New applications of survival analysis modeling: Examining intercollegiate athletic donor relationship dissolution

2.1Survival analysis

In various forms, survival analysis has been applied widely across several academic fields to analyze the duration of time leading to and factors important to an event occurrence. Alternatively known as event history analysis (demography), duration analysis (econometrics), and failure-time analysis (engineering; Box-Steffensmeier & Jones, 2004), survival analysis has advantages over the traditional regression technique, especially regarding the application to longitudinal data. The analysis accounts for staggered entry and censored observations, or events for which the final duration is unknown (given that they are currently ongoing). In addition, survival analysis accommodates a dual-natured dependent variable (whether the event happened and the duration of time until the event occurred) as well as typically skewed datasets (Meyers et al., 2016). Past use of survival analysis ranged from the study of United Nations peacekeeping missions, military interventions, the careers of Congress members, to marriages (Box-Steffensmeier & Jones, 2004). In their exhaustive review, Singer and Willett (2003) noted that Cooney et al. (1991) employed the technique to examine the duration of after-care programs for alcoholics (with the event in question being a relapse to alcohol use), Bolger et al. (1989) examined the duration of time before an undergraduate student ideates about suicide, while Furby et al. (1989) investigated recidivism (return to prison) among criminals. In the case of the current study, the survival analysis approach can be employed to study those individuals who are still active donors, those who have ended the relationship, and those donors that entered the relationship at different times.

Survival analysis can also be utilized to analyze the effect of either time-invariant or time-varying covariates (i.e., variables that change values over time; Singer & Willett, 2003). For example, Bolger et al. (1989), in their investigation into the timing of suicidal ideation, not only identified that such thoughts begin to increase around age nine, but also uncovered influential circumstances surrounding the onset of suicidal thoughts. An individual’s gender and race affected the risk of suicidal thought emergence and the absence of a parent increased the risk of suicidal thought especially in preadolescence. In the study of athletic donor relations, survival analysis can be employed to discover how covariates, such as a donor’s relationship with the university and whether or not the athletic department enjoys a successful football season, affect the probability of donordefection.

According to Singer and Willett (2003), in addition to arranging an appropriate set of potential predictors, three important concepts are essential to understanding and applying survival analysis for use on longitudinal data: the survivor function, the hazard rate, and the median lifetime. To begin, the Kaplan-Meier (1958) survivor function estimate, S(t_ij), is defined by Singer and Willett (2003) as the “probability that individual i will survive past time period j” (p. 334). For this to occur, the individual (in this case, the athletic department donor) i cannot experience the event occurrence in the jth time interval, and survives to the end of time period j. In other words, the random variable for time (T_i) for individual i exceeds j. The survivor function is defined by the formula below:

Of arguably more utility than the survivor function is the hazard function, or hazard rate. The hazard rate is defined as the rate in which the duration or event ends (i.e., the event has been experienced), given that the target event or the duration has not ended prior to that particular time interval (Box-Steffensmeier & Jones, 1997). Given that T_i represents the time period T for individual i, the discrete-time hazard rate can be represented as follows (Singer & Willett, 2003):

The median lifetime is defined by Singer and Willett (2003) as “that value of T for which the value of the estimated survivor function is 0.5” (p. 337). In the example of this study, the median lifetime is the point at which exactly half of the intercollegiate athletic donors in the dataset have ended their relationship, while half are still active. To determine the exact median lifetime, the formula provided by Miller (1981) can be utilized to linearly interpolate the exact time at which the survivor function of 0.5 falls between two values of (t_j). Miller’s (1981) formula involves letting m represent the last time interval in which the survivor function is above 0.5, letting Sˆ(tm) equal the survivor function in that particular time interval, and letting Sˆ(tm+1) equal the survivor function for the next time interval. The formula is as follows:

One can easily see the benefit of survival analysis application to sport customer relationship management, and in this case, athletic donor relationship management. The method furthers an understanding of the probability that an individual will end his or her relationship with an organization and an understanding of the factors that contribute to that probability. Despite its widespread use across several academic fields, survival analysis has not been fully leveraged in sport literature. Recent sport-focused work in survival analysis modeling demonstrates the utility of this particular analysis to the business side of sport and lends evidence for the potential future impact of survival analysis application.

2.2Survival analysis applied to sport

Early work implementing survival analysis in the sport context applied the method to game and player analytics. In studies that assessed factors impacting the length of an athlete’s career, both draft order (Staw & Hoang, 1995) and race (Hoang & Rascher, 1999) were significant predictors of career longevity. The approach has also been utilized to study the effect of a soccer match’s first goal on the timing of a subsequent goal (Nevo & Ya’acov, 2012). Researchers noted time-dependent effects in their analysis. Five minutes after a first goal was scored, the second goal hazard rate was 1.288 times greater than the hazard at the time of the first goal scored. Thirty minutes after, the hazard was 1.71 times greater. Additionally, the timing of the second goal score as it related to the first goal score (if at all) depended on when the first goal was scored, with an increased probability if the first goal occurred toward the end of the game.

