The influence of return-to-work coordinators on the
recovery of disabled employees
S.B.Kramer
The influence of return-to-work coordinators on the
recovery of disabled employees
Sybren Binne Kramer
December 19, 2011
Abstract
size, and occupations in the sectors construction; accommodation and food service activities; and the sector comprising other services activities.
Keywords: return-to-work, sickness-absence.
1
Introduction
Way back in 1990, Prime Minister Ruud Lubbers said ”The Netherlands are sick”. This was of course figurative speech, but Lubbers wanted to make a point that the public costs of sickness-absence were skyrocketing. His famous phrase set a wave of change in motion in the Dutch social legislation.
It started in 1993 when the committee Buurman was appointed to investigate what caused the large amount of incapacitated employees receiving unemployment benefits. It appeared that social welfare for incapacitation was improperly used for severance pay after reorganizations, and for cheap early retirement. The committee also concluded that industrial insurance boards had little incentive to minimize the influx of the so-called WAO-instromers. This led to the birth of the Wet Terugdringing Ziekteveruim (WTZ) in 1994, which imposed a deferment period of two weeks on employers of small firms, and a deferment period of six weeks on employers of large firms. During this deferment period the employer was obliged to continue the income payments of their employees in case of sickness for at least 70%, before the government would take over.
rehabilitating the large amount of WAO-instromers, despite its expertise and financial ca-pabilities. This large amount of WAO-instromers was envisaged to put to a halt by passing on the rehabilitation incentives to the employers.
Employer obligations increased again when the government enacted the Wet Verbeter-ing Poortwachter (WVP) on the 1st of April, 2002. For instance, the Dutch arbodienst should get involved and a return-to-work (RTW) coordinator must be appointed1. The en-actment of the WVP was aimed to reduce long-term sickness-absence under the philosophy that this could be achieved by appropriate early interventions.
A further reduction of long-term sickness-absence was projected with the Wet verlenging loondoorbetalingsverplichting bij ziekte (Wvlz), that came into force January 1st, 2004. From then on employers were obliged to continue the income payments of their disabled employees for two years instead of one, hereby increasing the responsibility of both the employer and the employee to reduce sickness-absence.
Although the shift of risk and the financial consequences of sickness-absence away from the public sector towards the private sector led to a strong decline of sickness-absenteeism, it also causes the private sector a headache. According to a survey conducted by Mercer under 556 employers in 14 European countries, Dutch employees are on average 7 days per year absent due to sickness2. Each sick day costs employers on average e1603. With nearly 12 billion hours of labor, and a sickness-absence percentage of 4.2%, this amounts to around 10 billion euro’s of costs in 2010 for the private sector4. The same survey shows that the average rise per employee cost for health-related benefits from 2009 to 2010 in The Netherlands equals 3.7%, considerably more than domestic HICP-inflation which was 1.2% in 2009 and 1.3% in 20104. The cost of health benefits as a percentage of total payroll
1Throughout this thesis, we will take the liberty to refer to the arbodienst as the occupational health
service.
2Mercer’s 2010 Survey Report: Pan-European Employer Health Benefits Issues. 3http://img.en25.com/Web/AON/Aon-ESLI-Report.pdf .
(including bonuses) was 2.3% in 2009.
Yet, these are only the direct costs for the employer. Indirect costs arise as, for in-stance, absenteeism lowers productivity, reduces revenue, and damages employee morale. Nicholson et al. (2006) conclude that indeed the cost of missed work to a firm is often greater than (direct) wage costs only. Although the results differ per job, actual costs to the firm are quantified to exceed wage costs by 28% on average.
If we turn the camera around, we see that the duration of time until return-to-work also has important consequences for the employees. Interventions to prevent work disability are likely to be most effective if implemented early (after the first few weeks), due to the risk of chronicity (Frank and Sinclair (1998)). If return is delayed, employers may be induced to find replacements to maintain continuity of production. In addition, they can stigmatize incapacitated workers, making them less successful applicants for future jobs, for 33% of the employers include employees’ sickness-absence records in their performance appraisals2. Moreover, skills and work habits depreciate naturally when people are off work for a long time.
Delayed return also affects the human psyche. Being off work or experiencing significant life changes, as are often brought about by injury or illness, can alter a person’s psycholog-ical well-being, leading to problems such as stress, anxiety and depression. This, in turn, can affect his ability to carry out aspects of the work, cf. Briand et al. (2008), McKee-Ryan et al. (2005), Marhold et al. (2002) and Goedhard and Goedhard (2005)5. Furthermore, issues to do with confidence and motivation (such as worries about ability to return to the workplace, or perform in the job) are also reported to affect work-ability, especially for in-dividuals who have been off work for longer than a few weeks, cf. MacEachen et al. (2007) and Magnussen et al. (2007). Equally important to many stakeholders is the consideration that being in paid employment often contributes positively to a person’s well-being, cf.
Ross and Mirowsky (1995), Steadman-Pare et al. (2001).
It is evident that both employers and employees have a lot to gain from a fast re-covery process in case of disability. There is, however, another stakeholder that benefits from short(er) durations until return-to-work. Now that the private sector has become re-sponsible to maintain the income payments of their disabled employees, disability poses a significant amount of financial risk, especially to small firms. And where there is risk, there is a possibility to insure against this risk. When the financial risk of disability is passed on to the insurance company, they have an incentive to facilitate the recovery process as well. Our data sponsor is such an insurance company, where a RTW coordinator fulfills the role as a facilitator. And because responsibility and accountability are two sides of the same coin, it is important for the company to monitor the performances these RTW coordinators.
partial-and the full recovery rate of the claimants, as well as their influence on the fall-back rate, while concurrently correcting for the other risk factors that are at our disposal.
recov-ery rates. With regard to other risk factors, old age slows down the recovrecov-ery process, and we also find lower full- and partial recovery rates for claimants that work for firms with over 100 employees. Lastly, just as in Spierdijk and Koning (2011), the fall-back rate is predominantly unpredictable. Only claimants of medium-sized firms show an economically significant result; they have lower fall-back rates.
