Multistage Logistic Regression Model for Analyzing Survival from Colorectal Cancer

Colorectal cancer, which is also known as bowel cancer, colon cancer, or rectal cancer, is the third most common cancer worldwide, and the second most common in Malaysia. In most situations, the tumor/cancer may return even after the tumor removal. The impact of the type of surgery performed for tumor removal on the occurrence of a new tumor and the impact of a patient’s state at previous follow-up on the occurrence of a new tumor in the next follow-up are of interest. Thus, the probability of surviving with no tumor recurrence, the probability of surviving but with tumor recurrence, and the probability of not surviving can be obtained. A multistage logistic regression, which was designed for longitudinal data, was used. Data from 161 colorectal cancer patients who experienced tumor removal through surgery and were followed-up for two years were used in this study. The results showed that in the first year after tumor removal surgery, regardless of whether the patients had undergone elective or emergency surgery, the chance of patient survival with no tumor was approximately five times higher than the chance of dying; meanwhile, the chance of dying was approximately three times higher than the chance of developing a new tumor. Similar results have also been obtained for a period of 2 years after the tumor removal surgery. 

Colorectal cancer; Multistage logistic regression; Recurrence; Survival

This study was motivated by problems with the analysis of life historical data in clinical research. Most existing statistical models are based on concepts according to which a disease instantaneously occurs. Traditional survival analysis deals with analyzing follow-up time: the time elapsed from a starting point until a specific event occurs. Follow-up studies usually stop when the event of interest takes place. However, in most follow-up studies, individuals may experience more than one event at different stages of follow-up. The occurrence rates of these events may be of interest. The traditional survival model, however, is not suitable for analyzing follow-up studies in which more than one event of interest occurred. A multistage model is one of the available methods for analyzing follow-up studies in which more than one event of interest occurs. It can provide a more comprehensive view of a disease process, allowing the estimation of probabilities while making use of incomplete information efficiently and handling loss to follow-up problems appropriately. Examples of diseases from which patients may experience more than one event include all kinds of cancers, myocardial infarction, heart disease, cyst development, and diabetes.

Cancer is an uncontrolled growth of abnormal cells, also known as cancer cells, or malignant tumors anywhere in a body. Cancer cells can break away from their original form, travel through the blood and lymph systems, and invade other organs (Reboux, 2018). To stop the uncontrolled growth cycle of cancer cells, certain treatments must be considered. Surgery, chemotherapy, and radiotherapy are among the options available for the treatment of patients with cancer.

Colorectal cancer, which is also known as bowel cancer, colon cancer, or rectal cancer, is the third most common cancer worldwide. In Malaysia, colorectal cancer is the second most common cancer in males and the third most common cancer in females (Veettil et al., 2017). The incidence and mortality of colorectal cancer are higher in males compared to females. Meanwhile, in terms of ethnicity, those of Chinese ethnicity have the highest incidence of colorectal cancer (Hassan et al., 2016), followed by those of Malay and Indian ethnicities. In Malaysia, most patients with colorectal cancer are diagnosed at a very late stage (Goh et al., 2005; Rashid et al., 2009). This could be due to a lack of awareness of the symptoms and signs of colorectal cancer as well as the increasing incidence of colorectal cancers in Malaysia. Delay in looking for treatment or screening for colorectal cancer detection before any symptoms or signs occur may adversely impact recovery and survival. A national program for colorectal cancer screening should be implemented, especially in low-income communities (Tze et al., 2016)

Even though there are several choices of treatment for colorectal cancer patients, surgery is the most common treatment for tumors. Tumor surgery involves the removal of part of the healthy intestine and the nearby lymph nodes of patients. Medical surgery for tumor removal is suitable not only for younger patients but also for the elderly, as delayed mortality and an early survival rate can be expected among elderly patients (Hobler, 1986). In most situations, the tumor/cancer may recur after treatment, and it may affect the rectum, colon, or any other part of the body even though the surgery has been performed on the patients. Therefore, even after successful surgery, some patients may require chemotherapy to reduce the risk of the tumor returning. In other words, follow-up treatment is always a must for colorectal cancer patients. However, the question of how fast the new tumor can develop once it has been removed remains unanswered. This study examined the effect of the types of surgery that have been performed on patients, and the effect of patients’ conditions in the previous follow-up on the chance of new tumor recurrence in the subsequent follow-up.