The few research studies leveraging survival analysis for the business side of sport produced impactful conclusions for practitioners. Researchers illuminated factors contributing to the survival or dissolution of sport organizations (Cobbs et al., 2017) and business to business marketing partnerships (Jensen & Turner, 2017). In an evaluation of business relationships with global sport mega-events, sponsorship agreements were less likely to survive and most susceptible to dissolution in the first two renewal periods (Jensen & Turner, 2017). In addition, subsequent analysis of the effects of covariates found that inflation, clutter (i.e, the number of sponsors), brand equity and congruence between the sponsor and property are statistically significant predictors of either the continuance or dissolution of therelationship (Jensen & Cornwell, 2017). Armed with this information, managers tasked with sponsor retention can channel relationship cultivation efforts for that critical time when relationships are most likely to lapse, as well as monitor these conditions carefully throughout the relationship.

However, survival analysis has not previously been employed to investigate the duration of a sport organization’s relationships with its consumers, such as athletic department donors. The nature of survival analysis lends itself well to informing strategic customer retention efforts; understanding the timing of stakeholder relationship vulnerability is of utmost importance to this scenario. Literature informing donor retention efforts has yet to capture this timing. In this paper we resolve this gap in the literature through application of survival analysis modeling to quantitatively analyze and predict the potential dissolution of the intercollegiate athletic department-donor relationship.

5.1Nonparametric survival models

We generated results by employing and analyzing what Meyers et al. (2017) described as nonparametric survival models, where no assumptions are made about the shape of the hazard function nor the influence of covariates. This class of models includes the life table and Kaplan-Meyer survival analyses. The recommended first step in any survival analysis project is the construction of the life table (Singer & Willett, 2003), as it includes a summary of both the survivor functions and hazard rates at each time period, as well as the overall hazard rate. The life table is also used to compute the median lifetime, or as explained above, the point at which the survivor function equals 0.5. A life table was constructed for our dataset (Table 1). Within this table, the total number of individuals (a total of 2,979) and whether they continued or ceased their relationship at the end of each time period were identified.

A review of the survivor functions in the life table (Table 2) easily demonstrates when the largest percentages of individuals were lost from the dataset. The survivor function after the first time period (0.5955) indicates that 40.45% were lost after just the first year. A survivor function of 0.4549 after the second year demonstrates that another 14.06% were lost in the second year, with only 45.49% of donors surviving after two years. However, the survivor function was reduced to only 0.3866 after the third time period and to only 0.3391 after the fourth, indicating that the function leveled off after the first two time periods. This phenomenon is depicted in Figure 1, a graphical representation of the survivor function over the 10-year period. Only 3.69% were lost after the fifth time period (equating to a survivor function of 0.3022) and only 1.71% dropped outafter the sixth (a survivor function of 0.2851). Overall, the life table indicates that after losing 54.51% of the individuals after the first two years, only 19.29% were lost over the subsequent five years, an average of only 3.86% each year.

Fig.1

Graph of survivor function for donor survival over time (with 95% CI).

The hazard functions in Table 2 indicate when the probability of event occurrence was highest. Similar to the analysis of survivor functions, the highest hazard function was during the first time period, with a hazard function of 0.4045 indicating the probability of an individual exiting the dataset was 40.45%. The hazard functions then decreased, from 0.2351 after the second time period, to 0.1501 after the third, 0.1229 after the fourth, 0.1087 after the fifth, and 0.0566 after the sixth, as a smaller percentage of individuals exited the dataset in each subsequent time period. This is represented in Fig. 2, which depicts the hazard function sloping downward in a fairly linear fashion. There was a small increase in the hazard function after the seventh time period, as it rose to 0.0811 and to 0.0921 after the eighth. However, overall, the hazard functions depict that the probability of event occurrence was generally much lower the longer the individual remained in the dataset. These results conflict with those of Jensen & Turner (2017), who found that the probability of a sponsorship ending increased from the first to the second time period in two different datasets, with the hazard function the highest for both after the second year. The overall hazard rate is also depicted in the life table (0.2392). This corresponds to an overall probability of the donor’s relationship ending during any particular time period (23.92%). The hazard rate can also be utilized tocompute the organization’s overall renewal rate over the 10-year period (76.08%).

Fig.2

Graph of smoothed hazard function for donor survival over time (with 95% CI).

Finally, through analyzing the survivor functions in the life table depicted in Table 2, the median lifetime was computed. Given that the median lifetime is the point at which the survivor function is exactly 0.5 and the survivor function after the second time period is 0.4549, it is evident that the median lifetime occurred sometime between the first and second years. Using Miller’s (1981) formula, the median lifetime of athletic department donors was found to be 1.68. While in the case of this study the survivor function experienced the highest drop after the first year, the hazard function was also highest after the first year, and the survivor function equaled 0.5 during the first and second years, it is not always the case that these three metrics tell similar stories (Jensen & Turner, 2017; Singer & Willett, 2003).