2
Problem Formulation
Employers in The Netherlands are obliged to continue the income payments of their dis-abled employees during the first two years of disability. One can imagine that this poten-tially puts a huge financial strain on the employer, especially for employers with a small number of employees. Luckily, employers can insure themselves against this financial risk at insurance companies, and one of them is actually our data sponsor. Besides a cushion against this financial risk, this insurance company also provides support to meet legislative obligations, as laid down in the Wet Verbetering Poortwachter. Because the financial risk is now passed on to the insurance company, they have an incentive to get the incapacitated back to work as quickly as possible.
In this respect, a central role is played by the so-called process director, or return-to-work coordinator. The return-to-return-to-work coordinator is the contact between employer and the insurance company, and decides together with the arbodienst on the steps that will be taken to facilitate the recovery of the incapacitated employee. The Dutch arbodienst is an independent organization that supports employers/companies with the provision of safe working conditions for their employees, and also assists with disability policy, notably via assigning suitable doctors.
80% of the income payments for this respective employee. Following Spierdijk and Koning (2011), the loss of capacity to meet occupational demands in percent will be referred to as the replacement rate. Furthermore, note that a replacement rate of X percent means that the disabled employee can work for 100-X percent of the time he would be able being healthy. This replacement rate is determined after deliberation of the employer with the RTW coordinator of the insurance company that is responsible for the disabled employee.
So, we basically have two research questions to answer:
1. What is the influence of return-to-work coordinators on the complete recovery of their disabled employees?
2. What is the influence of return-to-work coordinators on the partial recovery of their disabled employees?
3
Description of the data
This section starts out with a description of the data, and follows up with a section about the explanatory variables where we will motivate our choices regarding their use. We end with a description of related findings in the literature.
3.1
Data description
the censored status. Average disability durations of employees vary from 21 to 32 days for the RTW coordinators in Team 1, and from 7 up to 36 days for their colleagues of Team 2. However, this average of 7 days is obtained for a RTW coordinator who was responsible for only two disabled employees, rendering this average non-informative as it is very much prone to idiosyncrasies. That being said, a first glance over these averages shows that there are some - not negligible - differences, even if we disregard RTW coordinator 14 (and maybe even also number 17) of Team 2. The occupational health service-centers in Tilburg and Eindhoven take on the largest share of disabled employees with 17.9%, and 16.1%, respectively. Average disability durations for this variable vary between 23 and 29 days, disregarding this figure for Zwolle as it is only based on 9 observations. The largest occupational sector in our data set is the wholesale and retail-sector providing work to over a quarter of all claimants, 26.1%, followed by the human health & social work activities-sector as the second largest occupational sector with 15.1% of the claimants. The least represented are the energy sector and the sector responsible for water supply and waste management activities, which together make up for barely 0.05% of the claimants. Just as we have seen with the RTW coordinators, inter-sectoral differences in the average disability duration are clearly present, ranging from 14 to 39 days if we ignore the smallest two sectors for the moment. Another striking difference exists between claim incidence in 2010 and 2011, and between the length of their average disability spells. These differences are, however, likely due to the fact that the observation window covers only a little less than four months of 2011, and disability spells starting in this year thus have a lower upper limit. An overview of most of the aforementioned figures, and many others, is given in Table 2 starting on page 62.
The choice for three health states is first and foremost constrained by the computational power we have at our disposal, and secondly, by our reluctance to group variables which reduces the number of parameters that need to be estimated, but at the expense of their interpretation. Computational limits are a significant factor as for the multi-state analysis the already large data set will be extended in such a way that the number of rows will double. The three health states together allow for six different state transitions, namely D100→D50, D100→H, D50→D100, D50→H, H→50, and H→100. However, we are not going to model the transitions H→D50, and H→D100, because the available data does not include information about employees that did not enter a disability spell during our observation window. This means that there would be a selection effect, making the data not suitable for modeling claim incidence. The three health states together yield 37941 transitions in total. Censored durations are not included in this figure as the exit state remains unknown. Transition frequencies from one state to another are shown in Table 3 on page 67. The majority of the transitions, 81.9%, were from state D100 to state H. Table 4 on page 67 displays that this transition took 11 days on average, distinctively less than the average of any other transition. This is because this transition includes short mundane sicknesses like the flu, a cold, Monday (morning) sickness, and head- and stomach ache, all of which together explain the large number of short-term durations, see figure 1 on page 68. Table 3 also shows that 91.2% of all transitions initiated in state D100. Besides short-lived sicknesses, this state contains severe disabilities that recover slowly, which is reflected in the higher average number of days before entering a state with a lower replacement rate compared to this average for a similar transition from state D50. Furthermore, Table 3 also shows that 88.7% of all transitions led to full recovery.
cor-responding transition-specific survival function decreases sharply during the first (roughly) 25 days. The same survival function remains practically constant from 150 days on, when only severely disabled are left in D100. Complete recovery from state D50 generally takes more time, witness the slower decline in its corresponding survival function over the first 25 days. The latter catches up after 25 days, however, when the decline in the latter survival function is sharper, which makes sense as one expects complete recovery to be more likely at a lower replacement rate. As a result, a larger share of disabled employees in state D50 have been fully recovered after approximately 250 days, compared to their equivalents in state D100. Similarly, we observe that recovery is faster for lower replacement rates, since the decline of the survival function for complete recovery from D50 is sharper than the decline of the survival function for partial recovery from state D100 to D50. We have already pointed this out in the previous paragraph; Table 4 shows that a departure from state D100 to state D50 takes 57 days on average, against 31 days on average for complete recovery from state D50. Not much can be said at this point about the survival function for the transition D50 to D100, where disabilities worsen, other than that the cutoff of this function before reaching zero is because of the presence of censored durations that take longer than the last observed duration. Finally, and not surprisingly, the general shape of the survival functions is convex, indicating negative duration dependence.
3.2
Explanatory variables
type, either with a deferment period of a number of days, or a policy of stop-loss type. It is hard to argue that any of these three variables would have an effect on the disability spells of the insured employees. In addition, the variable conventional is correlated with the variable Deferment period and contains even less information than the latter.
