The program begins by creating a 'logistic' dataset simulating a dose-response relationship. It then uses the NLIN procedure to fit a log-logistic model using three different parameterizations. The objective is to show how the choice of parameters influences measures of nonlinearity (such as Hougaard's bias) and the reliability of confidence intervals.
Data Analysis
Type : CREATION_INTERNE
The data is generated directly in the code via a DATA step and DATALINES statements.
1 Code Block
DATA STEP Data
Explanation :
Creation of the 'logistic' dataset containing the 'dose' and 'y' variables, as well as a logarithmic transformation of the dose.
Creation of the 'logistic' dataset containing the 'dose' and 'y' variables, as well as a logarithmic transformation of the dose.
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| 1 | DATA logistic; |
| 2 | INPUT dose y; |
| 3 | logdose = log(dose); |
| 4 | DATALINES; |
| 5 | 0.009 106.56 |
| 6 | 0.035 94.12 |
| 7 | 0.07 89.76 |
| 8 | 0.15 60.21 |
| 9 | 0.20 39.95 |
| 10 | 0.28 21.88 |
| 11 | 0.50 7.46 |
| 12 | ; |
2 Code Block
PROC SGPLOT
Explanation :
Graphical visualization of the data as a scatter plot with a logarithmic scale on the x-axis.
Graphical visualization of the data as a scatter plot with a logarithmic scale on the x-axis.
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| 1 | PROC SGPLOT DATA=logistic; |
| 2 | scatter y=y x=dose; |
| 3 | xaxis type=log logstyle=linear; |
| 4 | RUN; |
3 Code Block
PROC NLIN
Explanation :
First adjustment of the nonlinear model with parameters alpha, beta, and gamma. The 'bias', 'hougaard', and 'nlinmeasures' options request diagnostics on nonlinearity and parameter bias.
First adjustment of the nonlinear model with parameters alpha, beta, and gamma. The 'bias', 'hougaard', and 'nlinmeasures' options request diagnostics on nonlinearity and parameter bias.
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| 1 | PROC NLIN DATA=logistic bias hougaard nlinmeasures; |
| 2 | parameters alpha=100 beta=3 gamma=300; |
| 3 | delta = 0; |
| 4 | Switch = 1/(1+gamma*exp(beta*log(dose))); |
| 5 | model y = delta + (alpha - delta)*Switch; |
| 6 | RUN; |
4 Code Block
PROC NLIN Data
Explanation :
Second adjustment with a reparameterization replacing gamma with LD50 (lethal dose 50%). This formulation is often more interpretable. Predicted results are saved in the 'nlinout' table.
Second adjustment with a reparameterization replacing gamma with LD50 (lethal dose 50%). This formulation is often more interpretable. Predicted results are saved in the 'nlinout' table.
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| 1 | PROC NLIN DATA=logistic bias hougaard; |
| 2 | parameters alpha=100 beta=3 LD50=0.15; |
| 3 | delta = 0; |
| 4 | Switch = 1/(1+exp(beta*log(dose/LD50))); |
| 5 | model y = delta + (alpha - delta)*Switch; |
| 6 | OUTPUT out=nlinout pred=p lcl=lcl ucl=ucl; |
| 7 | RUN; |
5 Code Block
PROC NLIN Data
Explanation :
Third adjustment with another reparameterization using 'mustar' (predicted value at a fixed dose xstar). This approach aims to further reduce the nonlinearity of the parameters.
Third adjustment with another reparameterization using 'mustar' (predicted value at a fixed dose xstar). This approach aims to further reduce the nonlinearity of the parameters.
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| 1 | PROC NLIN DATA=logistic bias hougaard nlinmeasures; |
| 2 | parameters alpha=100 mustar=20 LD50=0.15; |
| 3 | delta = 0; |
| 4 | xstar = 0.3; |
| 5 | beta = log((alpha - mustar)/(mustar - delta)) / log(xstar/LD50); |
| 6 | Switch = 1/(1+exp(beta*log(dose/LD50))); |
| 7 | model y = delta + (alpha - delta)*Switch; |
| 8 | OUTPUT out=nlinout pred=p lcl=lcl ucl=ucl; |
| 9 | RUN; |
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