5.2Semiparametric survival models

After the results of nonparametric survival models were analyzed, including the use of a life table to compute and examine survivor functions, hazard rates, and median lifetimes, we employed what Meyers et al. (2017) described as a semiparametric model. Using the aforementioned Cox proportional hazards model, covariates were inserted into the model to better understand how the various characteristics related to donors and the athletic department affect the probability of relationship dissolution. As noted, a systematic approach was utilized to ascertain whether groups of variables (economic, demographic, marketing, and athletic success) each predicted a statistically significant amount of the variance in the hazard for relationship dissolution. As indicated in Table 3, the group of control variables related to economic issues was inserted into the model first, to ensure that these variables were controlled for throughout the subsequent analysis. As expected, this grouping of variables did not predict a significant amount of the variance in the hazard for dissolution, χ²(3) = 1.57, p = 0.666.

Next, in the second step, the grouping of demographic variables was inserted into the model. As displayed in Table 3, this group of variables did predict a significant amount of incremental variance, χ²(4) = 57.40, p < 0.001. In addition, the variable related to whether the individual lived in the same state as the university was highly significant, z = –7.30, p < 0.001. The coefficient’s hazard ratio (0.67) showed that the donor living in-state decreased the hazard of dissolution by 32.3%. The variable related to the donor’s employment status was also significant at the α= 0.01 level, z = –2.74, p = 0.006. The hazard ratio (0.82) demonstrated that being retired decreased the hazard for dissolution by 18.2%. Conversely, inserting a variable indicating that the person is actively employed serves to increase the odds that the relationship will end, z = 2.77, p = 0.006, with a hazard ratio of 1.22 indicating it increased the hazard for dissolution by 21.9%. The effects of both of these variables are depicted graphically in Fig. 3, which illustrates the differential in the hazard function over time based on whether the individual lives in the same state or not (Graph A) and whether he or she is actively employed (Graph B). The marketing-related variable was then inserted into the model, reflecting the effect of the number of times donors were contacted by the athletic department. The results included in Table 3 reveal a significant effect, z = –5.79, p < 0.001. The hazard ratio of 0.98 shows that each time the individual was contacted by the athletic department the probability of the relationship ending decreased by 1.6%.

Fig.3

Graphs of smoothed hazard functions based on differentials for donor location (Graph A) and employment status (Graph B).

Finally, the grouping of variables reflecting the on-field performance of the athletic department in each season was inserted. This group of variables also predicted a significant amount of the variance, χ²(2) = 9.56, p = 0.008. The variable reflecting success in men’s basketball was significant at the α= 0.01 level, z = –2.82, p = 0.005. The hazard ratio (0.87) indicated that each win for the men’s basketball team in the NCAA championship tournament decreased the probability of ending the relationship by 12.84%. The variable reflecting football success, which indicated a win in a postseason bowl game, was nonsignificant.

6.1Limitations

It should be noted that while the data analyzed in this study are from an institution that participates at the highest level of NCAA designation (the Football Bowl Subdivision), it is not a member of one of the five major athletic conferences (i.e., the Power Five). Thus, these results may not be generalizable to those NCAA institutions playing in the Atlantic Coast Conference, Big Ten, Big 12, Pac-12 Conference, or Southeastern Conference. The results may also not be generalizable to institutions with different historical records of athletic success; fan base expectations and reactions to athletic success achievement may vary. It is recommended that the modeling approaches utilized in this study be applied to data from a Power Five institution or to institutions with different athletic success histories, to investigate whether the results generalize to institutions competing at other levels. In addition, while these data were longitudinal in nature, only 10 years of data were available for analysis. In the future, we recommend that the survival of the donor relationship be analyzed over a period of longer than 10 years. Finally, in this study we were necessarily limited to an examination of the explanatory variables that were tracked by the athletic department over the 10-year period. There may be supplementary covariates that could prove to be significant predictors, but the effects of which were unable to be analyzed in this study, including other demographic variables such as education orhousehold income.

6.2Future research

Multi-venue research incorporating additional covariates will inform a more efficient and effective customer retention process. Given the advances of customer relationship management platforms, it is recommended that athletic departments collect and future analyses include further variables that might unearth additional insights for those seeking to maximize donor retention. Within the context of athletic donors, this could include behavioral variables such as collecting ticket and merchandise purchasing patterns, giving level, patterns of university integration, additional demographic variables such as gender, as well as operationalizing the quality of athletic department-donor interactions. While the geographic location of the donor was noted in the model based on whether or not the donor resided in the same state as the university, a continuous variable indicating the donor distance from campus would be a preferred approach for measuring the impact of this distance on relationship dissolution. For the intercollegiate athletic environment, specifically, this analysis could also be applied to the length of time that an institution spends in an athletic conference, and the factors that may affect that duration.

This study offers impactful conclusions for FBS athletic departments and serves as a template for future and wide-ranging applications of survival analysis modeling to sport customer relationship management, for customers at all levels of sport including single and season ticket sales buyers, health club attendees, corporate sponsors and beyond. Where retaining customers is an organizational goal, applying survival analysis can be instrumental to informing successful customer relationship strategies.