# sample size and covariates connection

Currently I am applying negative binomial regression. My total sample size is 669 as this is a follow up data. Count variable (dependent variable) is mental health visits, primary independent variable bullying victimization 0=No, and 1= yes, other are covariates which I need to adjust. 609 participants has 0 frequency of mental health visits and the remaining has various frequencies of visits ranging from 1-31. I have total 17 confounders/covariates including these two independent and dependent variables, to adjust in the model (like the final model adjusted for all the covariates). So my question is can we build such kind of model? One as crude IRR with only dependent and independent variable. Do you think that is sample size is too low for adjusting 17 covariates in a model? Is there any rule of thumb or guidelines that this sample size is needed for this many covariates?

• so just to be clarify: theree are 669 data in total, but only 60 with a nonzero count? Jul 25, 2023 at 12:36
• Yes I guess 60 has no zero count. It starts from 1. Jul 26, 2023 at 9:13

In general, no there is not a rule of thumb about number of covariates you can adjust in a model like this one. "One in ten" has been discussed a lot (one variable per 10 records), but this is not an omnibus. There are well balanced situations when you can well powered inference having fewer than 10 records per variable. The power of an analysis doesn't solely depend on the actual distribution of the response, but on the joint distribution of the covariates and the response. This is what we can refer to as a "design" or quasi-experimental design - even in an observational study such as this.

To know the precise impact of a particular design, you need to perform a power calculation - note this is not a post-hoc power calculation. You can use assumptions about the distribution of response and the effect related to the covariates in the model. Note, most power calculators are woefully unprepared for non-randomized designs, so we often obtain the result through simulation to show the impact of covariates.

In my experience, it takes days of ardent collaboration with subject matter experts and literature review to identify even one covariate for inclusion into a model as a confounder. In addition to providing a rationale that it's causally a confounder, you require estimates of the weight of association with the predictor and the outcome of interest, and (most importantly) its relation to other covariates. Therefore I'm surprised to see a number as large as 17 "confounders/covariates". (Further note: if any of these are categorical, you may consider each category its own confounder - minus 1).

Perhaps here the analyst has missed an opportunity to provide guidance when selecting the possible confounders for adjustment. During this time, an analyst typically draws a DAG (directed acyclic graph) showing causal links between the possible values. A prudent analyst can quickly identify "mediators" that are conflated with confounders, and exclude them straightaway. Most often a group of confounders lie on the same causal path and therefore its only necessary to satisfy the "backdoor criterion" reducing the dimension but expressing its impact in a statistically better behaved construct; what I mean by this is to just adjust for one or two variables. As an example, "socio-economic status" is not a well-defined term, but we often measure direct consequences of this construct, highest education achieved, employment status, annual household income, etc. Adjusting for typical categories for each of these may alone be 12 effects or more! But perhaps there's alignment with SMEs that annual household income is the most pertinent and useful value for a particular analysis.

So in short - your intuition is correct - you probably shouldn't adjust for 17 covariates with only 60 observations taking a non-zero value in a negative binomial model. Even if you could, all the advice above still applies. In two parts:

• Use simulation to understand the power of your design before setting out to complete any analysis.
• Identify confounders for adjustment using a sound and rigorous technique that strikes the balance of addressing the science of the problem, and of being adequate for the particular dataset.
• Thank you so much for the detailed information. As you have mentioned about the sound and rigorous technique for selecting covariates, I wanted to apply step forward or backward method as we do in logistic regression analysis in Spss. So that we can select the highly relevant covariates. However I did not find such option here in negative binomial regression. Do you have any suggestions on which technique to apply for suitable covariates selection? That would be a great help. Thank you in advance. Jul 26, 2023 at 9:11
• @ManishaHamal I do not suggest backward covariate selection at all in your case. Jul 26, 2023 at 12:56