This simulated tutorial is similar with respect to techniques covered to the full Weibull analysis tutorial by Fulton Findings (TM). The complete tutorial includes:
…Review of classic benchmark case studies using SuperSMITH(R) Weibull software.
…Detailed instructions for setup and data entry.
…Explanation and interpretation of results.
The tutorial example below comes from Gerald Lawless, Statistical Models and Methods for Lifetime Data, Wiley, 1982. He is a pioneer in the use of likelihood analysis techniques. The data is from an actual study on the effectiveness of a particular leukemia treatment, drug 6-MP. It can be used as a benchmark for checking the accuracy of Weibull analysis software.
Likelihood Ratio Confidence Example
Symptom return times are shown in the Weibull plot for drug 6-MP and a placebo. The drug 6-MP was administered to a group of 21 people. Twelve of those did not have symptoms at the end of testing. These twelve were considered suspensions (non-failures). The other nine people given drug 6-MP had return of symptoms. All 21 people given a placebo indicated return of symptoms. The data are given below.
Example 4.2.1, Page 175 in Lawless :
Leukemia patients received either drug 6-MP (left column) or a placebo (right column). The Xvalues are times in weeks until cancer symptoms return. The original study validated the benefits of drug 6-MP to significantly control these symptoms.
Data for likelihood ratio confidence interval sample problem. Weeks until symptoms return. Note: negative numbers indicate suspensions where symptoms did not return within test period.
Drug 6-MP, Placebo (comma used for separation not decimal symbol)
To analyze in SuperSMITH:
1) Copy the data into the clipboard.
2) Start SuperSMITH Weibull (SSW).
3) Clear the program with the New button (blank page icon) on the main screen and make sure that you are analyzing with Weibull equations (computer icon).
4) Click the Method button (showing regression ./. and mle ^ symbols), make sure Point-By-Point/Standard button is selected and then click the Method mle button (^). At the Main Screen, the only buttons depressed should be the Method button and possibly the Plot/Report button.
5) Paste the data into the program spreadsheet.
The benchmark reference gives beta=1.35 and eta=33.77 for the data in the left column (drug 6-MP), and beta=1.37 and eta=9.482 for the data in the right column (placebo). Using SuperSMITH you should get the same values.
6) Click on the Confidence button (fit line between 2 confidence lines), select the Likelihood Ratio confidence button (lr) and choose No to the Save Contour question.
7) Select the Double Confidence button and enter 95 for % confidence level. The program will take a few moments while it performs lr calculations and then you should see the plot with confidence lines unless Report is already selected.
8) Click on the Plot/Report button (notebook or colored fit lines), choose Bvalue-Select, 1 value, 50 (for 50th percentile) and then select Report (ccc+Bvalue) to change the results from plot to table output.
9) Click on the small table to enlarge.
Set 1, drug 6-MP, should read Betal=.72 and Betau=2.2 (benchmark is .72 and 2.21) and B50 from 16.2 to 51.4 (benchmark is 16.2<B50<51.6). Set 2, placebo, should read Betal=.95 and Betau=1.88 (same as benchmark) and B50 from 4.755 to 10.3 (benchmark is 4.75<B50<10.3). SuperSMITH is slightly more accurate than the benchmark here. You can also verify probability confidence range at Xvalue=10 matches closely the benchmark values of 63.7%-93.1% (Set 1) and 19.7%-51.3% (Set 2) by using the Predict button (4 arrows) from the main screen.