23        -0.95            1        -0.99
    beta_3        -0.41         0.41        -0.16         0.91        -0.99            1

                                 Parameter Estimates
                                                         95.0% Wald Confidence Interval
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit
         lalpha          9.88711          15.0342            -19.5793             39.3535
            rho         -6.97149          8.77078            -24.1619             10.2189
         beta_0          5.65863        0.0697728             5.52188             5.79539
         beta_1       0.00124345         0.020928          -0.0397746           0.0422615
         beta_2     -0.000452908       0.00139175         -0.00318069          0.00227488
         beta_3     6.28146e-006     2.03946e-005       -3.36912e-005        4.62541e-005

     Table of Data and Estimated Values of Interest
 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev   Scaled Res.
------     ---   --------     --------   -----------  -----------   ---------
    0    24       5.67         5.66         0.37        0.334          0.182
 11.9    20       5.62         5.62        0.358        0.342         0.0408
24.05    19       5.47         5.51        0.252        0.365         -0.537
49.57    25       5.39         5.37        0.446          0.4          0.257
 Warning: Likelihood for fitted model larger than the Likelihood for model A3.
 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = exp(lalpha + rho*ln(Mu(i)))
Model A3 uses any fixed variance parameters
that were specified by the user

 Model  R:         Yi = Mu + e(i)
            Var{e(i)} = Sigma^2

                       Likelihoods of Interest
            Model      Log(likelihood)   # Param's      AIC
             A1           45.536214            5     -81.072428
             A2           48.828168            8     -81.656336
             A3           45.896524            6     -79.793047
         fitted           45.896524            6     -79.793047
              R           41.220967            2     -78.441934

                   Explanation of Tests
 Test 1:  Do responses and/or variances differ among Dose levels?
          (A2 vs. R)
 Test 2:  Are Variances Homogeneous? (A1 vs A2)
 Test 3:  Are variances adequately modeled? (A2 vs. A3)
 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)
 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest
   Test    -2*log(Likelihood Ratio)  Test df        p-value
   Test 1              15.2144          6         0.01865
   Test 2              6.58391          3         0.08641
   Test 3              5.86329          2         0.05331
   Test 4        -4.84164e-011          0              NA

The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levelsIt seems appropriate to model the data

The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate

The p-value for Test 3 is less than .1.  You may want to consider a different variance model

NA - Degrees of freedom for Test 4 are less than or equal to 0.  The Chi-Square test for fit is not valid

             Benchmark Dose Computation
Specified effect =          0.05
Risk Type        =     Relative deviation
Confidence level =          0.95
             BMD =        42.4735
            BMDL =        19.7354

====================================================================
   	  Polynomial Model  -  2[nd] Order. (Version: 2.17;  Date: 01/28/2013)
 	  Input Data File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.(d)
  	  Gnuplot Plotting File:  C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.plt
 							Thu Sep 12 15:31:05 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   The form of the response function is:

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = Mean
   Independent variable = Dose
   Signs of the polynomial coefficients are not restricted
   The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho)

   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values
                         lalpha =     -1.98839
                            rho =            0
                         beta_0 =      5.68636
                         beta_1 =  -0.00953107
                         beta_2 = 7.10263e-005

           Asymptotic Correlation Matrix of Parameter Estimates
                 lalpha          rho       beta_0       beta_1       beta_2
    lalpha            1           -1        -0.26         0.49        -0.53
       rho           -1            1         0.26        -0.49         0.52
    beta_0        -0.26         0.26            1        -0.72         0.59
    beta_1         0.49        -0.49        -0.72            1        -0.97
    beta_2        -0.53         0.52         0.59        -0.97            1

                                 Parameter Estimates
                                                         95.0% Wald Confidence Interval
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit
         lalpha          11.3774          13.6414            -15.3592             38.1139
            rho         -7.84161          7.96162            -23.4461             7.76288
         beta_0          5.66132        0.0685418             5.52698             5.79566
         beta_1      -0.00486813       0.00853414          -0.0215947           0.0118585
         beta_2    -1.99964e-005      0.000168622        -0.000350489         0.000310497