Old age is widely accepted to prolong the disability duration, see for instance Tate (1992), MacKenzie et al. (1998) and Spierdijk et al. (2009) among many others. The reasoning is straightforward, as the years evolve we become more fragile and we need more time to recover. As a consequence, Fenn (1981), Fenn and Vlachonikolis (1986), Cheadle et al. (1994) and Oleinick et al. (1996) find that sickness-absence under older workers is an important consideration for (early) retirement.
sector. We conjecture, however, that the reason for the prolonged sickness-absence in both these sectors has to do with the physical nature of its jobs. Physically intensive labor is shown to lower return-to-work rates in Lanier and Stockton (1988), Høgelund (2000) and Krause et al. (2001). Evidence for shorter sickness-absence was found for employees in the financial and insurance activities sector in Linder (2005); in the services sector by Maeland and Havik (1986); and finally, with a public employer in Infante-Rivard and Lortie (1996). Rehabilitation prospects in the public sector are presumably favored by ample availability of modified jobs and tasks.
to find contradictory results on the subject of return-to-work after disability, given the bulk of available literature about it, though it should make us humble in advertising our knowledge about causality.
The focus of our study is on the individual effect of the RTW coordinators on the recovery of their employees. As we have already mentioned in section 2, the literature is supportive to the influence of the efforts of RTW coordinators on the recovery of injured workers, e.g. Franche and Krause (2002), Bernacki and Tsai (2003), Morrison et al. (1998) and Spierdijk et al. (2009).
We mentioned in section 3.1 that there is quite a difference in average disability dura-tions for the employees of the various RTW coordinators. The two-sample log-rank test applied to the variable RTW coordinator results in a P-value of 0, so we can expect dif-ferences between them. Somewhat surprisingly - the average duration observed for Team 1 equals that of Team 2 - a differential effect may also be observed for the variable Team (P-value 0.002).
4
The Model
The model we will be using to answer the research questions is the famous Cox Proportional Hazards (CPH) model, after Cox (1972). It has since then been the most widely applied model for modeling duration data. First and foremost because no assumptions have to be made with regard to the baseline hazard, and second, because of the straightforward interpretation of the results after a suitable CPH model has been fitted. A fundamental assumption of the CPH model is that the relative hazard rate (here, the instantaneous probability of recovering from a disability) is constant over time for different categories, and for different values of the continuous variables6. For instance, if disabled employees of RTW coordinator 28 are twice as likely to recover than their companions of misfortune of RTW coordinator 1 on the tenth day of disability, they are also twice as likely to do so on the twentieth day, on the ninetieth day, and so on. In this section we will outline the CPH model in continuous time, and we will use terminology that is suitable for our study. In addition, we will outline choices concerning frailty, the baseline hazard and two time scales. This section ends with a subsection that gives some insight in a relevant data preparation, and in the manual implementation of the likelihood function that is adapted to our specific choice of capturing frailty.
4.1
The single-state model
Let T be defined as the random variable that gives the time of recovery, measured in some time unit since the start of the disability spell. The hazard rate λ(t) is then defined as
λ(t) = lim ∆t→0+
P r(t ≤ T < t + ∆t|t ≤ T )
∆t . (1)
Now suppose that for each employee a vector x of k characteristics is known, x = (x1, x2, . . . , xk), where the x0s may be functions of time. Cox’s Proportional Hazards model relates these k regressors to the hazard rate in the following way
λ(t|x) = λ0(t) exp(xβ), (2)
where β is a k × 1 vector of unknown parameters that describe the effect of x on the hazard rate, and λ0(t) is an unknown function giving the baseline hazard function for the case when x = 0. In his original paper Cox points out that (xβ) can be replaced by any known function h(x, β), but we will stick to the former. An important feature of the hazard function in equation (2) is that the exponential form ensures positivity of λ(t|x), provided λ0(t) is positive for all t, and thus β can be estimated freely. Furthermore and conveniently, in order to be able to estimate β and draw inferences no assumptions have to be made with regard to the shape of the baseline hazard function, as we will see shortly.
The estimation of β proceeds along the lines of partial likelihood, as put forward in Cox (1972, 1975). However, it was not until Cox (1975) that he called a spade a spade, as Cox himself admits that in Cox (1972) he misleadingly called it conditional likelihood. Assume that recovery occurs at distinct (uncensored) times t1 < t2 < . . . < tm, and in addition that at tl, l ∈ {1, 2, . . . , m}, a set of k characteristics, xl = (xl1, xl2, . . . , xlk), is known for employee h. The conditional probability that disability spell l ends at time tl, given that any of the m − l + 1 ongoing spells could have ended at tl equals
λ(tl|xl) m X g=l λ(tl|xg) = mλ0(tl) exp(xlβ) X g=l λ0(tl) exp(xgβ) , (3)
is as follows L(β) = m X l=1 ( xlβ − log " m X g=l exp(xgβ) #) . (4)
The βξ’s, ξ ∈ {1, 2, . . . , k}, are then found by differentiating equation (4) with respect to the βξ, ∂L(β) ∂βξ = m X l=1 xlξ− m X g=l xgξexp(xgβ) m X g=l exp(xgβ) , (5)
equating it to zero, and finally solving it for the βξ’s.
In practice we hardly ever deal with data sets for which all disability spells end at distinct observed times. If a spell is censored between tl and tl+1, it appears in the de-nominator of the likelihood function of ordered uncensored observations 1 through l, and nowhere else. Censored spells do not enter the numerator of the likelihood function at all. Ties contribute to the likelihood function with their own (unique) numerator, but they all share the same denominator.
