Abstract
Survival analysis is applied in different sectors with the aim of improving performance outcomes of organizations and individuals. This paper focuses on discussing the issue of survival analysis from two perspectives. Prior to providing a methodology and three applications of survival analysis and frailty, the paper provides a concrete introduction.
In the methodology section, it provides the research methodology and design, sample selection, data sources and selection, data analysis procedure, theoretical framework, and methodological issues. In the applications section, summaries are provided, which are linked with the purpose and hypotheses of studies. Finally, the findings of the studies that are discussed in the paper show the usefulness of survival analysis.
Introduction
Scholars view survival analysis as a segment of statistics that deals with the assessment of periods prior to the happening of an event or multiple events (Aalen, 2013). It is applied with the aim of evaluating various phenomena. For example, one may be interested in determining how some characteristics may impact the probability of survival.
Over the years, scholars have utilized the discipline in the field of medicine in order to study the specificity of death as an event that might happen based on a variety of factors. However, in the late 1970s the trend in the usage of survival economics took a completely different turn. Intellectuals in the field of economics and business merged the discipline with statistical analysis to unearth the occurrence of business-related events (Bagdonavicius, 2014).
Nevertheless, even academicians in business and economics borrowed the term death from medicine to show the failure of one or more events (Epstein, 2014). As opposed to quantitative analysis, data used for assessment in the context of survival analysis differ for the reason that they usually lack normality in distribution. In addition, such data do not have the aspect of completeness of the information collected.
The cloaked information, coupled with distribution-related abnormalities, culminates in specificity in terms of methodologies and arithmetical methods that are necessary for proper analysis. According to Diana (2013), survival analysis has increasingly become essential when conducting research studies in the filed of socio-economics.
Such studies satisfy the need to investigate complicated incidents that involve unemployment, price escalation, demand, and supply. In fact, the areas may have critical impacts on loans from financial institutions, product life cycles, and producer-consumer relationships. This paper intends to produce a survival analysis methodology, provide its application, and produce results from three applicability examples.
Methodology
Research methodology and design
In this context, methodology takes the form of a case-cohort study. The approach in research came into existence after inception and formulation by Prentice in 1986 (Epstein, 2014). According to modern-day scholars, case-cohort studies have become common because they offer researchers the ability to minimize research costs by adopting fewer participants (Haberman, 2014). This becomes possible by defying the normal research routines that must follow a large number of subjects.
Therefore, the study presented in this paper takes into account a single subject rather than multiple subjects, and analyzes data collected about the single subject. Nevertheless, the single cohort or subject comes from a randomly selected group. In order to arrive at a single subject, each subject can only become a part of the study after meeting the requirements of the event of interest.
It is, therefore, necessary to identify a particular procedure used for the selection of samples or subjects prior to arriving at the cohort from which to choose a sub-cohort, and then narrow down to a single subject of study (Haberman, 2014).
Sample selection
In order to attain a sample that ultimately provides the most suitable subjects for study, it was necessary to identify two groups of industries from which to select a variety of samples. These are the airline and the healthcare industries. The process identified five companies representing each corresponding industry. The reason for choosing these two types of industries was to provide a high level of diversity.
According to Karagrigoriou (2013), it is always vital to determine events after choosing a cohort when dealing with research from the case-cohort perspective. Thus, the event selected to determine qualification of subjects to participate in the sub-cohort was based on players in these two industries.
It is vital to note that prior to the selection of companies from the airline and the healthcare sectors, impartiality was critically considered (Hougaard, 2013). Although most scholars believe that random picking of cases is more suitable, Weidler (2013) opines that randomness has a negative effect on the accuracy and viability of a research activity.
Consequently, impartiality is vital due to its capacity to consider detailed information before adopting samples in a sub-cohort. The sub-cohort from the five companies was based on the discriminating event. After the acquisition of the sub-cohort, a second condition came into place to help narrow down to a single study subject. The discriminating event, in this case, aimed at identifying one company in the sub-cohort with the most resilient department.
More specifically, it aimed at knowing the firm that defied “death” even during the toughest times. The factor also considered the use of survival models and the various operational factors that impact operations in a particular organization (Snapinn, 2014). These models and factors act as the final platform on which the sub-cohort should be evaluated. In this context, the outcome was a single subject for the study. It is important to consider the procedures that were employed in the collection of data to achieve an effective process as described above.
Data sources and collection
The process of data collection proves tiresome and more demanding when researchers fail to consider and scrutinize the sources needed for the task (Snapinn, 2014). In support of the assertion, Williams (2013) argues that lack of proper knowledge in relation to the information necessary prior to data collection negatively impacts the credibility of research-based conclusions. For purposes of clarity, collection of data was performed by considering both secondary and primary sources (Hougaard, 2013).
Collection of data through the primary procedure adopted the form of key informers from the two industries prior to establishing the cohort. In addition, procedures that covered secondary information considered government publications. Taking into consideration the complexity of the task involving the identification of subjects suitable for the cohort, searching for the information from the internet became one of the best methods of essential information (Haberman, 2014).