     Table of Data and Estimated Values of Interest
 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev   Scaled Res.
------     ---   --------     --------   -----------  -----------   ----------
    0    24       5.67         5.66         0.37         0.33          0.144
 11.9    20       5.62          5.6        0.358        0.344          0.291
24.05    19       5.47         5.53        0.252        0.361         -0.769
49.57    25       5.39         5.37        0.446        0.406          0.273

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = exp(lalpha + rho*ln(Mu(i)))
     Model A3 uses any fixed variance parameters that
     were specified by the user

 Model  R:         Yi = Mu + e(i)
            Var{e(i)} = Sigma^2

                       Likelihoods of Interest
            Model      Log(likelihood)   # Param's      AIC
             A1           45.536214            5     -81.072428
             A2           48.828168            8     -81.656336
             A3           45.896524            6     -79.793047
         fitted           45.840013            5     -81.680026
              R           41.220967            2     -78.441934

                   Explanation of Tests
 Test 1:  Do responses and/or variances differ among Dose levels?
          (A2 vs. R)
 Test 2:  Are Variances Homogeneous? (A1 vs A2)
 Test 3:  Are variances adequately modeled? (A2 vs. A3)
 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)
 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest
   Test    -2*log(Likelihood Ratio)  Test df        p-value
   Test 1              15.2144          6         0.01865
   Test 2              6.58391          3         0.08641
   Test 3              5.86329          2         0.05331
   Test 4             0.113021          1          0.7367

The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levels. It seems appropriate to model the data

The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate

The p-value for Test 3 is less than .1.  You may want to consider a different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems to adequately describe the data

             Benchmark Dose Computation
Specified effect =          0.05
Risk Type        =     Relative deviation
Confidence level =          0.95
             BMD =        48.4891
            BMDL =         19.737

====================================================================
   	  Linear Model (Polynomial Model, 1[st] order). (Version: 2.17;  Date: 01/28/2013)
  	  Input Data File: C:/Bmds/BMDS240/Data/lin_NMP_Saillenfait_BW_Cmax_Opt.(d)
  	  Gnuplot Plotting File:  C:/Bmds/BMDS240/Data/lin_NMP_Saillenfait_BW_Cmax_Opt.plt
 							Thu Sep 12 15:36:49 2013
 ====================================================================
 BMDS Model Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   The form of the response function is:
	   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...
   Dependent variable = Mean
   Independent variable = Dose
   Signs of the polynomial coefficients are not restricted
   The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho)

   Total number of dose groups = 4
   Total number of records with missing values = 0
   Maximum number of iterations = 500
   Relative Function Convergence has been set to: 1e-008
   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values
                         lalpha =     -1.98839
                            rho =            0
                         beta_0 =      5.66456
                         beta_1 =   -0.0058728

           Asymptotic Correlation Matrix of Parameter Estimates
                 lalpha          rho       beta_0       beta_1
    lalpha            1           -1        0.077        -0.11
       rho           -1            1       -0.077         0.11
    beta_0        0.077       -0.077            1        -0.72
    beta_1        -0.11         0.11        -0.72            1

                                 Parameter Estimates
                                                         95.0% Wald Confidence Interval
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit
         lalpha          10.5323          11.5553            -12.1157             33.1803
            rho          -7.3476          6.75178            -20.5809             5.88566
         beta_0           5.6673        0.0554004             5.55871             5.77588
         beta_1      -0.00591414       0.00209746          -0.0100251         -0.00180319

     Table of Data and Estimated Values of Interest
 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev   Scaled Res.
------     ---   --------     --------   -----------  -----------   ----------
    0    24       5.67         5.67         0.37        0.331         0.0549
 11.9    20       5.62          5.6        0.358        0.346          0.337
24.05    19       5.47         5.53        0.252        0.363         -0.673
49.57    25       5.39         5.37        0.446        0.402          0.235

