This script analyzes biological assay data (Ames salmonella assay). It begins by creating an internal dataset, then fits several models: a simple Poisson regression, a two-component Poisson mixture model with constrained effects (via EQUATE and RESTRICT), and finally examines the impact of an outlier by refitting the models on a subset of data.
Data Analysis
Type : CREATION_INTERNE
The 'assay' data is created directly in the script using a DATA step and the DATALINES statement.
1 Code Block
DATA STEP Data
Explanation :
Creation of the 'assay' dataset containing quinoline doses and observed colony counts. The 'logd' variable (log of dose) is calculated.
Creation of the 'assay' dataset containing quinoline doses and observed colony counts. The 'logd' variable (log of dose) is calculated.
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| 1 | DATA assay; |
| 2 | label dose = 'Dose of quinoline (microg/plate)' |
| 3 | num = 'Observed number of colonies'; |
| 4 | INPUT dose @; |
| 5 | logd = log(dose+10); |
| 6 | DO i=1 to 3; INPUT num @; OUTPUT; END; |
| 7 | DATALINES; |
| 8 | 0 15 21 29 |
| 9 | 10 16 18 21 |
| 10 | 33 16 26 33 |
| 11 | 100 27 41 60 |
| 12 | 333 33 38 41 |
| 13 | 1000 20 27 42 |
| 14 | ; |
2 Code Block
PROC FMM
Explanation :
Fitting a standard Poisson regression model (k=1 by default) to model colony count as a function of dose.
Fitting a standard Poisson regression model (k=1 by default) to model colony count as a function of dose.
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| 1 | |
| 2 | PROC FMM |
| 3 | DATA=assay; |
| 4 | model num = dose logd / dist=Poisson; |
| 5 | RUN; |
| 6 |
3 Code Block
PROC FMM
Explanation :
Fitting a two-component Poisson mixture model (k=2). The 'equate=effects(dose logd)' option forces the regression coefficients for 'dose' and 'logd' to be identical across both mixture components.
Fitting a two-component Poisson mixture model (k=2). The 'equate=effects(dose logd)' option forces the regression coefficients for 'dose' and 'logd' to be identical across both mixture components.
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| 1 | PROC FMM DATA=assay; |
| 2 | model num = dose logd / dist=Poisson k=2 |
| 3 | equate=effects(dose logd); |
| 4 | RUN; |
4 Code Block
PROC FMM
Explanation :
An alternative to the EQUATE option using the RESTRICT statement to force parameter equality between the two components (dose 1 = dose 2 and logd 1 = logd 2).
An alternative to the EQUATE option using the RESTRICT statement to force parameter equality between the two components (dose 1 = dose 2 and logd 1 = logd 2).
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| 1 | PROC FMM DATA=assay; |
| 2 | model num = dose logd / dist=Poisson k=2; |
| 3 | restrict 'common dose' dose 1, dose -1; |
| 4 | restrict 'common logd' logd 1, logd -1; |
| 5 | RUN; |
5 Code Block
PROC FMM
Explanation :
Refitting the two-component Poisson mixture model (k=2) excluding an outlier observation (num=60) to see its impact on the fit.
Refitting the two-component Poisson mixture model (k=2) excluding an outlier observation (num=60) to see its impact on the fit.
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| 1 | PROC FMM DATA=assay(where=(num ne 60)); |
| 2 | model num = dose logd / dist=Poisson k=2 |
| 3 | equate=effects(dose logd); |
| 4 | RUN; |
6 Code Block
PROC FMM
Explanation :
Refitting the simple Poisson model excluding the outlier observation.
Refitting the simple Poisson model excluding the outlier observation.
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| 1 | |
| 2 | PROC FMM |
| 3 | DATA=assay(where=(num ne 60)); |
| 4 | model num = dose logd / dist=Poisson; |
| 5 | RUN; |
| 6 |
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