Balance Diagnostics by SMD after Matching

[Atika Jabeen]

I have a matched case control data, in which there is one continuous variable, and several categorical variables.
A combination of matching was used. Some variables were matched exactly on the covariates (like sex and nationality), for age 10-year age groups were matched. Cases and controls were matched on death date in the same calendar month.

I would like to assess the balance of the covariates before and after matching.
I have come across the following commands. I did not come across a consolidated review, and therefore in the scattered literature and help files that I found, I understood the following. I would like to know please if my understanding is correct (please correct me where I am wrong) and I also have some queries in general and regarding the different commands.

1. Is the Standardised difference and the Standardised Mean Difference (SMD) the same. Are these words used synonymously in the literature?

1. STDDIFF:

• This command is useful for both continuous and categorical variables.
• For specification of categorical variable, we have to put “i.var” to specify an indicator variable.
• The command provides an overall Standardised Difference, not the standardised difference of the different categories.)
• The command does not have the option to incorporate weights.
• When comparing the stddiff command with the next 2 commands, I note that stddiff gives me the absolute values by default even though I have not specified “abs”, so I cannot determine the direction of the difference.

Questions:
A: Is there a way to determine the direction using the stddiff command?
B: Can this command be used to check balance after any type of matching (exact matching, combination of matching techniques or is it only/especially used for propensity score matching?)

1. COVBAL

• Weights can be incorporated. (This had prompted me to shift from the stddiff command.)
• In addition to SMD, it also assesses the balance by providing variance ratios.
• The direction of the difference is provided by default, and should I need I can specify absolute values in options.

Question:
A: Can I use this command for both continuous and categorical variables? It is not specifically mentioned in the stata ‘help covbal’ file. I do get an output. But can I use this output?

1. PBALCHK

• Weights can be incorporated.
• The direction of the difference is provided by default.
• For categorical variables, if “xi:pbalchk treatvar i.catvar” is used, it provides the SMD for each category, but not the overall SMD. If this is not specified, I get one value for the SMD.

Questions:
A: How do I use this command to get overall SMD for categorical variables, since I am interested in an overall value for SMD, not of the individual categories.
B: Can this command be used to check balance after any type of matching (exact matching, combination of matching techniques or is it only/especially used for propensity score matching?)

1. When I compare the three commands mentioned above, for some of my variables, the result is the same in all 3 commands, but for other matched variables, the result I am getting in stddiff is different from that of covbal and pbalchk. Covbal and pbalchk are giving me the same result (slight difference in the third or fourth decimal places in some instances) It makes me wonder if I am using the command correctly or if there are any underlying differences in the theory of these commands, or how they are calculating SMDs that I am unaware of.

Any advice, help, guidance to relevant resources is appreciated.