Using Cox Regression to Forecast of Survival of Women with Multiple Malignant Neoplasms

Abstract

Recently, an increase in the incidence of multiple primary malignant neoplasms has been observed, specifically, when two or more unrelated tumors originate from different organs and appear in the body simultaneously or sequentially, one after another. During past few years, the interval between the first and second reproductive cancer diagnosis has decreased in 6 times – from 11 to just 2 years while probability of surviving the next 3 years after 8.5 years past initial diagnosis has decreased from 0.995 to 0.562. Using performed analysis, this paper provides details of survival modelling for women with breast cancer with the aim to find the most significant factors affecting the likelihood of survival not by chance alone. The data used for research were obtained from Ukrainian National Institute of Cancer covering 1981–2017 period.
 The modelling was performed using Cox regression with forward effect selection method and stay in p-value boundary equal to 0.15. The forward method firstly computes the adjusted chi-square statistics for each variable. Then, it examines the largest computed statistics and if particular one is significant, the corresponding variable is added to the model. Once the variable is entered, it is never removed from the model. 3 out of 4 factors that appeared to be significant according to forward selection method were confirmed as the significant ones by stepwise selection method.
 The results of modelling proved the possibility of prediction the survival using certain set of disease features and subjects’ characteristics. Testing of global hypothesis for Beta resulted in rejecting of null hypothesis (Beta = 0) in favor of the alternative one (Beta ≠ 0) thus it was confirmed that the models make sense and can be used to predict survival in women with breast cancer. According to obtained results, the most significant disease features and subjects characteristics appeared to be: type of multiple processes (synchronous or metachronous), presence of relapse and/or metastasis, type and combination of treatment, stage of disease.
 Cancer with synchronous processes is characterized by greater aggressiveness and it reduces survival by almost 13 times compared with cancer where metachronous processes take place. Even though chemotherapy significantly increases the survival rate of patients, it also impacts the probability of relapses and metastasis occurrence, which are 16 times more likely to occur if chemotherapy was a part of treatment. This gives grounds for assumption that it has an indirect effect on survival and hence needs to be analyzed considering its negative impact on the relapses and metastasis occurrence probability, which, in turn, reduces survival by 10 times. This fact, in our opinion, introduces the need for further in-depth analysis. The significant difference between survival rates in patients with the first and third stages of cancer has been proved – the chances to survive with the disease at the first stage are almost 12 times higher than with disease at the third stage. At the same time, the difference in the survival rates in women with the disease at the second and the third stages is not so big and it is only 1.6 times. The modern method of conducting surgery compared with the standard one appeared to be capable to reduce the risk of relapses and metastases by 2.6 times, while breast conservative surgery in multiple oncological processes – by 3 times compared with mastectomy, which allows to state that both factors have a positive effect on the survival probability and reduce the risk of mortality.
 Regarding subgroup models built for patients having synchronous process and patients with metachronous processes separately, an increase in the sample size is needed to assess assumed difference in factors affecting survival and to improve predictive abilities of models. This, in turn, requires additional studies during which the necessary amount of data can be collected.

A Statistical Analysis of the Factors with Nonrandom Impact on the Survival Rate of Women with Breast Cancer, by Type of Medical Treatment

“…Grouptrt Фактори до моделі додавалися покроковим методом (stepwise selection). На кожному кроці розглядається змінна для додавання або віднімання з набору пояснювальних змінних на основі певного попереднього критерію [12]. У регресії Кокса такий критерій -тести типу 3 (Type 3 Tests).…”

“…Сутність моделі полягає в тому, що за результатами перевірки глобального тесту нульові гіпотеза (Beta[i] = 0) відхиляється на користь альтернативної (Beta[i] ≠ 0), а це говорить про те, що кінцеві моделі мають сенс і можуть прогнозувати виживаність [12]. За результатами перевірки глобального тесту гіпотеза про відсутність істотних невипадкових чинників, що визначають виживаність, перевірялася на істотність і була відхилена на користь альтернативної, що говорить про можливість прогнозування виживаності для загальної моделі на рівні істотності 0,05 (табл.…”

Kaplan-Meyer Survival Curves: Simulation Technique

“…Окремі аспекти вивчення кривих виживаності за методом Каплана -Мейєра та регресії пропорційних ризиків Кокса висвітлені у працях Девіда Мачина [1], Авіви Петрі та Каролайн Сабін [2], Девіда Клейнбаума та Мітчела Кляйна [3], П. Рум'янцевої та В. Саєнка [5], інших зарубіжних авторів. З-поміж вітчизняних дослідників слід згадати роботи Н. Ковтун [4] та З. Федоренко зі співавторами [6,7].…”