The Proportionate Mortality Ratio Small Sample Bias

INTRODUCTION:  The proportionate mortality ratio (PMR) is the proportion of observed deaths from a given cause in a study population divided by the proportion of deaths expected from this cause in a standard population. A study population of the PMR analysis is regarded as small when the number of deceased cases is small in relation to the number of causes of death that all deaths are being categorized into.  In this situation, small numbers of cases are likely distributed in a subset of disease categories, leaving other disease categories with no observed cases. 

METHODS:  Bias arising from a subset of disease categories with zero observed case in PMR analysis of a small study population is identified and quantified using simple algebra.  Simulations that assigned cases randomly into individual disease categories, according to expected disease proportions, allowed an estimation of mean biases and their 95% confidence intervals by the number of cases.

RESULTS:  PMRs are biased and overestimated in small population studies; the smaller the number of cases and the greater the number of disease categories, the larger the overestimates of PMRs. Correction for the bias (larger than 3% overestimate of a PMR) is recommended for small study populations in which the ratio of the number of cases to the number of disease categories is less than 5.

CONCLUSIONS: The PMR small sample bias (which has not been discussed in the literature) is identified and the bias correction methodology is developed. The relationship between the bias and the number of cases is determined by the number of disease categories and the expected disease proportions.