As Barros and Hirakata (2003) suggested in their article, Poisson regression and Cox regression with robust variance gave the best estimate of RR in a cross-sectional study design. When using logistic regression, especially when the outcome is not rare, the estimated OR will overestimate the association. Wilber and Fu (2010) also illustrated this point in their paper.
However, I still have several remaining questions that confused me:
a) If logistic regression almost always overestimate the association and Poisson regression can be used instead in a cross-sectional study, in what situation a logistic regression should be preferred?
b) What if we have a case-control, will this conclusion be different?
c) Are there other reasons in addition to convenience for the majority of the cross-sectional study and case-control study to use logistic regression.
Thank you ahead for your attention and help. :)
Reference:
1. Barros, Aluísio JD, and Vânia N. Hirakata. "Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio." BMC medical research methodology 3.1 (2003): 21.
2. Wilber, Scott T., and Rongwei Fu. "Risk Ratios and Odds Ratios for Common Events in Cross‐sectional and Cohort Studies." Academic Emergency Medicine 17.6 (2010): 649-651.
When you say 'When using logistic regression, especially when the outcome is not rare, the estimated OR will overestimate the association' are you referring to the fact that the odds ratio is greater than the relative risk, and that this difference becomes more marked as outcome prevalence increases? If so, then the explanation is simple : RR and OR are not the same thing. Granted the RR is easier to explain and understand, but it is also far harder to model. An RR of 2, for example, where baseline risk is 60% gives an expected risk of 120%!
Thank you for your explanation, Dr. Conroy. I do agree with you and the reference that RR is preferred when you can calculate them (especially for the reasons you mentioned). However, I am still confused why there are so many cross-sectional studies that used logistic regression instead. Do you have any insight on this? :)
Logistic regression is widely used because it a) cannot give 'impossible' predicted values (because it maps the interval 0-1 onto the interval minus-to-plus infinity), b) outperforms other binary regression models, including many machine learning ones, in terms of generalisability and c) everyone has it on their computer.
Working with proportions rather than ratios is hard, and the models often fail to converge. I get about 60% of them to converge, but I have a colleague who claims that less than 10% of his converge.
Risk ratios do not generalise well to different prevalence settings, while odds ratios do.
Dr. Conroy, thank you so much for your answer. It really helped solved questions confused me for a long time. Try to summarize, in a real world study, we should consider couple things before we choose between logistic and Poisson regression:
1. What's our study design (if c-c study, then logistic regression)
2. What's our research question and what's the population that we want to generalize
(OR are more generalizable if our sample population have different prevalence than the target population)
3. Whether the model converge
Does this sound right to you?
a) If logistic regression almost always overestimate the association and Poisson regression can be used instead in a cross-sectional study, in what situation a logistic regression should be preferred?
AN: Can be used when the disease (outcome) is rare, or when controls in a case control study are sampled with incidence density sampling.
b) What if we have a case-control, will this conclusion be different?
AN: Can be used when the disease (outcome) is rare, or when controls in a case control study are sampled with incidence density sampling.
c) Are there other reasons in addition to convenience for the majority of the cross-sectional study and case-control study to use logistic regression.
AN: Logistic regression is often appropriate in a case-control study. The over-estimation potential of the OR is not well recognized out side of epidemiology nor is the use of Poisson or Negative Binomial regression to estimate RR well known yet.
See this paper for another take on use of OR vs RR https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3446823/
These questions have been prowling my thoughts in the last years. Thanks all for questions and for answers!
After reading above questions and responses, I understood that we can use Poisson for a cross-sectional study. My concern is that I am using National Health Interview Survey data set and my outcome variable is in a range of 0-24. Would it be better to use Poisson or Logistic regression? For logistic regression, I will make a dependent variable with binary outcomes. Does it make sense?
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