Now suppose a CPH model has been fitted successfully. We are interested in the effect of the explanatory variables on the instantaneous recovery rate of employee w. In order to interpret the estimated coefficient for one of the variables, say βξ, we can take a look at the ratio
λ(t|xw1, xw2, . . . , xwξ+ 1, . . . , xwk) λ(t|xw1, xw2, . . . , xwξ, . . . , xwk)
= exp(βξ), (6)
100(exp(βξ) − 1)%. Similarly, if we want to assess whether RTW-coordinator 28, say, with indicator variable xw28, does a better job than RTW-coordinator 1, with indicator variable xw1, we can calculate
λ(t|xw1= 0, xw28 = 1, xw−)
λ(t|xw1= 1, xw28 = 0, xw−)
= exp(β28− β1), (7)
where xw− is a vector with the remaining k − 2 characteristics, and this would mean that
employees under the wing of RTW-coordinator 28 have a relative advantage/disadvantage in their recovery rate of 100(exp(β28− β1) − 1)%.
4.2
The multi-state model
For the multi-state model we constructed three health states, namely D50, D100 and H. For notational convenience, we will refer to these states in consecutive order as state 2, 1 and 3. This results in four possible transitions, as we have already argued in section 3.1 that we are not going to model claim incidence. The hazard rate for transition i → j for an individual with risk characteristics vector x is then given by
λij(t|x) = λij,0(t) exp(xβij), (8)
4.3
Unobserved heterogeneity
In section 3.1 we pointed out that we lack information about two often significant determi-nants for the expected length of a disability duration, namely gender and disability type. So it is unlikely that the reasons for the variability in the hazard rate will be fully captured by the set of risk characteristics that are at our disposal. This statement remains erect even if we would have had information about gender and the type of disability. Think for instance of unobserved differences in the willingness to adhere to steps in an occupational rehabilitation program, or inevitably, in an employee’s recovery potential due to genetic differences. The presence of unobserved individual-specific risk factors leads to unobserved heterogeneity, or frailty, in the hazard rate. This may lead to incorrect inferences about the results of the modeling estimation. For example, positive duration dependence will be underestimated, and negative duration dependence will be overestimated, cf. Ridder and Verbakel (1983); Hougaard (2000). In addition, the magnitude of regression coefficients will be underestimated, cf. Ridder and Verbakel (1983); Lancaster (1985); Hougaard (2000), and the response of the hazard rate to a unit change in a regressor is no longer constant, instead, it declines over time, cf. Lancaster (1979); Hougaard (2000). Aside from these obvious pitfalls, the last fact seriously jeopardizes the application of the CPH-model due to the emanating risk of a proportionality violation.
this discrete frailty distribution is not subject to restrictions besides the obvious ones (value of each mass-point is unique and the probabilities sum up to unity). In contrast, a necessary restriction for continuous frailty distributions is E(W ) = 1 to avoid the problem of identification. We do have to impose a restriction ourselves, however, on the number of estimated parameters for the frailty distributions of the multi-state model. For the frailty distribution in the single-state model we will estimate at most four or five mass-points, which, together with their associated probabilities, will require the estimation of at most seven or nine frailty parameters because we need to estimate N mass-points and N − 1 associated probabilities. This is no problem. Following the same approach for our multi-state model with 4 transitions, though, requires the estimation of 4(2N − 1) frailty parameters, which is already a serious challenge for the Millipede Cluster7 for N = 2. In order to reduce this number we are going to use a so-called one-factor loading specification just as in Spierdijk and Koning (2011). So we assume that the n-th transition-specific frailty term for transition i → j, vij,n, relates to two constants aij, bij and an N mass-point individual-specific discrete random variable W with PN
n=1P (W = wn) = 1 such that vij,n = aijwn+ bij. Together with the normalization restrictions, a12= 1 and b12= 0, this one-factor loading specification requires the estimation of 2N + 5 parameters, hereby saving 6N − 9 parameters. By its very nature, N ≥ 2 otherwise there would be no frailty. Hence, with two individual-specific mass-points we would save the estimation of three frailty parameters, which saves a considerable amount of computational time, and in addition eases the optimization procedure. Inclusion of the unobserved heterogeneity variables expands equation (2) to
λ(t|x, w) = λ0(t) exp(xβ + w), (9)
7The Millipede Cluster is the supercomputer of the University of Groningen that is used by scientists
and equation (8) to
λij(t|x, vij) = λij,0(t) exp(xβij + vij), (10)
with w being a realization of the unobserved (individual-specific) heterogeneity distribution of the single-state model, and similarly for vij representing a transition-specific heterogene-ity term of the multi-state model. Our models assume that the unobserved heterogeneheterogene-ity is independent of both x, our vector of observed risk characteristics, and t, so that the frailty distribution does not change over the course of our observation period. The lat-ter assumption implies that the unobserved helat-terogeneity lat-term is identical for different durations (and different transitions) of the same claimant.
4.4
Duration dependence
Duration dependence is the phenomenon that the value of the hazard rate at time t depends on the time up to and including time t. When the hazard function slopes downwards there is negative duration dependence, and there is positive duration dependence if this function slopes upwards. Since we assume that only the baseline hazard function depends on t, the duration dependence is completely determined by the shape of this baseline hazard function. Common choices to describe this function are a Gamma hazard, a Weibull hazard and a piecewise constant function. Our preferred choice is the Weibull hazard, because it requires the estimation of only one parameter which does not put too much strain on the likelihood estimation procedure. Under the Weibull assumption, the baseline hazard of equation (10) (and similarly for equation (9)) are as follows
with αij > 0. Values of αij > 1 imply positive duration dependence, and αij < 1 implies negative duration dependence. If αij = 1 there is no duration dependence and the baseline hazard function is a result of an exponential distribution.
4.5
Time scales
however, incorrect inferences can still be expected as the explanatory variables will likely have a different impact upon λij(t∗), with t∗ > 0, for employees who have spent all their time so far (t∗ days) in health state i, as opposed to employees who have spent at least some time already in a different health state than i. An idea is to create an indicator variable to distinguish between these two groups. However, Spierdijk and Koning (2011) rightly points out that this will lead to a problem of identification with the included frailty term, and it does not make sense to leave out the frailty term as many unobserved characteristics will not be included in a substitute term. Another idea to reduce the chance of incorrect inferences is to estimate each transition-specific hazard rate in both the clock-forward and the clock-reset setting, which is exactly the strategy that we are going to adopt.
