LogXact Example from Actual Practice

Data with Missing Categorical Covariates: Logistic Regression Model(1) in air pollution study

The dataset is from a longitudinal study of the health effects of air pollution. The binary response is the wheezing status of the mother and the city of residence. We included two more binary covariates indicating the socioeconomic status and the previous medical condition of the child. We consider a subset of the data consisting 2106 subjects at baseline, where the baseline wheezing status is non-missing.

Six Cities Data ( partially shown)	Missing Patterns

In the above results, the complete case analysis (omitting all the missing observations), shows that:

• the covariate “smoke” is not a significant factor (p=0.2788).
• there is no significant interaction between covariates “smoke” and “soc” (p=0.0584)

However, the result from LogXact 7 with Cytel Studio shows:

• the covariate “smoke” is significant at 90% confidence level (p=0.087).
• the interaction between variables “smoke” and “soc” is significant (p=0.0494).

For imputing binary covariate, we used “Logistic” option in PROC MI. The “Logistic” option requires monotonic missing pattern in the data. In our data, the missing pattern is non-monotone. We have used a commonly used sequential imputation method. Notice that the covariates “soc” and “cond” are always missing together. So, we could impute “cond” and “soc” together. We have used two different sequences. In both the sequences, the output from SAS shows that the interaction term “smoke*soc” is highly non-significant. In Output-1 from SAS, the covariate “smoke” is significant, but it is not significant in Output-2. The covariate “city” is not significant at the 99% confidence level. However, it is significant in complete case analysis as well as in missing data analysis of LogXact 7 with Cytel Studio.

References:

Ibrahim, JG (1990), “Incomplete Data in Generalized Linear Models”, JASA, 85, 765-769.

Lipsitz, SR and Ibrahim, JG (1996a), ``A Conditional Model For Incomplete Covariates in Parametric Regression Models”, Biometrika, 83, 916-922.