Health insurance claims distributions Robert Cole NZ Society of Actuaries conference Nov 2010

Disclaimer Thanks to my former employer for making the data available for this analysis All opinions, errors & omissions are my own

Exec summary – why claims distributions are important Proportion of nil-claimers Member behaviour and value perceptions Low claims rewards Claim size distribution Member anti-selection Product design (maximums, excesses, etc) Pricing (rate cards, rating factors, large corporate schemes) Multi-year correlations in claiming A very significant component of claims costs

Exec summary – key findings Significance of high-claiming members 80/20 (or 80/8) - in any year >80% of total claims $ from 20% of claiming (about 8% of all) members Total costs over large $ thresholds (eg $10k) growing faster than average Material differences by factor Age, gender, plan type Multi-year correlations in claiming High-claiming members tend to remain high- claiming for long periods of time, and vice versa

Analysis method Total amount of claims paid summed up for every member by financial year from 03/04 to 09/10 Can be zero or $ amount (up to about $110,000) Member attributes at mid year (ie 31 December) Age, gender, plan type, excess, individual or group, subsidy

20% claiming members (8% all) = 80% claims $, share of $ from high-claimers is growing

Claim $ paid for members claiming large $ a year is growing faster than overall (>$0)

Lower proportions of nil-claimers old ages, female, comprehensive plans

Older ages have more members with large annual claims than at younger ages

More high-claiming males

Higher proportions of females claiming up to about $15,000 in a year

Claim difference is smaller than excess amount for major medical excess plans …

… and also for comprehensive excess plan

Serial correlations High-claiming members in a period are more likely to be high-claiming members in next period Low (or nil)-claiming members in a period are more likely to be low (or nil)-claiming members in next period holds if period is 1-year, 2-years or 3-years holds if consecutive periods are overlapping or non- overlapping Relevant for low claims reward design proportions of members gaining or losing reward proportions qualifying

1-year claims conditional on prior 1-year eg $0 given $0 =1.3 times as likely, $30+k given $30+k = 18.5 times

1-year claims conditional on prior 2-years bigger effect than prior 1-year

1-year claims conditional on prior 3-years bigger effect still

Any questions?