* Glim-Logistic-Example-04Feb03

1 1/* GliM-logistic-example-04feb03.doc 2 Example of SAS statements used to compare the concentration-mortality curves for fathead minnows 3 exposed to pentachlorobenzene or dichlorobenzene [6]. 4Ref: Oris, J.T. and Bailer, A.J. (1997) Equivalence of concentration-response distributions in aquatic 5toxicology: testing and implications for potency estimation. Environmental Toxicology and 6Chemistry16: 2204-2209 7 8 Data taken from Groetsch (1996) Short-term toxicity, pharmacokinetics, and critical body residues for 9 1,1,2,2,-tetrachloroethane, 1,4-dichlorobenzene, pentachlorobenzene, and hexachlorobenzene in larval 10 fathead minnows (Pimephales promelas). MS Thesis, Miami University, Oxford, OH, USA. 11 12 chem = chemical tested where PCBZ is pentachlorobenzene and DCBZ is dichlorobenzene 13 conc = concentration of compound in micromoles per liter (measured) 14 mort = number of organisms dead after 96 hours exposure to respective chemical 15 n = number of organisms on test at each concentration 16*/ 17 18/* 19 Create a variable 'i' equal to 0 for DCBZ and 1 for PCBZ. 20 Variable 'i' is used to generate beta2 (additional intercept parameter PCBZ). 21 Variable 'ic' is used to generate beta3 (additional slope parameter for PCBZ). 22 NOTE: log10(conc) generates a "missing" value for conc=0 conditions, and thus, the 23 conc=0 data are not used in the analysis. 24*/ 25 26data crcomp; 27 input chem $ conc mort n; 28 i = (chem = 'PCBZ'); 29 lconc=log10(conc); 30 ic = i*lconc; 31datalines; 32 PCBZ 0 13 200 33 PCBZ 23.3 35 192 34 PCBZ 34 54 203 35 PCBZ 40.8 79 164 36 PCBZ 50.6 126 162 37 PCBZ 75.2 204 207 38 DBCZ 0 14 200 39 DBCZ 262 55 197 40 DBCZ 376 80 151 41 DBCZ 650 210 219 42; 43proc logist; 44 model mort/n=lconc i ic; 45 title 'FULL MODEL -- All Parameters Specified'; 46 run; 47 48proc logist; 49 model mort/n=lconc; 2 3 1 4 50 title1 'Remove Extra Parameters for Both Intercept and Slope from 51 Full Model to Test Hypothesis 1:'; 52 title2 'Beta2=Beta3=0? (if reject, then intercepts and/or slopes 53 differ)'; 54 run; 55 56proc logist; 57 model mort/n=lconc ic; 58 title1 'Remove Extra Parameter for Intercept from Full Model to 59 Test Hypothesis 2:'; 60 title2 'Beta2=0? (if reject, then intercepts differ)'; 61 run; 62 63proc logist; 64 model mort/n=lconc i; 65 title1 'Remove Extra Parameter for Slopes from Full Model to Test 66 Hypothesis 3:'; 67 title2 'Beta3=0? (if reject, then slopes differ)'; 68 run; 69 70*************************************************************************** 71* Sort data by chemical , and perform logistic regression using Proc Probit in order to 72* obtain point estimates for LCx values and their associated confidence limits. 73***************************************************************************; 74proc sort; by chem; 75proc probit; by chem; 76 model mort/n = lconc / d=logistic inversecl; 77 title1 'LCx estimation by chemical'; 78 run; 79 80

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81 FULL MODEL -- All Parameters Specified 1 82 83 The LOGISTIC Procedure 84 85 Model Information 86 87 Data Set WORK.CRCOMP 88 Response Variable (Events) mort 89 Response Variable (Trials) n 90 Number of Observations 8 91 Model binary logit 92 Optimization Technique Fisher's scoring 93 94 Response Profile 95 96 Ordered Binary Total 97 Value Outcome Frequency 98 99 1 Event 843 100 2 Nonevent 652 101 102NOTE: 2 observations were deleted due to missing values for the response or explanatory variables. 103 104 Model Convergence Status 105 106 Convergence criterion (GCONV=1E-8) satisfied. 107 108 Model Fit Statistics 109 Intercept 110 Intercept and 111 Criterion Only Covariates 112 AIC 2050.041 1411.845 113 SC 2055.351 1433.085 114 -2 Log L 2048.041 1403.845 115 116 The LOGISTIC Procedure 117 118 Testing Global Null Hypothesis: BETA=0 119 Test Chi-Square DF Pr > ChiSq 120 Likelihood Ratio 644.1959 3 <.0001 121 Score 551.8853 3 <.0001

