This example illustrates the pattern-mixture model approach to multiple imputation under the MNAR assumption by using specified shift parameters to adjust imputed continuous values.
Suppose that a pharmaceutical company is conducting a clinical trial to test the efficacy of a new drug. The trial consists
of two groups of equally allocated patients: a treatment group that receives the new drug and a placebo control group. The
variable Trt
is an indicator variable, with a value of 1 for patients in the treatment group and a value of 0 for patients in the control
group. The variable Y0
is the baseline efficacy score, and the variables Y1
and Y2
are the efficacy scores at two successive follow-up visits.
Suppose the data set Fcs1
contains the data from the trial that have possible missing values in Y1
and Y2
. Output 61.16.1 lists the first 10 observations in the data set Fcs1
.
Output 61.16.1: Clinical Trial Data
First 10 Obs in the Trial Data |
Obs | Trt | y0 | y1 | y2 |
---|---|---|---|---|
1 | 0 | 11.4826 | 11.0428 | 13.1181 |
2 | 0 | 9.6775 | 11.0418 | 8.9792 |
3 | 0 | 9.9504 | . | 11.2598 |
4 | 0 | 11.0282 | 11.4097 | . |
5 | 0 | 10.7107 | 10.5782 | . |
6 | 1 | 9.0601 | 8.4791 | 10.6421 |
7 | 1 | 9.0467 | 9.4985 | 10.4719 |
8 | 1 | 10.6290 | 9.4941 | . |
9 | 1 | 10.1277 | 10.9886 | 11.1983 |
10 | 1 | 9.6910 | 8.4576 | 10.9535 |
Also suppose that for the treatment group, the distribution of missing Y1
responses has an expected value that is 0.4 lower than that of the corresponding distribution of the observed Y1
responses. Similarly, the distribution of missing Y2
responses has an expected value that is 0.5 lower than that of the corresponding distribution of the observed Y1
responses.
The following statements adjust the imputed Y1
and Y2
values by –0.4 and –0.5, respectively, for observations in the treatment group:
proc mi data=Fcs1 seed=52387 nimpute=5 out=outex16; class Trt; fcs nbiter=25 reg( /details); mnar adjust( y1 /shift=-0.4 adjustobs=(Trt='1')) adjust( y2 /shift=-0.5 adjustobs=(Trt='1')); var Trt y0 y1 y2; run;
The MNAR statement imputes missing values for scenarios under the MNAR assumption. The ADJUST option specifies parameters
for adjusting the imputed values for specified subsets of observations. The first ADJUST option specifies the shift parameter
for the imputed Y1
values for observations for which TRT=1. The second ADJUST option specifies the shift parameter for the imputed Y2
values for observations for which TRT=1.
Because Trt
is listed in the VAR statement, it is used as a covariate for other imputed variables in the imputation process. In addition,
because Trt
is specified in the ADJUSTOBS= suboption, it is also used to select the subset of observations from which the imputed values
for the variable are to be adjusted.
The “Model Information” table in Output 61.16.2 describes the method that is used in the multiple imputation process.
Output 61.16.2: Model Information
Model Information | |
---|---|
Data Set | WORK.FCS1 |
Method | FCS |
Number of Imputations | 5 |
Number of Burn-in Iterations | 25 |
Seed for random number generator | 52387 |
The “FCS Model Specification” table in Output 61.16.3 describes methods and imputed variables in the imputation model. The MI procedure uses the regression method to impute all the variables.
Output 61.16.3: FCS Model Specification
FCS Model Specification | |
---|---|
Method | Imputed Variables |
Regression | y0 y1 y2 |
Discriminant Function | Trt |
The “Missing Data Patterns” table in Output 61.16.4 lists distinct missing data patterns and their corresponding frequencies and percentages.
Output 61.16.4: Missing Data Patterns
Missing Data Patterns | |||||||||
---|---|---|---|---|---|---|---|---|---|
Group | Trt | y0 | y1 | y2 | Freq | Percent | Group Means | ||
y0 | y1 | y2 | |||||||
1 | X | X | X | X | 39 | 39.00 | 10.108397 | 10.380942 | 10.606255 |
2 | X | X | X | . | 29 | 29.00 | 10.207179 | 10.626839 | . |
3 | X | X | . | X | 32 | 32.00 | 9.604041 | . | 10.396557 |
The “MNAR Adjustments to Imputed Values” table in Output 61.16.5 lists the adjustment parameters for the five imputations.
Output 61.16.5: MNAR Adjustments to Imputed Values
MNAR Adjustments to Imputed Values |
||
---|---|---|
Imputed Variable |
Observations | Shift |
y1 | Trt = 1 | -0.4000 |
y2 | Trt = 1 | -0.5000 |
The following statements list the first 10 observations of the data set Outex16
in Output 61.16.6:
proc print data=outex16(obs=10); var _Imputation_ Trt y0 y1 y2; title 'First 10 Observations of the Imputed Data Set'; run;
Output 61.16.6: Imputed Data Set
First 10 Observations of the Imputed Data Set |
Obs | _Imputation_ | Trt | y0 | y1 | y2 |
---|---|---|---|---|---|
1 | 1 | 0 | 11.4826 | 11.0428 | 13.1181 |
2 | 1 | 0 | 9.6775 | 11.0418 | 8.9792 |
3 | 1 | 0 | 9.9504 | 11.1409 | 11.2598 |
4 | 1 | 0 | 11.0282 | 11.4097 | 10.8214 |
5 | 1 | 0 | 10.7107 | 10.5782 | 9.4899 |
6 | 1 | 1 | 9.0601 | 8.4791 | 10.6421 |
7 | 1 | 1 | 9.0467 | 9.4985 | 10.4719 |
8 | 1 | 1 | 10.6290 | 9.4941 | 10.7865 |
9 | 1 | 1 | 10.1277 | 10.9886 | 11.1983 |
10 | 1 | 1 | 9.6910 | 8.4576 | 10.9535 |