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I've just done a multivariate regression analysis, using a p-value from bivariate regression analyses of <0.20 as a cut-off to determine which variables will be included in the multivariate model.

I have a total sample of 628 patients, and the crosstabs shows just right. The bivariate regression analyses also seems normal. However, when I try to converge all the eligible variables, the output seems to unrealistic

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Here are some additional information on the model:

enter image description here

While it seems that most of the cases were excluded in the analysis, I think this is not the case... The other analyses I performed also showed that a considerable number of observations were observed, but the models still converged well and aligns with the cross-tabulations.

enter image description here

^These are the summary of the model.

I also tried changing the method from ENTER to FORWARD: LR, but the model failed to converge. enter image description here

Does anyone know what problems may cause the above phenomenon? I have previously tried performing multivariate regression analyses with less sample sizes and more variables, but they all went well. This is the first time I've encountered such a problem.

Thank you very much in advance.

amedicalenthusiast
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    What is your sample size? You should not use stepwise methods ... see [Algorithms for automatic model selection](https://stats.stackexchange.com/questions/20836/algorithms-for-automatic-model-selection). You probably have separation in the data see https://stats.stackexchange.com/questions/11109/how-to-deal-with-perfect-separation-in-logistic-regression and search this site – kjetil b halvorsen Sep 15 '21 at 02:37
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    Selecting variables on the basis of p-values is invalid, and especially ruins confidence intervals of remaining variables. – Frank Harrell Sep 15 '21 at 02:37
  • @kjetilbhalvorsen The total sample size is 628.. However, I presume that if case-wise (deletes a case if at least one variable is missing) deletion instead of list-wise deletion (omits the missing variable instead of omitting the case), only 104 observations were left for analysis – amedicalenthusiast Sep 15 '21 at 13:45

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I don't mean to dog pile, but you really should not be doing stepwise regression. I won't include reasons why, kjetil has already listed some and you can search for key terms on this site if needed (or just google "Stepwise Regression" and "Frank Harrell" who has already commented here for the definitive list of reasons why not to use stepwise). Additionally, high standard errors likely mean there is some sort of separation in your data (which is unsurprising given how many variables there are and how few observations).

As to your point about about missing data,if SAS (or whatever it is you're using ) says only 104 osbervations were included then it probably isn't lying and you're probably wrong on this. Let's see why this might be the case.

Consider a dataset with only 3 rows and 3 columns (ignoring the outcome). Along the diagonal are missing data (so column 1 row 1 is missing, column 2 row 2 is missing, and so on). Were you to fit a univariable model as you do then you would only drop one row because in each column only one row is missing.

But, when you go to fit the full model, you drop every row in the data, because case wise deletion means we drop the row if it has any missing data. I can't say for certain that this is happening in your data, but if you don't drop many observations when you fit univariable models but you drop near all of it when you fit the full model then I highly suspect this is the reason.

Demetri Pananos
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  • I see.. Thank you very much for your explanation.. Can we use listwise deletion in multivariate regressions? Or is the option confined only to casewise deletion? Also, thanks for your insights on the model selection! – amedicalenthusiast Sep 15 '21 at 02:56
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    @amedicalenthusiast I'm not sure what listwise deletion is, but I would highly recommend you not drop any data. Dropping data can bias results of the regression because there may be a reason the data are missing, and excluding those observations means your sample is systematically different in some appreciable way. Have you looked into imputation methods? – Demetri Pananos Sep 15 '21 at 03:18
  • @amedicalenthusiast Listwise deletion, casewise deletion, and complete case analysis are identical in practice. Observations (cases) with a missing value for any variable in the analysis are deleted. Identically, but stated a different way, the analysis is based on observations (cases) with no missing values for any variable in the analysis. – Diana Petitti Sep 15 '21 at 19:28
  • @medicalenthusiast With stepwise regression (using "usual" software-defined defaults for missing data), observations (cases) with missing values on ANY of the variables used in the "model" will be deleted. That is because the stepwise analysis "needs" to look at every variable in order to "do its work." The subset of observations (cases) in your analytic dataset (remaining observations AKA cases after deletions) comprised of only 104 of 628 observations (cases). This makes the problem of missing data in stepwise regression even worse than it can be for "regular" regression. – Diana Petitti Sep 16 '21 at 00:03