title: Analysis of sparse data in logistic regression in medical research: A newer approach.
abstract: OBJECTIVE
  In the analysis of dichotomous type response variable, logistic regression is usually used. However, the performance of logistic regression in the presence of sparse data is questionable. In such a situation, a common problem is the presence of high odds ratios (ORs) with very wide 95% confidence interval (CI) (OR: >999.999, 95% CI: <0.001, >999.999). In this paper, we addressed this issue by using penalized logistic regression (PLR) method.
  
  
  METHODS
  Data from case-control study on hyponatremia and hiccups conducted in Christian Medical College, Vellore, Tamil Nadu, India was used. The outcome variable was the presence/absence of hiccups and the main exposure variable was the status of hyponatremia. Simulation dataset was created with different sample sizes and with a different number of covariates.
  
  
  RESULTS
  A total of 23 cases and 50 controls were used for the analysis of ordinary and PLR methods. The main exposure variable hyponatremia was present in nine (39.13%) of the cases and in four (8.0%) of the controls. Of the 23 hiccup cases, all were males and among the controls, 46 (92.0%) were males. Thus, the complete separation between gender and the disease group led into an infinite OR with 95% CI (OR: >999.999, 95% CI: <0.001, >999.999) whereas there was a finite and consistent regression coefficient for gender (OR: 5.35; 95% CI: 0.42, 816.48) using PLR. After adjusting for all the confounding variables, hyponatremia entailed 7.9 (95% CI: 2.06, 38.86) times higher risk for the development of hiccups as was found using PLR whereas there was an overestimation of risk OR: 10.76 (95% CI: 2.17, 53.41) using the conventional method. Simulation experiment shows that the estimated coverage probability of this method is near the nominal level of 95% even for small sample sizes and for a large number of covariates.
  
  
  CONCLUSIONS
  PLR is almost equal to the ordinary logistic regression when the sample size is large and is superior in small cell values.
authors.forename: S
authors.initials: S
authors.lastname: Devika
authors.affiliation: Department of Biostatistics, Christian Medical College, Vellore, Tamil Nadu, India.
authors.forename: L
authors.initials: L
authors.lastname: Jeyaseelan
authors.forename: G
authors.initials: G
authors.lastname: Sebastian
mesh_terms: D035843:Biomedical Research; D003198:Computer Simulation; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006606:Hiccup / Q000209:etiology*; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D018401:Sample Size