 Model Descriptions for likelihoods calculated
 Model A1:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)
           Var{e(ij)} = exp(lalpha + rho*ln(Mu(i)))
Model A3 uses any fixed variance parameters
that were specified by the user

 Model  R:         Yi = Mu + e(i)
            Var{e(i)} = Sigma^2

                       Likelihoods of Interest
            Model      Log(likelihood)   # Param's      AIC
             A1           45.536214            5     -81.072428
             A2           48.828168            8     -81.656336
             A3           45.896524            6     -79.793047
         fitted           45.831033            4     -83.662065
              R           41.220967            2     -78.441934

                   Explanation of Tests
 Test 1:  Do responses and/or variances differ among Dose levels?
          (A2 vs. R)
 Test 2:  Are Variances Homogeneous? (A1 vs A2)
 Test 3:  Are variances adequately modeled? (A2 vs. A3)
 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)
 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest
   Test    -2*log(Likelihood Ratio)  Test df        p-value
   Test 1              15.2144          6         0.01865
   Test 2              6.58391          3         0.08641
   Test 3              5.86329          2         0.05331
   Test 4             0.130982          2          0.9366

The p-value for Test 1 is less than .05.  There appears to be a difference between response and/or variances among the dose levels.  It seems appropriate to model the data

The p-value for Test 2 is less than .1.  A non-homogeneous variance model appears to be appropriate

The p-value for Test 3 is less than .1.  You may want to consider a different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems to adequately describe the data

             Benchmark Dose Computation
Specified effect =          0.05
Risk Type        =     Relative deviation
Confidence level =          0.95
             BMD =        47.9131
            BMDL =        30.6591


[Federal Register: October 1, 2010 (Volume 75, Number 190)]
[Notices]
[Page 60861-60862]
[DOCID:fr01oc10-127]

-----------------------------------------------------------------------

DEPARTMENT OF TRANSPORTATION

Federal Motor Carrier Safety Administration

[Docket No. FMCSA-1998-4334; FMCSA-2000-8398; FMCSA-2002-11714; FMCSA-
2006-24015; FMCSA-2008-0106; FMCSA-2008-0174]

Qualification of Drivers; Exemption Renewals; Vision

AGENCY: Federal Motor Carrier Safety Administration (FMCSA), DOT.

ACTION: Notice of final disposition.

-----------------------------------------------------------------------

SUMMARY: FMCSA previously announced its decision to renew the
exemptions from the vision requirement in the Federal Motor Carrier
Safety Regulations for 59 individuals. FMCSA has statutory authority to
exempt individuals from the vision requirement if the exemptions
granted will not compromise safety. The Agency has concluded that
granting these exemptions will provide a level of safety that will be
equivalent to, or greater than, the level of safety maintained without
the exemptions for these commercial motor vehicle (CMV) drivers.

FOR FURTHER INFORMATION CONTACT: Dr. Mary D. Gunnels, Director, Medical
Programs,<PHONE_NUMBER><EMAIL_ADDRESS>FMCSA, Department of
Transportation, 1200 New Jersey Avenue, SE., Room W64-224, Washington,
DC 20590-0001. Office hours are from 8:30 a.m. to 5 p.m. Monday through
Friday, except Federal holidays.

SUPPLEMENTARY INFORMATION:

Background

    Under 49 U.S.C. 31136(e) and 31315, FMCSA may grant an exemption
for a 2-year period if it finds ``such exemption would likely achieve a
level of safety that is equivalent to, or greater than, the level that
would be achieved absent such exemption.'' The statute also allows the
Agency to renew exemptions at the end of the 2-year period. The comment
period ended on August 26, 2010 (75 FR 44050).

Discussion of Comments

    FMCSA received no comments in this proceeding.