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122 Wald 371.6279 3 <.0001 123 124 Analysis of Maximum Likelihood Estimates 125 Standard Wald 126 Parameter DF Estimate Error Chi-Square Pr > ChiSq 127 Intercept 1 -24.7579 2.0672 143.4347 <.0001 128 lconc 1 9.7744 0.8118 144.9578 <.0001 129 i 1 8.8778 2.3238 14.5951 0.0001 130 ic 1 0.2029 1.0481 0.0375 0.8465 131 132 133 Odds Ratio Estimates 134 Point 95% Wald 135 Effect Estimate Confidence Limits 136 lconc >999.999 >999.999 >999.999 137 i >999.999 75.429 >999.999 138 ic 1.225 0.157 9.556 139 140 Association of Predicted Probabilities and Observed Responses 141 142 Percent Concordant 81.1 Somers' D 0.696 143 Percent Discordant 11.5 Gamma 0.752 144 Percent Tied 7.4 Tau-a 0.343 145 Pairs 549636 c 0.848 146 147 Remove Extra Parameters for Both Intercept and Slope from Full Model to Test Hypothesis 1: 148 Beta2=Beta3=0? (if reject, then intercepts and/or slopes differ) 149 150 The LOGISTIC Procedure 151 Model Information 152 Data Set WORK.CRCOMP 153 Response Variable (Events) mort 154 Response Variable (Trials) n 155 Number of Observations 8 156 Model binary logit 157 Optimization Technique Fisher's scoring 158 159 Response Profile 160 Ordered Binary Total 161 Value Outcome Frequency 162 1 Event 843

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163 2 Nonevent 652 164 165NOTE: 2 observations were deleted due to missing values for the response or explanatory variables. 166 167 Model Convergence Status 168 Convergence criterion (GCONV=1E-8) satisfied. 169 170 Model Fit Statistics 171 Intercept 172 Intercept and 173 Criterion Only Covariates 174 AIC 2050.041 1939.181 175 SC 2055.351 1949.801 176 -2 Log L 2048.041 1935.181 177 178 The LOGISTIC Procedure 179 Testing Global Null Hypothesis: BETA=0 180 Test Chi-Square DF Pr > ChiSq 181 Likelihood Ratio 112.8598 1 <.0001 182 Score 109.3727 1 <.0001 183 Wald 104.4225 1 <.0001 184 185 Analysis of Maximum Likelihood Estimates 186 Standard Wald 187 Parameter DF Estimate Error Chi-Square Pr > ChiSq 188 Intercept 1 -1.9683 0.2213 79.1251 <.0001 189 lconc 1 1.1288 0.1105 104.4225 <.0001 190 191 Odds Ratio Estimates 192 Point 95% Wald 193 Effect Estimate Confidence Limits 194 lconc 3.092 2.490 3.839 195 196 197 Association of Predicted Probabilities and Observed Responses 198 199 Percent Concordant 67.9 Somers' D 0.433 200 Percent Discordant 24.6 Gamma 0.468 201 Percent Tied 7.4 Tau-a 0.213 202 Pairs 549636 c 0.717 203 14 15 5 16

204 Remove Extra Parameter for Intercept from Full Model to Test Hypothesis 2: 205 Beta2=0? (if reject, then intercepts differ) 206 207 Model Information 208 209 Data Set WORK.CRCOMP 210 Response Variable (Events) mort 211 Response Variable (Trials) n 212 Number of Observations 8 213 Model binary logit 214 Optimization Technique Fisher's scoring 215 216 Response Profile 217 Ordered Binary Total 218 Value Outcome Frequency 219 1 Event 843 220 2 Nonevent 652 221 222NOTE: 2 observations were deleted due to missing values for the response or explanatory variables. 223 224 Model Convergence Status 225 Convergence criterion (GCONV=1E-8) satisfied. 226 227 Model Fit Statistics 228 Intercept 229 Intercept and 230 Criterion Only Covariates 231 AIC 2050.041 1425.778 232 SC 2055.351 1441.708 233 -2 Log L 2048.041 1419.778 234 Remove Extra Parameter for Intercept from Full Model to Test Hypothesis 2: 235 Beta2=0? (if reject, then intercepts differ) 236 237 Testing Global Null Hypothesis: BETA=0 238 Test Chi-Square DF Pr > ChiSq 239 Likelihood Ratio 628.2631 2 <.0001 240 Score 529.9242 2 <.0001 241 Wald 351.2285 2 <.0001 242 243 Analysis of Maximum Likelihood Estimates 244 Standard Wald

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245 Parameter DF Estimate Error Chi-Square Pr > ChiSq 246 Intercept 1 -18.2513 0.9858 342.7528 <.0001 247 lconc 1 7.2314 0.3859 351.2237 <.0001 248 ic 1 4.2233 0.2402 309.1825 <.0001 249 250 Odds Ratio Estimates 251 Point 95% Wald 252 Effect Estimate Confidence Limits 253 lconc >999.999 648.803 >999.999 254 ic 68.256 42.628 109.291 255 256 Association of Predicted Probabilities and Observed Responses 257 Percent Concordant 81.1 Somers' D 0.696 258 Percent Discordant 11.5 Gamma 0.752 259 Percent Tied 7.4 Tau-a 0.343 260 Pairs 549636 c 0.848 261 262 Remove Extra Parameter for Slopes from Full Model to Test Hypothesis 3: 7 263 Beta3=0? (if reject, then slopes differ) 264 265 Model Information 266 267 Data Set WORK.CRCOMP 268 Response Variable (Events) mort 269 Response Variable (Trials) n 270 Number of Observations 8 271 Model binary logit 272 Optimization Technique Fisher's scoring 273 274 Response Profile 275 Ordered Binary Total 276 Value Outcome Frequency 277 278 1 Event 843 279 2 Nonevent 652 280 281NOTE: 2 observations were deleted due to missing values for the response or explanatory variables. 282 283 Model Convergence Status 284 Convergence criterion (GCONV=1E-8) satisfied. 285 20 21 7 22