So far, the discussion about the different time scales that are available for the multi-state model has circled around the notion of the Markov property, without actually mentioning it. Loosely speaking, the Markov property states that the future is only influenced by the present, and not by the past. As a consequence, a multi-state model is said to be Markovian if transitions to the next state, and the times at which they occur, are only influenced by the presence in the current state. Putter et al. (2007) put forward that only clock-forward models can be Markov models, arguing that for clock-reset models the Markov property cannot hold since the time scale itself depends on the history through the time since the current state was reached. However, both the clock-forward- and the clock-reset multi-state model are so-called semi-Markov models when we assume that the sojourn times in every state only depend on the presence in this state, and in addition, on the elapsed time since entry of that same state8.
8Consider a stochastic process {X
t, t = 0, 1, 2, . . .} that takes on a countable number of possible values.
If Xt= i, then the process is said to be in state i at time t. Define Pij = P (Xt+1= j|Xt= i). Suppose
that each time a process enters state i it remains there for a random amount of time, and then makes a transition into state j with probability Pij. Such a process is called a (first-order) semi-Markov process.
4.6
Implementation
As we have already written in section 3.1, for the multi-state analysis our data set for the single-state analysis will be extended. Because we defined three health states, the number of rows will double, which intuitively makes sense. For instance, when an employee starts a disability spell with a replacement rate of 100% and recovers after 21 days such that he can take on 40% of his workload would he be healthy, he moves from state D100 to state D50. This transition gets an uncensored status. However, this employee could have recovered in such a way that he moved into state H. Therefore, the row of the data set that belongs to this disability spell is replicated, and this replicate is added to the data set. Subsequently, the end state of this new row is changed into state H, and this transition receives the censored status.
Furthermore, we have chosen to capture unobserved heterogeneity in our models by means of a discrete probability distribution with at least two mass-points. Unfortunately, there is no built-in code in R that supports this way of capturing frailty9. So we have to program this ourselves, and that includes programming the likelihood function that needs to be maximized. For employee w, the likelihood looks as follows:
Lw(v) = K(w)
Y r=1
S(twr|xw, v)1−cwrf (twr|xw, v)cwr, (12)
where the variables are defined as:
• cwr is the censoring indicator for employee w with spell r. cwr = 0 for a censored duration;
• K(w) denotes the number of spells of employee w;
9R: A language and environment for statistical computing. R Foundation for Statistical Computing,
• twr is the length of spell r of employee w;
• v is the frailty value for employee w (constant over r);
• xw is a vector of length k containing the personal risk characteristics of employee w;
• S(t|·) is the survival function, the contribution to the likelihood function for censored durations;
• f (t|·) is the density function returning the probability of ending a spell at time t. It equals the contribution to the likelihood function for uncensored durations.
We will derive the likelihood function for the case that the frailty distribution has two mass-points. It can be easily extended to a situation where this distribution has more mass-points. For two mass-points the likelihood function then becomes:
L(v) = Ω Y w=1
[Lw(v1) ∗ p1+ Lw(v2) ∗ p2] , (13)
where Ω is the total number of (unique) employees. Writing the likelihood function like this suggests that it should only be optimized over v. This is not the case.
For the Cox model, we have the relation
S(t|x, v) = [S0(t)]λ, (14) with S0(t) = exp(− Z t 0 λ0(u)du), (15)
baseline hazard, we can derive the required survival function, it equals
S(t|x, v) = exp(−λtα), (16)
where λ is as before. It now follows that
f (t|x, v) = exp(−λtα)αtα−1λ, (17)
because f (t) = d(1−(S(t))dt .
5
Results
This section starts out with a part about variable selection and other choices that we had to make before, and during the estimation process. It follows up with a section that gives the (quantitative) results for each transition. Subsequently, we give an interpretation of these results, and the last section covers the incorporation of frailty and the outcome of this.
5.1
Variable selection and other choices
Due to the large amount of variables at our disposal, it was not possible to successfully fit a multi-state model to the data using all variables. Rather than leaving out some variables based on taste and argumentation, or grouping them for similar reasons, we decided to first fit a single-state model to see if we could get some empirical support for our variable selection. The results of this model are shown in table 5 that starts on page 71.
Let us begin to make clear that the sole purpose of the estimation of the single-state model is variable selection, nothing more. A multi-state model is more advanced and therefore its results are considered to be more meaningful. Moreover, the results that we will get with a multi-state model specifically match those required to answer our research questions.
each of these four sectors did not make us object against this group composition, though we may have raised an eyebrow or two for the presence of the human health & social work activities-sector.
The whole variable selection process described above resulted in a reduction of 100! parameters to be estimated for the multi-state model (25 fewer parameters for 4 different transitions), which was both substantial and necessary. As a result, we got a model with which we are able to assess the individual performances of the RTW coordinators, while taking into account contract features and other personal characteristics. In other words, we are ready to answer our research questions.
5.2
Estimation results
This section consists of four parts, one for each transition. The results for each transition are shown in Tables 6-9 on pages 75-81. Each table displays the results of the clock-forward state model, which is our preferred model. For the results of the clock-reset multi-state model we refer to Tables 12-15 on pages 84-90 in the Appendix. They reveal that both the time-in-system- and the time-in-state setting produce results that are qualitatively the same, and quantitatively somewhat different.
The differences in the hazard rates as a result of a change in the variables discussed below are marginal effects, that is, under the ceteris paribus assumption. Furthermore, the main objective of this section is to translate the mathematical results into words. Explanation and interpretation of these is given in section 5.3.
5.2.1 Transition from state D100 to state D50 (partial recovery)
also recorded for contracts of which the total sum assured is larger, the difference being 22% per million insured euro’s. In addition, if it is not an umbrella contract, one can add 20% to the recovery rate. The last contract feature to be discussed here is the variable describing the number of insured employees on the insurance policy. Insurance policies with over a hundred insured employees feature 26% lower recovery rates.
