# The MIANALYZE Procedure

### Example 76.1 Reading Means and Standard Errors from a DATA= Data Set

This example creates an ordinary SAS data set that contains sample means and standard errors computed from imputed data sets. These estimates are then combined to generate valid univariate inferences about the population means.

The following statements use the UNIVARIATE procedure to generate sample means and standard errors for the variables in each imputed data set:

```proc univariate data=outmi noprint;
var Oxygen RunTime RunPulse;
output out=outuni mean=Oxygen RunTime RunPulse
stderr=SOxygen SRunTime SRunPulse;
by _Imputation_;
run;
```

The following statements display the output data set from PROC UNIVARIATE shown in Output 76.1.1:

```proc print data=outuni (obs=10);
title 'UNIVARIATE Means and Standard Errors (First 10 Imputations)';
run;
```

Output 76.1.1: UNIVARIATE Output Data Set

 UNIVARIATE Means and Standard Errors (First 10 Imputations)

Obs _Imputation_ Oxygen RunTime RunPulse SOxygen SRunTime SRunPulse
1 1 47.0120 10.4441 171.216 0.95984 0.28520 1.59910
2 2 47.2407 10.5040 171.244 0.93540 0.26661 1.75638
3 3 47.4995 10.5922 171.909 1.00766 0.26302 1.85795
4 4 47.1485 10.5279 171.146 0.95439 0.26405 1.75011
5 5 47.0042 10.4913 172.072 0.96528 0.27275 1.84807
6 6 47.2949 10.6135 169.969 0.95669 0.24533 2.06949
7 7 46.9617 10.5080 171.701 0.93181 0.27111 2.28368
8 8 46.9729 10.5222 170.622 0.94561 0.25687 1.69879
9 9 46.9864 10.5545 171.356 0.93664 0.26233 1.71076
10 10 46.9587 10.5518 171.197 0.94270 0.25214 1.89054

The following statements combine the means and standard errors from imputed data sets, The EDF= option requests that the adjusted degrees of freedom be used in the analysis. For sample means based on 31 observations, the complete-data error degrees of freedom is 30.

```proc mianalyze data=outuni edf=30;
modeleffects Oxygen RunTime RunPulse;
stderr SOxygen SRunTime SRunPulse;
run;
```

The "Model Information" table in Output 76.1.2 lists the input data set(s) and the number of imputations.

Output 76.1.2: Model Information

The MIANALYZE Procedure

Model Information
Data Set WORK.OUTUNI
Number of Imputations 25

The "Variance Information" table in Output 76.1.3 displays the between-imputation variance, within-imputation variance, and total variance for each univariate inference. It also displays the degrees of freedom for the total variance. The relative increase in variance due to missing values, the fraction of missing information, and the relative efficiency for each imputed variable are also displayed. A detailed description of these statistics is provided in the section Combining Inferences from Imputed Data Sets and the section Multiple Imputation Efficiency.

Output 76.1.3: Variance Information

Variance Information (25 Imputations)
Parameter Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Oxygen 0.026098 0.925531 0.952673 27.354 0.029325 0.028556 0.998859
RunTime 0.002938 0.068197 0.071253 26.918 0.044810 0.043035 0.998282
RunPulse 0.598494 3.345356 3.967790 23.196 0.186059 0.158595 0.993696

The "Parameter Estimates" table in Output 76.1.4 displays the estimated mean and corresponding standard error for each variable. The table also displays a 95% confidence interval for the mean and a t statistic with the associated p-value for testing the hypothesis that the mean is equal to the value specified. You can use the THETA0= option to specify the value for the null hypothesis, which is zero by default. The table also displays the minimum and maximum parameter estimates from the imputed data sets.

Output 76.1.4: Parameter Estimates

Parameter Estimates (25 Imputations)
Parameter Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Oxygen 47.084579 0.976050 45.0831 49.0861 27.354 46.850020 47.499541 0 48.24 <.0001
RunTime 10.549499 0.266933 10.0017 11.0973 26.918 10.428848 10.680797 0 39.52 <.0001
RunPulse 171.388418 1.991931 167.2697 175.5071 23.196 169.881385 173.125658 0 86.04 <.0001

Note that the results in this example could also have been obtained with the MI procedure.