286 Model Fit Statistics 287 Intercept 288 Intercept and 289 Criterion Only Covariates 290 AIC 2050.041 1409.883 291 SC 2055.351 1425.812 292 -2 Log L 2048.041 1403.883 293 Remove Extra Parameter for Slopes from Full Model to Test Hypothesis 3: 8 294 Beta3=0? (if reject, then slopes differ) 295 296 Testing Global Null Hypothesis: BETA=0 297 Test Chi-Square DF Pr > ChiSq 298 Likelihood Ratio 644.1586 2 <.0001 299 Score 551.8829 2 <.0001 300 Wald 371.7373 2 <.0001 301 302 Analysis of Maximum Likelihood Estimates 303 Standard Wald 304 Parameter DF Estimate Error Chi-Square Pr > ChiSq 305 Intercept 1 -25.0695 1.3096 366.4572 <.0001 306 lconc 1 9.8970 0.5134 371.6439 <.0001 307 i 1 9.3176 0.5044 341.2444 <.0001 308 309 310 Odds Ratio Estimates 311 Point 95% Wald 312 Effect Estimate Confidence Limits 313 lconc >999.999 >999.999 >999.999 314 i >999.999 >999.999 >999.999 315 316 Association of Predicted Probabilities and Observed Responses 317 Percent Concordant 81.1 Somers' D 0.696 318 Percent Discordant 11.5 Gamma 0.752 319 Percent Tied 7.4 Tau-a 0.343 320 Pairs 549636 c 0.848 321 322 LCx estimation by chemical 9 323 324------chem=DBCZ ------325 Probit Procedure 326 23 24 8 25

327 Model Information 328 329 Data Set WORK.CRCOMP 330 Events Variable mort 331 Trials Variable n 332 Number of Observations 3 333 Number of Events 345 334 Number of Trials 567 335 Missing Values 1 336 Name of Distribution Logistic 337 Log Likelihood -261.612762 338 Algorithm converged. 339 340 Type III Analysis of Effects 341 Wald 342 Effect DF Chi-Square Pr > ChiSq 343 lconc 1 144.9583 <.0001 344 345 Analysis of Parameter Estimates 346 Standard 95% Confidence Chi- 347 Parameter DF Estimate Error Limits Square Pr > ChiSq 348 Intercept 1 -24.7584 2.0673 -28.8102 -20.7067 143.44 <.0001 349 lconc 1 9.7746 0.8119 8.1834 11.3658 144.96 <.0001 350 351 352------chem=DBCZ ------353 354 Probit Procedure 355 Probit Model in Terms of Tolerance Distribution 356 357 MU SIGMA 358 2.53292819 0.10230563 359 360 Estimated Covariance Matrix 361 for Tolerance Parameters 362 MU SIGMA 363 MU 0.000123 -0.000007 364 SIGMA -0.000007 0.000072 365 366------chem=DBCZ ------367 Probit Procedure

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368 369 Probit Analysis on lconc 370 371 Probability lconc 95% Fiducial Limits 372 0.10 2.30814 2.25675 2.34675 373 0.50 2.53293 2.51058 2.55473 374 0.90 2.75772 2.72143 2.80570 375 376------chem=PCBZ ------377 Probit Procedure 378 Model Information 379 Data Set WORK.CRCOMP 380 Events Variable mort 381 Trials Variable n 382 Number of Observations 5 383 Number of Events 498 384 Number of Trials 928 385 Missing Values 1 386 Name of Distribution Logistic 387 Log Likelihood -440.30989 388 Algorithm converged. 389 390 Type III Analysis of Effects 391 Wald 392 Effect DF Chi-Square Pr > ChiSq 393 lconc 1 226.5363 <.0001 394 395 Analysis of Parameter Estimates 396 Standard 95% Confidence Chi- 397 Parameter DF Estimate Error Limits Square Pr > ChiSq 398 Intercept 1 -15.8803 1.0615 -17.9607 -13.7999 223.82 <.0001 399 lconc 1 9.9774 0.6629 8.6781 11.2767 226.54 <.0001 400 401 Probit Procedure 402 Probit Model in Terms of Tolerance Distribution 403 MU SIGMA 404 1.59162452 0.10022643 405 406 Estimated Covariance Matrix 407 for Tolerance Parameters 408 MU SIGMA

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409 MU 0.000070 -0.000002 410 SIGMA -0.000002 0.000044 411 412 Probability lconc 95% Fiducial Limits 413 0.10 1.37140 1.33348 1.40157 414 0.50 1.59162 1.57506 1.60803 415 0.90 1.81184 1.78260 1.84852

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