The script analyzes data from 15 patients to predict a recovery prognosis index (prog) based on the number of hospitalization days (days). First, it uses a DATA step to create the 'patient' table from embedded data (cards). Then, it fits an exponential nonlinear regression model `prog = a0*exp(a1*days)` with PROC NLIN. It generates predictions, residuals, and confidence intervals. Graphs (PROC GPLOT) are created to visualize raw data and model fit. In parallel, a second linear regression model is tested on the logarithm of the response variable (`ln(prog)`) with PROC REG to compare approaches.
Data Analysis
Type : CREATION_INTERNE
Data is created directly in the script via a DATA step and the 'cards' statement, forming the 'patient' table with 15 observations and 3 variables (prog, days, lnprog).
1 Code Block
DATA STEP Data
Explanation :
This block creates the 'patient' table in memory. It reads two variables, 'prog' (prognosis index) and 'days' (days of hospitalization), from the data provided via the 'cards' statement. It also calculates 'lnprog', the natural logarithm of 'prog'.
This block creates the 'patient' table in memory. It reads two variables, 'prog' (prognosis index) and 'days' (days of hospitalization), from the data provided via the 'cards' statement. It also calculates 'lnprog', the natural logarithm of 'prog'.
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| 1 | DATA patient; |
| 2 | INPUT prog days; |
| 3 | lnprog=log(prog); |
| 4 | CARDS; |
| 5 | 54 2 |
| 6 | 50 5 |
| 7 | 45 7 |
| 8 | 37 10 |
| 9 | 35 14 |
| 10 | 25 19 |
| 11 | 20 26 |
| 12 | 16 31 |
| 13 | 18 34 |
| 14 | 13 38 |
| 15 | 8 45 |
| 16 | 11 52 |
| 17 | 8 53 |
| 18 | 4 60 |
| 19 | 6 65 |
| 20 | ; |
| 21 | RUN; |
2 Code Block
PROC NLIN
Explanation :
This procedure fits a nonlinear regression model. The model has an exponential form: `prog = a0*exp(a1*days)`. Initial values for parameters `a0` and `a1` are provided. The procedure calculates parameter estimates and generates an output table 'a' containing predicted values, residuals, and 90% confidence and prediction intervals (alpha=0.1).
This procedure fits a nonlinear regression model. The model has an exponential form: `prog = a0*exp(a1*days)`. Initial values for parameters `a0` and `a1` are provided. The procedure calculates parameter estimates and generates an output table 'a' containing predicted values, residuals, and 90% confidence and prediction intervals (alpha=0.1).
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| 1 | PROC NLIN alpha=0.1; |
| 2 | parameters a0=10 |
| 3 | a1=-1; |
| 4 | model prog = a0*exp(a1*days); |
| 5 | OUTPUT out=a p=p r=resid lcl=lci ucl=uci lclm=l90 uclm=u90; |
| 6 | RUN; |
3 Code Block
PROC PRINT
Explanation :
Prints the content of table 'a' generated by PROC NLIN, which contains the modeling results (observed, predicted values, residuals, etc.).
Prints the content of table 'a' generated by PROC NLIN, which contains the modeling results (observed, predicted values, residuals, etc.).
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| 1 | PROC PRINT DATA=a; |
| 2 | RUN; |
4 Code Block
PROC PLOT
Explanation :
The PROC PLOT procedure is used to create a graph of residuals versus predicted values, to graphically assess the appropriateness of the nonlinear model.
The PROC PLOT procedure is used to create a graph of residuals versus predicted values, to graphically assess the appropriateness of the nonlinear model.
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| 1 | PROC PLOT; |
| 2 | plot resid*p; |
| 3 | RUN; |
5 Code Block
PROC GPLOT
Explanation :
This block configures graphical options (goptions, title, symbol, axis) to generate graphs. The first PROC GPLOT creates a scatter plot of the original data. The second superimposes the fitted model curve on the scatter plot to visualize the fit.
This block configures graphical options (goptions, title, symbol, axis) to generate graphs. The first PROC GPLOT creates a scatter plot of the original data. The second superimposes the fitted model curve on the scatter plot to visualize the fit.
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| 1 | goptions reset=global gunit=pct border cback=white |
| 2 | colors=(black blue green red) |
| 3 | ftitle=swissb ftext=swiss htitle=4 htext=4; |
| 4 | title1 'Prognostic index versus Days'; |
| 5 | symbol1 color=red |
| 6 | interpol=none |
| 7 | value=dot |
| 8 | height=3; |
| 9 | symbol2 color=red |
| 10 | interpol=join; |
| 11 | axis1 label=('Days') |
| 12 | order=(0 to 70 BY 10) |
| 13 | width=3; |
| 14 | axis2 label=('Pyrene') |
| 15 | order=(0 to 60 BY 10) |
| 16 | width=3; |
| 17 | |
| 18 | PROC GPLOT DATA=a; |
| 19 | plot prog*days/ haxis=axis1 vaxis=axis2; |
| 20 | RUN; |
| 21 | |
| 22 | PROC GPLOT DATA=a; |
| 23 | plot prog*days p*days/ overlay haxis=axis1 vaxis=axis2; |
| 24 | RUN; |
| 25 | QUIT; |
6 Code Block
PROC REG
Explanation :
For comparison purposes, this procedure performs a simple linear regression on the 'lnprog' variable (logarithm of the prognosis index) as a function of 'days'. The results, including predicted values and residuals, are stored in table 'b'.
For comparison purposes, this procedure performs a simple linear regression on the 'lnprog' variable (logarithm of the prognosis index) as a function of 'days'. The results, including predicted values and residuals, are stored in table 'b'.
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| 1 | PROC REG; |
| 2 | model lnprog=days; |
| 3 | OUTPUT out=b p=pln r=residln; |
| 4 | RUN; |
7 Code Block
PROC PLOT
Explanation :
This block uses PROC PLOT to display the residual plot of the linear model versus predicted values. This allows checking the homoscedasticity assumption (constant variance of residuals) for the log-linear model.
This block uses PROC PLOT to display the residual plot of the linear model versus predicted values. This allows checking the homoscedasticity assumption (constant variance of residuals) for the log-linear model.
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| 1 | PROC PLOT; |
| 2 | plot residln*pln; |
| 3 | RUN; |
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Copyright Info : Data source: Textbook 'Applied Linear Statistical Model', Kutner et al. (5th), p.515. Original file name: ch13-patient-nonlinear.sas