Moving on to the personal characteristics we find that the recovery rate decreases with age. Ten extra years of age result in a 16% lower recovery rate. The most anticipated results, however, are those concerning the RTW coordinators. There is evidence that claimants under attendance of RTW coordinator 4, 9, and 13, all of Team 1, have an impressive 45%, 39% and 61% higher recovery rate. Claimants under attendance of RTW coordinator 22 of Team 2 have an equally impressive 37% higher recovery rate. We found no evidence of a team effect here. Finally, the group consisting of the occupational sectors construction; accommodation and food service activities; and the sector comprising other services activities records 20% lower recovery rates. The group consisting of the occupa-tional sectors information & communication; real estate activities; professional, scientific and technical activities; and human health and social work activities records 43% higher recovery rates.
5.2.2 Transition from state D100 to state H (full recovery)
rates. The opposite is true for contracts with over 100 registered employees, the differ-ence being 24%. So, there is a nonlinear effect here; recovery rates first rise at 21 insured employees in order to decrease sharply at 100 insured employees. Significant differences are also recorded for different types of deferment periods. In comparison to a deferment period of up to and including 10 days, any of the other three types of deferment periods is associated with larger hazard rates. The contrast is 14% with a deferment period of 11-30 days, 25% with a deferment period above 30 days, and 34% for stop-loss-type contracts.
Concerning the personal characteristics there are no surprises in the age department. An extra ten years of age lowers the hazard rate with 21%. The best performing team of RTW coordinators is Team 2. Guidance from a RTW coordinator of Team 2 boosts your hazard rate 10% on average. RTW coordinators 2, 10, 16, 17, 19, 21, 25, 28 and 33 of Team 2 record larger hazard rates than any of the RTW coordinators of Team 1. This is not to say that everyone of Team 2 did better than anyone of Team 1, to the contrary, RTW coordinator 5, 8, 9 and 11 of Team 1 record 15-25% larger hazard rates than RTW coordinators 12, 22, 27, 30, and 32 of Team 2. In addition to this, RTW coordinator 11 of Team 1 also scored 4% better than his colleague number 20 of Team 2. Within Team 1, the best recovery rates are associated with RTW coordinator 11, the worst with RTW coordinator 23, the difference is 54%. The largest difference within Team 2 is 80% in favor of RTW coordinator 17, relative to his colleagues with number 12, 22, 27, 30 and 32. The biggest difference overalll between the RTW coordinators is thus observed between number 17 of Team 2, and number 23 of Team 1. The difference is a whopping 123%. Furthermore, there is no evidence of heterogeneous recovery rates between RTW coordinators 1, 3, 4, 6, 7, 12, 13, 18, 22, 24, 26, 27, 29, 30, and 32.
rates than the group consisting of the service centers in Alkmaar, Amsterdam, Goes, Haarlem, Rotterdam and Zaandam. Lastly, just as for the transition from state D100 to D50, the best recovery rates go with the Light occupational sector, the worst with the Heavy occupational sector. The difference with respect to the baseline category here equals, 42% and -23%, respectively.
5.2.3 Transition from state D50 to D100 (fall-back)
Only two contract features have a significant effect on the fall-back rate. First, the fall-back rate is positively related to the total sum assured on the insurance policy. The fall-back rate increases 20% per million euro’s that are added to the total sum assured. With the knowledge that we recorded a similar effect on the recovery rate for the transitions from state D100, this result immediately seems strange. We will come back to this in section 5.3. Second, an employee count between 21 and 100 is associated with a 25% lower fall-back rate compared to an employee count of 20 or less.
It looks like the fall-back rate is largely unexplainable with the given set of variables, which was also the case in Spierdijk and Koning (2011). This is not a huge surprise if we consider that it is also very hard to predict if and when an employee becomes incapacitated. In a way, fall-back occurrence is similar.
5.2.4 Transition from state D50 to state H (full recovery from mild illness)
respectively. Occupational class, occupational health service, and team composition do not significantly affect the recovery rate.
5.3
Interpretation of the results
Table 10 on page 82 provides an overview of the aforementioned results that makes a comparison easy. We observe that both partial recovery and full recovery is faster for claimants that are insured under brand name B. The difference between the two brands is in the way the insurance product is offered to entrepreneurs. Brand A is only sold via intermediaries who support entrepreneurs choosing a suitable insurance contract. Brand B is also sold via intermediaries, but mainly by banks that often offer a wide range of insurance products nowadays next to the practice of their ordinary day-to-day businesses. Whilst intermediaries often remain involved after they have sealed the deal by taking care of administrative work that surrounds sickness-absence, the banks do not. So the suspicion is that the extra link in the chain that goes with brand A, and therefore possible less commitment from the side of the entrepreneur, causes slower recovery.
the full wage without having to work the full 100%, however, again this form of moral hazard then affects every employee irrespective of the total sum assured. So, we have no explanation for the fact that fall-back rates increase with the total sum assured. And even if we would have an explanation, the same variable that makes partial recovery from state D100 to D50 more likely at any given moment also makes it more likely to fall-back from state D50 to D100 concurrently. This means that a causal explanation for the effect of the total sum assured on the hazard rate of one these transitions immediately contradicts the effect of the total sum assured on the hazard rate of the opposite transition. Interpretation of the effect of this variable is therefore impossible.
diversify risk from absence more easily than small firms. Compared to contracts with 20 or less insured employees, full recovery is somewhat quicker for contracts with 21-100 insured employees. It is hard to find an explanation for this difference without contradicting the arguments we just gave concerning lower recovery rates for large firms. Maybe the difference is just due to mere chance. Whatever it is, the most important information to take away here is that large firms show significantly lower recovery rates for their employees, and that a contract with over 100 insured employees signals a sufficiently large firm for that matter. In addition, note that the effect that the number of employees has on the full recovery rate from a severe illness is not linear. Recovery rates from a severe illness are higher for employees of medium-sized firms, but distinctively lower for large firms. However, the economic impact of the difference between small- and medium sized firms is only modest. If sickness-absenteeism is shorter on contracts where the number of insured workers is between 21 and 100, it seems to make sense that the reverse is true for the fall-back rate. Fewer anonymity for the employees is experienced in medium-sized firms compared to large firms, making them less vulnerable to moral hazard, which may explain the difference of the fall-back rate between medium-sized and large firms. However, it does not explain the difference in the fall-back rate with the small firms. So, again we observe a nonlinear effect, and just as for the opposite effect on the full recovery rate for this variable, we remain in the dark for the underlying reasons.
