Analysis of sparse data in logistic regression in medical research: A newer approach

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.

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.

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.

PLR is almost equal to the ordinary logistic regression when the sample size is large and is superior in small cell values.