Modeling and Forecasting Morbidity and Disease-mortality of Chinese Impaired Lives with the General Chronic Diseases

1.1 Chinese general chronic diseases

Recently, more and more Chinese people pay attention to their health problems. Some reports have showed that the increased work pressure and busy life style have affect health. Maybe there are some arguments, but the hope away from diseases is universal for any people.

Taking general chronic diseases as an example, the statistical results remind us of more instructive information. That is the growing morbidity rate of the general chronic disease. Just from the newspaper, the number of potential diabetes is about 150 million and the number in treating course is 92 million now (male 50 million and female 42 million), morbidity rate is 9.7%, but the number was 78 million about ten years ago. The total population growing rate can’t explain it.

In medical field, the general chronic diseases include the mental disease, the cardiovascnlar and cerebrovascular diseases, chronic cancer, chronic respiratory disease and diabetes. Some statistical materials also gave that a large amount of Chinese people is tortured by the general chronic diseases. The following gives some surveys both in the disease view and in the time view.

1.2 Insurance products market

This is a huge market for the life insurance which has been ignored in the last 20 years. Furthermore, considering all the impaired lives with different chronic diseases, the number is about 300 million which is almost the population size of US. So it is a huge insurance market for insurance company and it is an important group for the government[2].

In Chinese insurance market, both the life insurance products and health insurance products are for the normal people without uncovered diseases although a few of impaired lives can be covered by increasing premium[3]. The increasing premium is not the actuarial results but the result of normal premium multiplying by a coefficient. It is not responsible for both insurers and policy holders. Even that, there are many impaired lives who can’t be accepted by the insurance companies. So how do they transfer the mortality risk or can they get some compensation when they died? It is reasonable just as the normal people do. And we also observed that the similar insurance demand is much stronger than the normal lives. The reason is direct that they face the greater risk[4−5].

For getting a persuasive result, we make a simple survey through a cooperated medical hospital. The samples are all patients with diabetes and the number is 532. A survey questionnaire with 10 questions was made. All the questions are about demand and advices of insurance products for impaired lives.

We choose a typical life insurance product which can be found in many insurance companies. The coverage is 400 thousands. When an investigation began, we introduce the simple life insurance knowledge without any inducing information. After that, we will take their patience to finish the form. Several questions is related with demands, such as the followings: Do you need the introduced life insurance products? If the premium is more than the normal premium, 1.3 times of normal premium, can you accept it? If the premium is 1.5 times of normal premium, can you accept it? Could you tell us what is the most reason to push you make this decision?

At last, we obtained 508 effective results after simple statistical calculation and it included 370 male samples and 238 samples. Table 2 gave a simple survey result of this investigation. It is obvious that the insurance demand of impaired lives is more than that of normal lives.

Always some people hesitate to the cost of impaired insurance products introduction. In fact, most insurance companies have accumulated much of experience of normal products. The pricing technique, the commission management and sale channel can be used in this new business. So it is a good market chance for the insurance companies.

1.3 Longevity views

Longevity risk become a general risk for any country in the world. Of course, we can observe the downwards mortality of Chinese people although the longevity data set has many problems like missing data, outliers and so on. But for a huge amount of population, it is necessary to consider different groups, like people in city or people in the rural area. Does the longevity risk exist in these subdivided group?

And the people with chronic diseases is first to consider since its large number and strong insurance demands. When the insurance markets have accepted the group, the longevity risk will come to the managers. Another fact also remind us of the impact of longevity that the intrinsic risk is more than the normal group. For insurance companies, maybe the longevity risk can be applied to hedging the other risk. Just like what we said, the risk is chance. Always, longevity risk means the risk with time. In other words, how much is the impact of time on the mortality. From the total population, the impact on the birth can’t be ignored. Both the birth rate and the mortality will bring the influence on the population. For the group with chronic diseases, the birth means morbidity whose result tell us how many normal people have enter the impaired group. So the longevity risk of impaired lives includes the analysis on the morbidity.

The article includes four parts: the first part is the data mining and to calculate the morbidity and normal mortality; the second part is to model and forecast the morbidity; the third part is to calculate the disease-mortality, and to model and forecast disease-mortality; the fourth part used the results to price the life insurance products for the impaired lives.

2.1 Calculating morbidity

Our work started from the underwriting data base since it is the most actual information of policyholders. But there is no statistical data of mortality statistics of impaired lives, we calculated the mortality of impaired lives according to the collected policy data of critical illness insurance and relevant data from Ministry of Health of China.