recover from injury, and this indeed seems to be the case. It also explains why the recovery rate rises more when the length of the deferment period extends over 30 days. One may then legitimately wonder why the employer’s confidence is indeed justified. It might be because the employer takes an active role in the recovery process of its employees, but there are many possible explanations. Even better recovery rates are recorded for policies that are of stop-loss type. With this type of deferment the insurance company will only start with benefit payments when the gross income payments of the employer have exceeded a certain amount of euro’s. Whether a deferment period is agreed upon in terms of time or in terms of money does not really matter, so management’s confidence in the recovery ability of their employees may very well be the case here as well. However, because that data does not contain any information about the height of the agreed amounts of money that should be exceeded before benefit payments commence, it is hard to give a more thorough interpretation.
When we decided to include a dummy variable to indicate whether an insurance policy was agreed upon beneficial conditions for the employer, it was surmised that we could associate this contract feature with faster recovery. The idea was that employers who take out an insurance policy sans beneficial conditions, thus for a higher price, signal fewer faith in the recovery potential of their employees. To the extent that their faith is justified, this would mean higher recovery rates for claimants that are insured on an umbrella contract. The actual result, however, turned out to be the exact opposite for partial- and full recovery from a severe illness, with no clear explanation available.
recovery from a severe illness, and somewhat smaller for full recovery from a mild illness. Concerning the sectoral differences, recovery rates differ as the group names suggest. The magnitude of the group effect is substantial, but it is not immediate that each group member contributes equally to the group effect. For instance, it might be that recovery takes longer in both the construction-sector and the other services-sector, but that there is no such thing in the accommodation and food service activities-sector. Or maybe it is the other way around, there is no way to tell. That is the price we have to pay for the grouping together of some occupational classes. It has been shown before, though, that the construction sector is one where recovery takes place at a relative slow pace, due to the physical nature of its tasks, and physical work is associated with longer sickness-absence. Jobs in the accommodation and food service activities-sector are usually physical as well, and in addition, can be very stressful at times. If this leads to a psychological type of disability, recovery prospects are often unfavorable, see for example Spierdijk and Koning (2011). A glance over the list of professions that fall under the other services-sector reveals that a vast amount of them is also physical (repair of various consumer products, hairdressing etc.). For the group of sectors that shows relatively short disability durations, the real estate sector is one that has had a hard time ever since the outbreak of the financial crisis late 2008, and its employees may want to recover as quickly as possible to avoid precarious performance appraisals. Motivation for fast recovery may also play an important role in the human health and social activities-sector, where employees are scarce, and one simply cannot be missed at the workplace. The information and communication-sector and the professional, scientific and technical activities-communication-sector predominantly involves work behind a desktop PC that is rather mental than physical, work that can be assumed to be resumed fairly quickly.
of the corresponding service centers. The subsequent knowledge that the working method to emphasize close cooperation between doctor and RTW coordinator was first adopted in the south-east then supports the regional difference. On the other hand, Spierdijk and Koning (2011) argue that employees possibly benefit from the dense network of health care services that the insurance company has established in the south over the years. And be-cause claimants enjoy care of the occupational health service-center based on geographical vicinity, there is also some wisdom in the latter interpretation. Anyway, just as for the sectoral differences, the occupational health service-centers were grouped together. It is not immediate that every group member contributes equally to the total group effect.
vicinity of their work, it is not a big surprise that there is a clear distinction in how the claimants are distributed over the different occupational health service-centers. Team 1 has claimants that are distributed over service centers in Eindhoven, Heerlen, Tilburg and Venlo; claimants of Team 2 are distributed over service centers in Alkmaar, Amsterdam, Goes, Haarlem, Rotterdam, Zaandam and also Breda10. Now notice that except for Breda, all service centers in the south-eastern part of The Netherlands are associated with Team 1. Also notice that the service centers in the south-eastern part of our country record higher full recovery rates from a severe illness compared to service centers in the western part of our country. So, if we had not included a dummy variable indicating the geographical positioning of the occupational health service-centers, we would have been likely to find higher full recovery rates for Team 1. But we have, so an explanation for the difference in the full recovery rate associated with the teams of RTW coordinators must be found elsewhere. Maybe the difference can be found in the way the team captains direct the process, as for instance both captains differ in their work experience. In any case, it is unlikely that there is a selection effect that causes Team 1 to get the relative unfortunate cases, because the group composition is merely based on the zip code of the company. In addition, both teams are responsible for a large group of employees, which should make these groups sufficiently homogeneous. A glance over the data confirms this assertion.
Zooming in on the RTW coordinators of Team 1, we see that claimants guided by coordinators 5, 8, 9 and 11 have the highest full recovery rates. Claimants guided by RTW coordinators 4, 9 and 13 show the highest partial recovery rates. The data reveals that 81% of all claimants that are guided by RTW coordinators 5, 8, 9 and 11, at the same time enjoy care of the occupational health service-centers of either Eindhoven or Tilburg. The same holds true for 86% of all claimants that are guided by RTW coordinators 4,
10Actually, also 12 employees guided by Team 1 were assigned to the occupational health service-center
9 and 13. So, it might be that these claimants reap the benefits of the fact that the collaboration between the RTW coordinators and the company doctors has the longest history in the south-eastern part of our country. Moving on to Team 2, we observe that 77% of the claimants that are supervised by RTW coordinator 33 concurrently enjoy care of the occupational health service in Goes, and 86% of the claimants supervised by either RTW coordinators 25 or 28 from the service center in Rotterdam. We have no explanation for the latter.
