Identification of risk factors for hospital admission using multiple-failure survival models: a toolkit for researchers

The UK population is ageing; improved understanding of risk factors for hospital admission is required. Linkage of the Hertfordshire Cohort Study (HCS) with Hospital Episode Statistics (HES) data has created a multiple-failure survival dataset detailing the characteristics of 2,997 individuals at baseline (1998–2004, average age 66 years) and their hospital admissions (regarded as ‘failure events’) over a 10 year follow-up. Analysis of risk factors using logistic regression or time to first event Cox modelling wastes information as an individual’s admissions after their first are disregarded. Sophisticated analysis techniques are established to examine risk factors for admission in such datasets but are not commonly implemented.

We review analysis techniques for multiple-failure survival datasets (logistic regression; time to first event Cox modelling; and the Andersen and Gill [AG] and Prentice, Williams and Peterson Total Time [PWP-TT] multiple-failure models), outline their implementation in Stata, and compare their results in an analysis of housing tenure (a marker of socioeconomic position) as a risk factor for different types of hospital admission (any; emergency; elective; >7 days). The AG and PWP-TT models include full admissions histories in the analysis of risk factors for admission and account for within-subject correlation of failure times. The PWP-TT model is also stratified on the number of previous failure events, allowing an individual’s baseline risk of admission to increase with their number of previous admissions.

All models yielded broadly similar results: not owner-occupying one’s home was associated with increased risk of hospital admission. Estimated effect sizes were smaller from the PWP-TT model in comparison with other models owing to it having accounted for an increase in risk of admission with number of previous admissions. For example, hazard ratios [HR] from time to first event Cox models were 1.67(95 % CI: 1.36,2.04) and 1.63(95 % CI:1.36,1.95) for not owner-occupying one’s home in relation to risk of emergency admission or death among women and men respectively; corresponding HRs from the PWP-TT model were 1.34(95 % CI:1.15,1.56) for women and 1.23(95 % CI:1.07,1.41) for men.

The PWP-TT model may be implemented using routine statistical software and is recommended for the analysis of multiple-failure survival datasets which detail repeated hospital admissions among older people.