# How to handle data with 2 variables that have same missingness pattern?

I've not had much academic coursework on imputation, and I can't find anything online or in any texts regarding how one could handle missing data where there are two (or more, possibly?) variables with the same missingness pattern.

For example, suppose that the data set I'm looking at has two blood pressure variables which takes in systolic and diastolic readings as two separate variables, but if a blood pressure reading wasn't taken for whatever reason (patient refusal, patient only in to speak with a doctor, staff forgot to take blood pressure, etc.) it would be regarded as missing.

Furthermore, suppose that as a researcher, you were asked to analyze this data. The standard approach, from what I recall from school and my research, is to perform multiple imputation, but that would generally be best on independent variables that have differing missingness patterns. If you did run a multiple imputation command on the data set (like mice/mi in R, or proc mi/mianalyze in SAS) to impute those missing blood pressure values, what effect would that have on the estimates? Are there any approaches to handling this missing data that would be better? I know listwise or pairwise deletion are some other options, but those are better for when the missing data is a small portion of the whole data set, right?; I'm curious on a more general level... suppose that nearly 40% of the blood pressure values were missing, or something that would make you feel as if list- or pairwise deletion would be inappropriate for forming accurate estimates.

I don't have a data set in mind or at hand, so I'm generate a set to help illustrate the issue I'm explaining:

ID    Age    Gender    Systolic    Diastolic
1     45      M (1)      125          76
2     33      F (0)      101          67
3     27      M (1)      NA           NA
4     51      M (1)      120          79
5     38      F (0)      119          77
6     64      M (1)      NA           NA
7     48      F (0)      NA           NA
8     83      F (0)      130          81
9     27      M (1)      99           66
10    55      F (1)      NA           NA
.      .      .           .           .
.      .      .           .           .
.      .      .           .           .

• Probably you are lucky the missing values are on the same observations: you then keep more complete observations. However, this might hide a systematic error. Patients without measurement might be patients that feel too well to wait for yet another doctor, or nurse to do the measurements, or they might be transferred to emergency. Jul 22, 2015 at 21:16
• I was looking more for how one might analyze this data and/or any errors that might crop up in estimates from analyzing this data via multiple imputation. Jul 27, 2015 at 12:33

## 1 Answer

The main concern I would have is the question of whether the missing values are random or systematic. Any means of dealing with missing values (e.g. pairwise deletion, listwise deletion, mean imputation) is based on the assumption that there is no systematic difference between the cases with missing values and the cases with complete data. If this assumption is not valid, then it doesn't matter what you do to "deal" with missing values--you will get biased results.

The scenario you described certainly sounds like there might be systematic bias. As one comment mentioned, it is quite possible that patients without blood pressure measurements feel more healthy than those with the measurements--if someone feels really sick, then none of the example reasons you gave ("patient refusal, patient only in to speak with a doctor, staff forgot to take blood pressure, etc.") would apply. These are all more likely to occur with patients that aren't as sick as others where none of those scenarios might be the case.

To be safe, I think you would need to test the assumption by doing a t-test on the complete-data vs. partial-data groups. Such a test should be conducted on variables that might reveal the suspected differences. In the sample data you gave, I don't think age or gender would reveal a sicker vs. less sick group. However, if you had, for example, temperature readings for the patients, then that might possibly be a good variable to test the assumption on. (I'm assuming that both temperature and blood pressure readings are correlated with illness; you can test this by verifying if there is a correlation between temperature and blood pressure readings for the data that is available.) If there is no significant difference in temperature readings between patients with vs. without blood pressure readings, then you might be somewhat justified in assuming that there is no systematic bias. However, without the data to make such a test, I would think that in your example is is more likely than not that the bias is systematic, and thus no missing value resolution could possibly be valid.