This example illustrates the pattern-mixture model approach to multiple imputation under the MNAR assumption by creating control-based pattern imputation.
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 variable Y1
is the efficacy score at a follow-up visit.
If the data set does not contain any missing values, then a regression model such as
can be used to test the treatment effect.
Suppose that the variables Trt
and Y0
are fully observed and the variable Y1
contains missing values in both the treatment and control groups. Multiple imputation for missing values often assumes that
the values are missing at random. But if missing Y1
values for individuals in the treatment group imply that these individuals no longer receive the treatment, then it is reasonable
to assume that the conditional distribution of Y1
given Y0
for individuals who have missing Y1
values in the treatment group is similar to the corresponding distribution of individuals in the control group.
Ratitch and O’Kelly (2011) describe an implementation of the pattern-mixture model approach that uses a control-based pattern imputation. That is, an imputation model for the missing observations in the treatment group is constructed not from the observed data in the treatment group but rather from the observed data in the control group. This model is also the imputation model that is used to impute missing observations in the control group.
Table 75.11 shows the variables in the data set. For the control-based pattern imputation, all missing Y1
values are imputed based on the model that is constructed using observed Y1
data from the control group (Trt=0) only.
Table 75.11: Variables
Variables |
||
---|---|---|
Trt |
Y0 |
Y1 |
0 |
X |
X |
1 |
X |
X |
0 |
X |
. |
1 |
X |
. |
Suppose the data set Mono1
contains the data from the trial that have missing values in Y1
. Output 75.15.1 lists the first 10 observations.
Output 75.15.1: Clinical Trial Data
The following statements implement the control-based pattern imputation:
proc mi data=Mono1 seed=14823 nimpute=15 out=outex15; class Trt; monotone reg (/details); mnar model( y1 / modelobs= (Trt='0')); var y0 y1; run;
The MNAR statement imputes missing values for scenarios under the MNAR assumption. The MODEL option specifies that only observations
where TRT=0 are used to derive the imputation model for the variable Y1
. Thus, Y0
and Y1
(but not Trt) are specified in the VAR list.
The "Model Information" table in Output 75.15.2 describes the method that is used in the multiple imputation process.
Output 75.15.2: Model Information
The "Monotone Model Specification" table in Output 75.15.3 describes methods and imputed variables in the imputation model. The MI procedure uses the regression method to impute the
variable Y1
.
Output 75.15.3: Monotone Model Specification
The "Missing Data Patterns" table in Output 75.15.4 lists distinct missing data patterns and their corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.
Output 75.15.4: Missing Data Patterns
By default, for each imputed variable, all available observations are used in the imputation model. When you specify the MODEL
option in the MNAR statement, the "Observations Used for Imputation Models Under MNAR Assumption" table in Output 75.15.5 lists the subset of observations that are used for the imputation model for Y1
.
Output 75.15.5: Observations Used for Imputation Models under MNAR Assumption
When you specify the DETAILS option, the parameters that are estimated from the observed data and the parameters that are used in each imputation are displayed in Output 75.15.6.
Output 75.15.6: Regression Model
Regression Models for Monotone Method | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Imputed Variable |
Effect | Obs-Data | Imputation | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
y1 | Intercept | -0.30169 | -0.174265 | -0.280404 | -0.275183 | 0.090601 | -0.457480 | -0.241909 | -0.501351 | -0.058460 | -0.436650 | -0.509949 | -0.542411 | -0.082799 | -0.243293 | -0.502742 | -0.213113 |
y1 | y0 | 0.69364 | 0.641733 | 0.629970 | 0.507776 | 0.752283 | 0.831001 | 0.970075 | 0.724584 | 0.623638 | 0.563499 | 0.621280 | 0.677104 | 0.562119 | 0.512430 | 0.693212 | 0.699355 |
The following statements list the first 10 observations of the output data set Outex15
in Output 75.15.7:
proc print data=outex15(obs=10); title 'First 10 Observations of the Imputed Data Set'; run;
Output 75.15.7: Imputed Data Set