We collected policy data from a life insurance company, and selected out policy data of critical illness insurance from 1999 to 2011, 13 years totally. We used actuarial moment estimation to calculate morbidity. Morbidity of a kind of critical illness was equal to the ratio of total number of claims of the critical illness insurance to total actuarial exposures of the critical illness insurance insured. For the critical illness insurance insured, in unit time (one year), if the policies are effective, over or withdrawn, their actuarial exposures are their real exposures, and if the claims are over in the year, the actuarial exposure is one year.

The procedure of calculating morbidity is showed below.

The first step, we needed to build a underwriting-claim database of critical illness insurance from the life insurance company’s policy data. First selected out the items that were needed in morbidity calculation from policy underwriting data such as insurance type, underwriting date, age, rider, birthday and policy claim data such as insurance type, claim date, claim type, claim reason, rider, settle type to build a underwriting database and a claim database separately. After that, we selected out critical illness insurance policies both from the underwriting database and claim database got above. Then joined the underwriting database and claim database of critical illness insurance together, and added items which were needed to calculate morbidity, such as exit date, exit reason, policy year, policy date, number of claims, exposures and so on.

The second step, for one year between 1999 and 2011, divided the year into two periods by the policy date where supposed that the policy date was consistent with the insured’s birthday. In each of the two periods, added policy year 1, age 1, number of claims 1, exposure 1 and policy year 2, age 2, number of claims 2, exposure 2 separately. There were also some adjustments needed to be done, such as adjustment of exit date, and if one policy has more than one claims, only one claim needed to be accounted. Then we calculated each policy’s number of claims 1, exposure 1 and number of claims 2, exposure 2 in each period of the year, when calculated exposures, the actuarial exposures should be used. After that, we summed up number of claims and exposures which were grouped by age separately, so we can get number of claims and exposures of different ages in the year, and the ratio of the two results was just the morbidity we need.

For each year from 1999 to 2011, we can repeat the processing method above and we can get numbers of claims, exposures and morbidity of different ages in every year. We can also sum up numbers of claims and exposures grouped by age of the 13 years and get morbidity of each age for the 13 years together. The third step, we can also repeat above two steps for different critical illness. When morbidity of different critical illness is calculated, it needed to separate the disease into several big types because of not enough data, for example, when it mentioned cancer, it meant a collection of thyroid cancer, breast cancer, cervical cancer and other species. After critical illness separation, the article calculated morbidity results of cancer and diabetes as the way showed above.

After getting the morbidity of different critical illness, we found that for some diseases, the morbidity results were not accurate enough because of little amount of policy data. According to the life insurance company’s experience, when the number of claims is less than 250, the company thinks that the morbidity is not accurate enough. So when we got the morbidity results of cancer and diabetes, both of the two diseases had some age bands which had inaccurate results, such as 0 to 24 and 60 to 74 years old for cancer, so only morbidity results of 25 to 59 years old can be used to calculate cancer patients’ mortality in the below.

2.2 Calculating mortality

As there is no statistical data of morality of impaired lives, we calculated mortality of impaired lives according to the morbidity which was calculated according to a life insurance company’s critical illness insurance policy data and mortality statistical data from Ministry of Health of China. But there was a question that the statistical calibers of the two kinds of data were different, one was calculated on the basis of the insured of a life insurance company’s critical illness insurance, and the other was counted on the basis of the whole urban residents of our country.

To solve this problem, we had done some adjustments to the morbidity results with Taiwan residents’ morbidity of cancer and diabetes. The method to adjust the insured’s morbidity was that the new morbidity which would be used to calculate mortality of impaired lives was equal to the sum of the insured’s morbidity multiplied by weight one and Taiwan residents’ morbidity multiplied by weight two, where the weight one was equal to the ratio of the number of critical illness insurance insured to the sum of the number of insured and the population of Taiwan, and the weight two was equal to 1 minus weight one. When calculating weight one, we used the mean of the insured’s exposures from 1999 to 2011 as the number of critical illness insurance insured, and the average of Taiwan population from 2005 to 2007 as the population of Taiwan.

For some chronic diseases we focus on, the adjustment is not enough to get the final 3-dimentional data set. We continued to use medical research and survey to fit and modify the above results. The Patient Tracing Division accumulated a large amount of information from patients with diabetes and chronic cancer (some selected types which seems to be modest). The data from medical institution is from 1995 to 2010. And most of data is for the age above 35, only some cancer are for the age above 23. Since the policyholders of insurance companies whose data we use are come from cities, we use city part of the data from medical institution and the city surveys in the Chinese healthy yearbook. In other word, our research is based on Chinese urban data and get the conclusion of Chinese urban impaired lives. Of course, the rural research is on the research way for us. Here, we also use some results from the public medical reports, like Chinese diabetes survey.