Conclusion

    The Agency has not received any adverse evidence on any of these
drivers that indicates that safety is being compromised. Based upon its
evaluation of the 59 renewal applications, FMCSA renews the Federal
vision exemptions for Catarino Aispuro, Gary R. Andersen, Edwin A.
Betz, Donald L. Carman, Mitchell L Carman, Christopher R. Cone, Walter
O. Connelly, Stephen B. Copeland, Armando P. D'Angeli, Donald R. Davis,
Ivory Davis, Louis A. DiPasqua, Jr., Henry L. Donivan, Randy J. Doran,
Robert E. Dukes, Roger D. Elders, James F. Epperson, Lucious J. Erwin,
Riche Ford, Kelly L. Foster, Kevin J. Friedel, Donald W. Garner, Paul
W. Goebel, Jr., Ronnie L. Hanback, Steven G. Harter, Michael C.
Hensley, George F. Hernandez, Jr., Scott A. Hillman, Charles S.
Huffman, Jesse P. Jamison, James A. Jones, Ronnie M. Jones, Andrew C.
Kelly, Jason W. King, James T. Leek, Billy J. Lewis, Velmer L.
McClelland, Larry McCoy, Sr., Robert W. McMillian, Danny W. Nuckles,
Richard A. Peterson, William R. Proffitt, Chad M. Quarles, Carroll G.
Quisenberry, Daniel S. Rebstad, Ryan J. Reimann, Ronney L. Rogers,
Manuel C. Savin, Brandon J. See, Douglas A. Sharp, Ricky L. Shepler,
LeTroy D. Sims, Robert M. Stewart, John L. Stone, Nils S. Thornberg,
Daniel W. Toppings, Kenneth E. Valentine, Christopher R. Whitson and
George L. Young.
    In accordance with 49 U.S.C. 31136(e) and 31315, each renewal
exemption will be valid for 2 years unless revoked earlier by FMCSA.
The exemption will be revoked if: (1) The person fails to comply with
the terms and conditions of the exemption; (2) the exemption has
resulted in a lower level of safety than was maintained before it was
granted; or (3) continuation of the exemption would

not be consistent with the goals and objectives of 49 U.S.C. 31136 and
31315.

    Issued on: September 28, 2010.
Charles A. Horan III,
Director, Office of Bus and Truck Standards and Operations.
[FR Doc. 2010-24726 Filed 9-30-10; 8:45 am]
BILLING CODE 4910-EX-P


[Federal Register: November 2, 2010 (Volume 75, Number 211)]
[Notices]
[Page 67450]
[DOCID:fr02no10-119]

-----------------------------------------------------------------------

DEPARTMENT OF TRANSPORTATION

Pipeline and Hazardous Materials Safety Administration

[Docket ID PHMSA-2010-0294]

Pipeline Safety: Control Room Management Implementation Workshop

AGENCY: Pipeline and Hazardous Materials Safety Administration (PHMSA),
DOT.

ACTION: Notice of workshop.

-----------------------------------------------------------------------

SUMMARY: PHMSA is conducting a workshop in conjunction with the
National Association of Pipeline Safety Representatives (NAPSR) on the
implementation of pipeline control room management. The workshop is
intended to foster an understanding of the Control Room Management Rule
issued by PHMSA on December 3, 2009, and is open to the public. Panel
discussions will provide insight on topics associated with fatigue
management and maximum hours of service, alarm management, and adequate
information. Those attending the workshop will have the opportunity to
ask questions about the rule while engaging in open discussions with
various stakeholders including representatives from the public,
regulatory, and industry. This workshop will also provide PHMSA input
to further refine guidance material currently in development.

DATES: The workshop will be held on November 17, 2010. Name badge pick
up and on-site registration will be available starting at 7:30 a.m.,
with the workshop taking place from 8 a.m. until approximately 5:15
p.m. Refer to the meeting website for updated agenda and times at
https://primis.phmsa.dot.gov/meetings/Mtg67.mtg. The workshop will not
be a live webcast, however, all workshop presentations and an audio
recording will be available on the PHMSA meeting website. Workshop
presentations will also be available on the meeting docket.

ADDRESSES: The workshop will be held at the Intercontinental Hotel,
2222 West Loop South, Houston, TX 77027. Hotel reservations under the
``USDOT CRM Meeting'' room block for the nights of November 16 and 17,
2010, can be made at 1-800-316-8645. A daily base rate of $109.00 is
available. The meeting room will be posted at the hotel on the day of
the workshop.