As Diana (2013) contends, collection of information from the internet makes work more interesting and speedy on the grounds that a researcher has the right keywords for executing online searches. Thus, information concerning the airline and the healthcare came mostly from journal articles, e-books, newspapers, and online books. However, for the purpose of writing this paper, articles from peer-reviewed journals ware used.
Consequently, through careful and in-depth investigation was performed vis-Ă -vis the companies that participated in the cohort, the sub-cohort. Finally, the single was subject chosen for the study. Careful consideration of the secondary sources was instrumental because it presented the opportunity to confirm information acquired from the informers.
Various aspects of information obtained via primary procedures were considered. Some of these were major company events, departmental performances, technical information, and major company decisions. It is worth to note that the primary sources of data were typified by relatively high levels of authentication, and they gained support from the secondary materials (Diana, 2013).
Data analysis
The analysis of the data collected took into consideration the two discriminative events that were aimed at assessing samples to select a single subject for the study. After the impartial selection of samples for entry into the cohort, information was obtained from both primary and secondary sources.
This helped to analyze the first ten companies. Moreover, the samples qualifying for entry into the sub-cohort became impartially subject to the second filtering event. According to Aalen (2013), filtering events help researchers to acquire credibility and form a basis for substantiating the reason for choosing their final research subjects. Subjecting the sub-cohort to the second principle of elimination helped to gain the insights required for selecting the most suitable subject for the study (Aalen, 2013).
Theoretical framework
Modern day intellectuals in the field of survival analysis have defied conventional assertions that frameworks used in research should prove correctness and relevance (Aalen, 2013). As opposed to the conventional belief system, Epstein (2014) points out that researchers should not deal with frameworks from the mere perspective that considers the “correct” or the “incorrect”.
On the other hand, researchers should consider more carefully the interesting nature and the ability of a theory to that can go along way in achieving the objectives of their studies (Haberman, 2014). The theoretical perspective of this study is founded on the Kaplan-Meier method.
Diana (2013) states that the Kaplan-Meier method evaluates death as an outcome, but this has changed in the recent times. The techniques has also gained popularity in the social sciences and industrial statistics due to the fact that it can be applied to achieve many goals. For example, a “researcher might quantify the length of time people remain unemployed after a job loss” (Diana, 2013, p. 49).
In addition, an engineer might assess all the time until the collapse of an appliance. A plot of the “Kaplan-Meier estimate of the survival function is a series of horizontal steps of declining magnitude, which, in case of a large sample offers the true survival function for that population” (Aalen, 2013, p. 24). The value of the survival function between successive distinct sampled assumes a state of constancy.
Methodological issues
Over the years, scholars have consistently engaged in heated debates in relation to the balance between merits and demerits associated with the use of survival analysis. While some have contended that the use of the discipline occurs on rare occasions, evidence indicates that its applications increase yearly as a result of its advantages.
These advantages fall into a series of categories. To begin with, some advantages, being descriptive in nature, offer a platform for clarity in examining selected sample subjects (Snapinn, 2014). In addition, the application of survival analysis offers researchers the ability to predict events in the future when handling the entire population.
The method also provides researchers with an opportunity to deploy comparison strategies that are aimed at achieving accuracy and objectivity (Snapinn, 2014). These merits indicate that survival analysis is a highly advantageous practice, especially in the fields of business and economics.
Nevertheless, the application of survival analysis does not produce anticipated results without prior considerations with regard to certain practical conditions. Importantly, these conditions are demanding for the reason that they should be observed simultaneously. The first condition, according to Weidler (2013), is that researchers should carefully evaluate empirically coded data for each individual subject in an investigation.
This involves separating and grouping subjects into two classes. The first group should contain conditions that satisfy chosen events, which are placed on the right and the left. In the second group, researchers should ensure that the inclusion of subjects in a study is executed in a simultaneous manner. This helps to avoid progressively censored data (Karagrigoriou, 2013).
Applications
It is important to “evaluate four applications that are associated with survival analysis” (Diana, 2013, p. 49). In this section, three articles are evaluated on the basis of their goals, hypotheses, and results.
Application one
Summary of the purpose
Diana (2013) conducted a study with the aim of evaluating how some variables could impact the periods that taxis took to ferry persons from to and from John F. Airport, New York. It is worth to note that airports are required to have high levels of efficiencies with regard to taking persons from there to other destinations. In addition, travelers need to be transported to airports so that they can catch their planes.
Thus, the researcher emphasized on the use of taxi operations in the firm due to the fact that they provide supportive services. The scholar also aimed at explaining “the differences that were observed in the 2006 and 2007 summers in the John F. Kennedy Airport” (Diana, 2013, p. 47).
In fact, the researcher developed an interest to investigate the variables for the reason of the notable differences between the two summers. It was expected that the results would go a long way in giving the management of the organization that would culminate in improved operational outcomes. Hourly departure records in the airport were evaluated.
Hypotheses
From a scientific perspective, a hypothesis is a critical component of a study for the reason that it helps a researcher to formulate assumptions that support data collection and analysis. The study hypothesized that there was no correlation between departure delays and arrival analysis.
