Dear All,
I am working on a data having cost of care as DV. This is a genuinely skewed data reflecting the socioeconomic gap and therefore healthcare financing gap among population of a developing country. Because of this skewness, my data violated normality assumption and therefore was reported using median and IQR. But I will like to analyze predictors of cost of care among these patients.
I need to know if I can go ahead and use MLR or are there alternatives?
The sample size is 1,320 and I am thinking of applying Central Limit theory.
Thanking you for your anticipated answers.
Dimeji
Oladimeji -
Yes, you can do this to estimate totals, but you likely need to categorize and estimate separately for your different population groupings. The following paper appears to be relevant. However, it also incorporates an approximation for the variance that was made to incorporate some flexibilities you may not need, and also ways to do small area estimation. If looking at something less complex, you can just let the estimation groups (EGs) I have there, and publication groups (PGs) be the same.
https://www.researchgate.net/publication/261586154_Using_Prediction-Oriented_Software_for_Survey_Estimation
Remember that though you do not want omitted variable bias, you don't want to throw in irrelevant variables either.
My papers were written with concern for estimating totals. But you could use this for exploration also. It might help you to decide on different regressors to use for different categories/groups. If you hold some data out separately for testing, you could look into validating models.
I am writing a paper to tie various papers together, but in the meantime, you might find other papers on my ResearchGate page helpful.
I am not so familiar with your application as the official statistics for which I was employing these methods, but you may find enough difference between the larger and smaller cases that you need to stratify or group data by size. However, other categories may already group data well enough. Random sampling can help avoid bias - though balanced sampling would do better - but if you have small categories, cutoff sampling, or quasi-cutoff compromises between questions as described in the following may help tremendously with efficiency.
https://www.researchgate.net/publication/261472614_Efficacy_of_Quasi-Cutoff_Sampling_and_Model-Based_Estimation_For_Establishment_Surveys_and_Related_Considerations
To get an idea of sample size needs for a given EG, you could use the following:
https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
There, an estimator for y (linear combination of regressors perhaps) could be used in place of the single regressor, x, as a size measure.
The central limit theorem applies to the estimated residuals, or more generally, the estimated random factors of the estimated residuals for weighted least squares regression. However, skewness of the y-values or regressors is not an issue.
Your goals may differ from what occurred to me, but if you are looking at cost for different categories, and regressors relevant to each, then I think you can group these data, if by size if nothing else, and apply multiple regression to each group.
The following paper found excellent results from grouping by size for financial data by authors who did not think that was going to be the case when they first started investigating, but were pleasantly surprised:
Karmel, T.S., and Jain, M. (1987), "Comparison of Purposive and Random Sampling Schemes for Estimating Capital Expenditure," Journal of the American Statistical
Association, Vol.82, pages 52-57.
You can still use random sampling, but I suggest categorizing your data first and sampling from within each group. Sampling with probability proportionate to size (PPS sampling) might be useful.
It occurs to me that you might have a set of y and corresponding data from regressors, with no way to know the population, and not estimating total costs, but only want to see how each regressor or set of regressors seem to impact cost for various groups/categories, perhaps just socioeconomically determined. That still means categorizing. Some might suggest dummy variables.
But if you are concerned about skewness, don't worry. That is not a problem. It will, however, mean that mean values will of course not be as easily interpretable, but that is unavoidable. You might even want to look at medians also.
Best wishes - Jim
PS - Oh, you did say you "...reported using median and IQR." That was not a bad idea. But I think you want to subdivide your population into categories for further investigation.
Article Efficacy of Quasi-Cutoff Sampling and Model-Based Estimation...
Article Using Prediction-Oriented Software for Survey Estimation
Conference Paper Projected Variance for the Model-based Classical Ratio Estim...
Thank you so much James. This is really detailed and it helps me alot!
I will take time to look at the resources you gave.
Hi Oladimeji,
This paper is a nice review of statistical methods to deal with skewness and other issues related to cost data.
Best, Bryce
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3470917/
a new proposal for skewness
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
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