FOR FURTHER INFORMATION CONTACT: Karen Butler at<PHONE_NUMBER>, or by e-
mail at<EMAIL_ADDRESS>
ADDRESSES: Registration: Anyone may attend this free workshop. To help
ensure that adequate space is provided, all attendees are encouraged to
register for the workshop at https://primis.phmsa.dot.gov/meetings/
Mtg67.mtg. Hotel reservations must be made by contacting the hotel
directly.
    Comments: Anyone may submit written comments, either before or
after the workshop. Comments should reference Docket ID PHMSA-2010-
0294. Comments may be submitted in the following ways:
     E-Gov Web Site: http://www.regulations.gov. This site
allows the public to enter comments on any Federal Register notice
issued by any agency. Follow the instructions for submitting comments.
     Fax: 1-202-493-2251.
     Mail: Docket Management System, U.S. Department of
Transportation, 1200 New Jersey Avenue, SE., Room W12-140, Washington,
DC 20590.
    Hand Delivery: DOT Docket Management System, Room W12-140, on the
ground floor of the West Building, 1200 New Jersey Avenue, SE.,
Washington, DC between 9 a.m. and 5 p.m., Monday through Friday, except
Federal holidays.
    Instructions: Identify the Docket ID at the beginning of your
comments. If you submit your comments by mail, submit two copies. If
you wish to receive confirmation that PHMSA has received your comments,
include a self-addressed stamped postcard. Internet users may submit
comments at http://www.regulations.gov. Note: Comments will be posted
without changes or edits to http://www.regulations.gov including any
personal information provided.
    Privacy Act Statement: Anyone may search the electronic form of all
comments received for any of our dockets. You may review DOT's complete
Privacy Act Statement in the Federal Register published April 11, 2000,
(65 FR 19477).
    Information on Services for Individuals with Disabilities: For
information on facilities or services for individuals with
disabilities, or to request special assistance at the meeting, please
contact Karen Butler at<PHONE_NUMBER>, or by e-mail at
<EMAIL_ADDRESS>by November 5, 2010.

SUPPLEMENTARY INFORMATION: On December 3, 2009, (74 FR 63310) PHMSA
issued a final rule ``Control Room Management/Human Factors'' which
became effective on February 1, 2010. The final rule amended the
Federal pipeline safety regulations to address human factors and other
aspects of control room management for certain pipelines where
controllers use supervisory control and data acquisition (SCADA)
systems. Under the final rule, pipeline operators must implement
methods to reduce the risk associated with controller fatigue. In
addition, certain operators must define the roles and responsibilities
of controllers and provide controllers with the necessary information,
training, and processes to fulfill these responsibilities. Affected
operators must also manage alarms, ensure control room considerations
are taken into account when changing pipeline equipment or
configurations, and review reportable incidents for accidents to
determine whether control room actions contributed to the event.
    The workshop will include presentations highlighting several
topical areas and the sharing of specific solutions based on initial
feedback received from stakeholders. The panel format will offer the
opportunity for dialogue and sharing of ideas to help PHMSA generate
guidance material.

Preliminary Workshop Agenda

    The preliminary agenda for the workshop includes:
    (1) Introduction and Overview.
    (2) Definitions and Control Room Specifics.
    (3) Fatigue and Maximum Hours of Service (panel).
    (4) Alarm Management (panel).
    (5) Roles and Responsibilities.
    (6) Adequate Information (panel).
    (7) Remaining Code Sections.
    (8) Open Question and Answer.
    (9) Wrap Up and Path Forward.
    Refer to the meeting Web site for a more detailed agenda: https://
primis.phmsa.dot.gov/meetings/Mtg67.mtg.

    Issued in Washington, DC on October 22, 2010.
Jeffrey D. Wiese,
Associate Administrator for Pipeline Safety.
[FR Doc. 2010-27564 Filed 11-1-10; 8:45 am]
BILLING CODE 4910-60-P