In other words, the time that the taxis in the facility were late in relation to taking persons from it was not significantly affecting the time that was taken for transporting persons to the airport. Furthermore, the scholar assumed that there were no remarkable differences between fixed and random effects.
Results
Cox regression methods used in the study demonstrated that overall delays and the proportion of airport used capacity were likely to improve the chances of relatively long taxi-out times. However, the times were in the context of meteorological factors that were compared with other aspects, for example, departure times and volume of departures. Moreover, frailty analysis showed that two key effects, which were fixed and random effects, did not significantly impact periods associated with moving out of taxis.
Application two
Kunisawa, Yamashita, Ikai, Otsubo and Imanaka (2014) focused on determining critical cancer trends in Japan using survival analyses. The study focused on a healthcare firm in Japan. Survival rates of patients suffering from cancer have been shown to impact the information that is used by policymakers in the healthcare industry. Kunisawa and colleagues (2014) conducted the study with the aim of the following:
- Utilizing administrative data to perform effective survival analyses.
- Assessing the variations in long-term survival levels in hospital settings based on the number of patients and the volume of outcomes.
- Revealing an up-to-date information about the survival rates of patients with high levels of validity.
Hypotheses
In this context, the scholars assumed that there could be no differences between patient volumes and clinical outcomes. In addition, they hypothesized that the selected sample could have only cancer, but no other health conditions affecting their wellbeing.
Results
The Kaplan-Meier method was utilized to calculate survival rates of persons at different stages of cancer. Postoperative five-year survival period for patients for persons suffering from cancer at the IA stage was determined to be 85.5%.
It was shown that hospitals with healthcare facilities with relatively high volumes were typified with better survival outcomes. From the findings, it can be concluded that techniques in survival analysis can be applied in assessing the expected survival period s of persons who suffer from specific diseases and/or health conditions.
Application three
Usman, Dikko, Bala and Gulumbe (2014) concentrated on applying the Kaplan-Meier estimator to determine the levels of distribution of persons presenting with breast cancer. The example is on the platform of playing survival analysis in a healthcare firm in Nigeria.
The chief goal of the study was to assess the survival rates of the subjects, which could go a long way in adopting better approaches that could improve the longevity of the cancer patients. Another purpose that was adopted in the study was to assess the effects of various variables, such as age and occupation, on the rates of survival of cancer patients.
Hypotheses
Usman and colleagues (2014) assumed that there were no significant variations in relation to age and survival rates of the subjects. In addition, they hypothesized that occupations of cancer patients did not impact their survival rates. By conducting analyses that were founded on the Kaplan-Meier platform, they focused on testing the validity of the hypotheses.
Results
The study based on the Kaplan-Meier method established that there were statistically significant variations in relation to experiences in cancer patients. “Age groups and the results of treatment demonstrated remarkable differences” (Usman et al., 2014, p. 136). However, occupations did not result in remarkable variations of survival rates among the subjects. In this context, it can be concluded that survival analysis is important in understanding factors that can influence life expectancies of patients.
Conclusion
Survival analysis is an approach that is based on the application of various statistical methods. Basically, the strategy is used to determine periods prior to occurrences of events. This paper has demonstrated that survival analysis is applicable across industries, for example, in the healthcare and business sectors.
The Kaplan-Meier method is one of the most common methods used to perform survival analysis in different settings. The three examples of applications highlighted in this paper have shown that the approach is instrumental in achieving goals that can result in improved outcomes across sectors.
References
Aalen, O. (2013). Survival analysis, longitudinal analysis and causal inference. Business Horizons, 1(1), 11-34.
Bagdonavicius, V. (2014). Analysis of survival data with cross-effects of survival functions. Business Horizons, 8(12), 415-445.
Diana, T. (2013). An application of survival and frailty analysis to the study of taxi-out time: A case of New York Kennedy Airport. Business Horizons, 8(21), 40-58.
Epstein, R. (2014). The Master’s Degree in Economics and Business. Journal of Business, 7(2), 71-98.
Haberman, S. (2014). Time series analysis of the probability of survival as unemployed. Journal of Business Research, 6(2), 215-235.
Hougaard, P. (2013). Frailty models for survival data. Journal of Business Research, 9(4), 255-273.
Karagrigoriou, A. (2013). Frailty Models in Survival Analysis. Journal of Business Research, 10(7), 198-298.
Kunisawa, S., Yamashita, K., Ikai, H., Otsubo, T., & Imanaka, Y. (2014). Survival analyses of postoperative lung cancer patients: an investigation using Japanese administrative data. SpringerPlus, 3(1), 1-8.
Snapinn, S. (2014). Survival Analysis with Uncertain Endpoints. Journal of Economics and Business, 21(13), 209-241.
Usman, M., Dikko, H. G., Bala, S., & Gulumbe, S. U. (2014). An application of Kaplan- Meier survival analysis using breast cancer data. Sub-Saharan African Journal of Medicine, 1(3), 132-137.
Weidler, W. (2013). Graduate Work in Economics and Business. Journal of Business, 5(3), 61-87.
Williams, R. (2013). Product-limit survival functions with correlated survival times. Journal of Economics and Business, 2(1), 171-186.