1.1.    Objectives of the Study

At every one-year follow-up time (also referred to as stage k), colorectal patients undergo a checkup to determine whether the tumor has returned. If it has, another surgery is performed. Generally, the impact of the type of surgery performed on a patient at time t_k-1 on the occurrence of a new tumor at time t_k, and the impact of a patient’s state at time t_k on the occurrence of a new tumor at t_k+1, are of interest. Thus, this study aimed to: (1) Model the effect of different types of surgery and the state of colorectal cancer patients in the previous follow-up on the probability of tumor recurrence; and (2) Obtain the probability of surviving with no tumor recurrence, the probability of surviving but with tumor recurrence, and the probability of not surviving.

The profile summary of the 161 hospital cases is consistent with that of the reported Malaysian data. Mainly, (i) Chinese had the highest incidence compared to other ethnicities, (ii) more males than females were diagnosed with cancer, (iii) most cases were diagnosed at the age of 50 or above. Out of the 161 colorectal cancer patients considered in this study, 28% died before the new tumor developed, while 5% died in the second year after tumor recurrence in their first year. Within two years after surgery for tumor removal, about one-half (57%) of the patients survived with no tumor recurrence.

In the main year of development or after one year of tumor removal, regardless of whether an elective or emergency medical procedure was performed, the probability of survival with no tumor was around five times higher than the probability of dying, while the probability of dying was roughly three times higher than the probability of tumor recurrence. A similar conclusion was made in view of the model in stage 1; accordingly, we can likewise infer that in the second year after the tumor removal medical procedure, the probability of survival with no tumor was around six times higher than the probability of dying, while the probability of dying was roughly 1.1 times higher than the probability of developing another tumor. This suggests that undergoing a medical procedure for tumor removal is superior to leaving the tumor in place, as surgery can boost the probability of survival.

As life expectancy continues to increase in Malaysia, as in the rest of the world, it is believed that the rate of colorectal cancer cases will continue to rise. If Malaysians continue to ignore the increasing incidence of colorectal cancer, there will be a lower chance of early detection and survival. Educating the public, especially high-risk groups for cancer, is necessary to increase awareness of colorectal cancer. A national program for colorectal cancer screening should be implemented, especially in low-income communities, to increase early detection and improve the survival rate of colorectal cancer patients. As the popular proverb goes, prevention is better than a cure. Various agencies working hand in hand with early screening for low-income communities could hopefully lower the colorectal cancer incidence rate in this demographic.

Finally, this study demonstrates that a multistage logistic model is suitable for studying patients’ progress in longitudinal studies, especially when follow-ups are made in the same time interval. The model has been widely used to make analysis easier, as it also allows different definitions of states in different stages. 

The authors would like to thank Universiti Utara Malaysia (RAGS S/O 12686), UKM Medical Centre (HUKM), and the National Registration Department of Malaysia (JPN) for their support in this research.

Abu Hassan, M.R., Ismail, I., Mohd Suan, M.A., Ahmad, F., Wan Khazim, W.K., Othman, Z., Mat Said, R., Tan, W.L., Mohammed, S.R., Soelar, S.A., Nik Mustapha, N.R., 2016. Incidence and Mortality Rates of Colorectal Cancer in Malaysia. Epidemiology and Health, Volume 38, pp. 1–5

Armitage, P., Doll, R., 1954. The Age Distribution of Cancer and a Multi-stage Theory of Carcinogenesis. British Journal of Cancer, Volume 8(1), pp. 1–12

Barus, L.S., Flores, H.M., Hadiwardoyo, S.P., Batoz, J.L., 2016. Intercity Mode Choice Modelling: Considering the Intracity Transport Systems with Application to the Jakarta-Bandung Corridor. International Journal of Technology, Volume 7(4), pp. 581–591

Danaei, G., Vander Hoorn, S., Lopez, A.D., Murray, C. J., Ezzati, M., 2005. Causes of Cancer in the World: Comparative Risk Assessment of Nine Behavioural and Environmental Risk Factors. The Lancet, Volume 366(9499), pp. 1784–1793

Dove-Edwin, I., Thomas, H.J., 2001. Review Article: The Prevention of Colorectal Cancer. Alimentary Pharmacology and Therapeutics, Volume 15(3), pp. 323–336

Ghee, L.K., 2014. A Review of Colorectal Cancer Research in Malaysia. Medical Journal of Malaysia, Volume 69, pp. 23–32

Goh, K.L., Quek, K.F., Yeo, G.T., Hilmi, I.N., Lee, C.K., Hasnida, N., Aznan, M., Kwan, K.L., Ong, K.T., 2005. Colorectal Cancer in Asians: A Demographic and Anatomic Survey in Malaysian Patients Undergoing Colonoscopy. Alimentary Pharmacology and Therapeutics, Volume 22(9), pp. 859–864

Hassan, M.R., Suan, M.A., Soelar, S.A., Mohammed, N.S., Ismail, I., Ahmad, F., 2016. Survival Analysis and Prognostic Factors for Colorectal Cancer Patients in Malaysia. Asian Pacific Journal of Cancer Prevention, Volume 17(7), pp. 3575–3581

Hobler, K.E., 1986. Colon Surgery for Cancer in the very Elderly; Cost and 3-year Survival. Annals Surgery, Volume 203(2), pp. 129–131

Holford, T.R., Zhang, Z., McKay, L.A., 1994. Estimating Age, Period and Cohort Effects using the Multistage Model for Cancer. Statistics in Medicine, Volume 13(1), pp. 23–41

Islam, M.A., Chowdhury, R.I., Chakraborty, N., Bari, W., 2004. A Multistage Model for Maternal Morbidity during Antenatal, Delivery and Postpartum Periods. Statistics in Medicine, Volume 23(1), pp. 137–158

Magaji, B.A., Moy, F.M., Roslani, A.C., Law, C.W., 2017. Survival Rates and Predictors of Survival among Colorectal Cancer Patients in a Malaysian Tertiary Hospital. BMC Cancer, Volume 17(1), pp. 339–346

Moolgavkar, S.H., 1978. The Multistage Theory of Carcinogenesis and the Age Distribution of Cancer in Man. The Journal of the National Cancer Institute, Volume 61(1), pp. 49–52

Muenz, L.R., Rubinstein, L.V., 1985. Markov Models for Covariate Dependence of Binary Sequences. Biometrics, Volume 41(1), pp. 91–101

Peng, C.Y.J., Lee, K.L., Ingersoll, G.M., 2002. An Introduction to Logistic Regression Analysis and Reporting. The Journal of Educational Research, Volume 96(1), pp. 3–14

Pompei, F., Wilson, R., 2001. Age Distribution of Cancer: The Incidence Turnover at Old Age. Human and Ecological Risk Assessment, Volume 7(6), pp. 1619–1650

Ramosacaj, M., Hasani, V., Dumi, A., 2015. Application of Logistic Regression in the Study of Students’ Performance Level. Journal of Educational and Social Research, Volume 5(3), pp. 239–244

Rashid, M.R., Aziz, A.F., Ahmad, S., Shah, S.A., Sagap, I., 2009. Colorectal Cancer Patients in a Tertiary Referral Centre in Malaysia: A Five Year Follow-up Review. Asian Pacific Journal Cancer Preview, Volume 10(6), pp. 1163–1166

Reboux, G., 2018. Cancer. World Health Organisation. Available Online at https://www.who.int/en/news-room/fact-sheets/detail/cancer, Accessed on October 30, 2018

Ritter, G., Wilson, R., Pompei, F., Burmistrov, D., 2003. The Multistage Model of Cancer Development: Some Implications. Toxicology and Industrial Health, Volume 19(7-10), pp. 125–145

Tze, C.N., Fitzgerald, H., Qureshi, A., Tan, H.J., Low, M.L., 2016. Pioneering Annual Colorectal Cancer Screening and Treatment Targeting Low Income Communities in Malaysia (2010-2015). Asian Pacific Journal of Cancer Prevention, Volume 17(7), pp. 3179–3183

Veettil, S.K., Lim, K.G., Chaiyakunapruk, N., Ching, S.M., Abu Hassan, M.R., 2017. Colorectal Cancer in Malaysia: Its Burden and Implications for a Multiethnic Country. Asian Journal of Surgery, Volume 40(6), pp. 481–489

Yusuff, H., Mohamad, N., Ngah, U.K., Yahaya, A.S., 2012. Breast Cancer Analysis using Logistic Regression. International Journal of Recent Research and Applied Studies (IJRRAS), Volume 10(1), pp. 14–22

Zangmo, C., Tiensuwan, M., 2018. Application of Logistic Regression Models to Cancer Patients: A Case Study of Data from Jigme Dorji Wangchuck National Referral Hospital (JDWNRH) in Bhutan. Journal of Physics: Conference Series, Volume 1039, pp. 1–10