The largest effect on the recovery rate is recorded for RTW coordinator 17 of Team 2. Although there was a sufficient amount of observations for this RTW coordinator to include this data in our model, at the same time we realize that compared to the amount of observations that are available for his colleagues, the data for RTW coordinator 17 remains sparse. This, in turn, means that this outcome is surrounded by more uncertainty, and should therefore be treated with more care. That being said, faster partial recovery from a severe illness is achieved with RTW coordinators 4, 9 and 13 of Team 1 and RTW coor-dinator 22 of Team 2, faster full recovery from a mild illness only with RTW coorcoor-dinators 16 and 22 of Team 2. The magnitude of the differences, ranging from +37% to +70%, is impressive. However, there is no evidence of a team effect for either transition. In addition, while there are a lot of differences in the performances of the RTW coordinators regarding the full recovery from a severe illness, the vast majority of the RTW coordinators show equal performances for the partial recovery from a severe illness, as well as for the full recovery from a mild illness.
mild illness. RTW coordinator 22 seems to present an odd case. He or she shows above av-erage results for partial recovery as well as for full recovery from a mild illness, but overall scores no better for full recovery from a severe illness. In fact, RTW coordinator 22 does only better here than RTW coordinators 15 and 23, and lacks behind many other RTW coordinators. This is odd, as one would expect positive results for partial recovery from a severe illness, and positive results for full recovery from a mild illness to go hand-in-hand with positive results on the overall recovery, that is full recovery from a severe illness. However, the multi-state mixed proportional hazards model only allows to estimate direct transitions. Now, partial recovery from a severe illness and subsequent full recovery from a mild illness for the same claimant, is in essence the same as full recovery from a severe illness. But as full recovery from a severe illness in this way is the result of two direct transitions, and hence indirect, this does not contribute at all to the results that we get for full recovery from a severe illness. This explains that it is not at all immediate with the multi-state model to expect positive results on one transition to show up in a similar transition as well. In addition, one could argue that full recovery is likely to be fastest while being 100% idle, and that working slows down the recovery process. When we zoom in on the risk characteristics of the claimants of RTW coordinator 22, it jumps the eye that 57% of his/her claimants are employed in the human health & social work activities-sector. This potentially explains the prosperous results of this coordinator for partial recovery, as the shortage of employees in the health care may induce claimants to resume part of their work fairly quickly.
of the headquarters of the company. Just as for the teams, it is not immediate that this would translate into an uneven distribution of claimants over the RTW coordinators. Still, it might occur that a RTW coordinator gets the responsibility over claimants of companies operating in sectors that feature a faster/slower recovery process. It is true that we adjusted for this, but the necessary grouping of the occupational sectors may have been too coarse. It is very likely that the differences we find for the RTW coordinators are due to factors that were not at our disposal, factors such as skill for example. Fact is that differences exist, and we know where, further scrutiny is now required to determine how one RTW coordinator distinguishes oneself from another.
5.4
Unobserved heterogeneity
6
Conclusion
In this thesis we analyzed a unique data set consisting of 36976 disability durations of 21728 different employees, that was provided by a Dutch insurance company. Several risk factors were at our disposal for each duration: factors such as age, occupational class, and most notably the assigned RTW coordinator. A RTW coordinator is assigned to every employer that insures the financial risk emanating from sickness-absence in order to facilitate the recovery process. Our goal was to identify the influence of RTW coordinators on the complete- and partial recovery of employees that are absent due to sickness.
claimants of medium-sized firms show an economically significant result; they have lower fall-back rates.
Before we discuss the consequences of the results, we would like to bring to mind that two important risk factors were not at our disposal. Both these risk factors, gender and disability diagnose, are often significant predictors for the length of the disability duration. We recommend to store these two factors in the future as well.
So, full recovery is best achieved under the supervision of RTW coordinators of Team 2. This could be attributed to the performances of the team captains, but this is far from sure. Further research is required to find the origin of the difference. The same holds true for the differences between the RTW coordinators. They might be due to differences in skill, experience, rehabilitation strategy, or an overlooked selection effect resulting in an uneven distribution of difficult cases, something that is outside the control of the RTW coordinators. It may be useful in this respect to consider that RTW coordinators 4, 5, 8, 9, 11 and 13 predominantly collaborate with company doctors of the occupational health services in Eindhoven and Tilburg. Additionally, RTW coordinator 33 mainly collaborates with company doctors of the occupational health service in Goes, whilst their colleagues number 25 and 28 mainly join forces with the company doctor of the service center in Rotterdam. An explanation for the prosperous partial recovery rates that are associated with RTW coordinator 22 of the second team are allegedly due to a selection-effect; the vast majority of his/her claimants are employed in the human health & social work activities-sector.
the RTW coordinator during a disability spell may be both impractical and undesirable, maybe even to the extent that it works counterproductive. We have seen that better partial recovery rates through guidance of a RTW coordinator not necessarily translate into better full recovery rates through guidance of the same RTW coordinator. We noticed that this may be due to a limitation of the multi-state model, and therefore realize that the effect of partial recovery on full recovery may be underestimated.
Higher recovery rates were associated with the occupational health service-centers in the south-east of our country, relative to those operating in the west. We were not able to distinguish the differences between the occupational health services in a more refined way, which is the next step in our opinion. We suspect that the relatively long history of collaboration between the RTW coordinators and the company doctors in the south benefits the recovery process of the claimants. Granted that this is true, it is first important to find out how exactly. This knowledge then can be turned to good account in the west as well. A more refined approach is also required to distinguish the recovery rates in different occupational classes.
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Tables & figures
Table 1: Explanatory variables Name Description
Contract features:
Brand dummy variable for the brand under which the insurance policy is sold, either brand A or brand B
Total sum assured amount of gross income assured for all employer’s employees together, this amount excludes employer’s financial obligations besides income payments (in euro’s per year)
Nr employees number of insured employees on the insurance policy
Employer obl perc percentage of employer’s financial obligations insured besides income payments
Deferment period number of days that the employee must be disabled before the insurer starts benefit payments
Umbrella contract dummy variable indicating whether the insurance policy is agreed upon beneficial conditions for the employer
Coverage yr1 percentage of gross income payments that is reimbursed during the first year of disability
Coverage yr2 percentage of gross income payments that is reimbursed during the sec-ond year of disability
Personal characteristics:
Age age in years of the employee at the start of the disability RTW coordinator return-to-work coordinator-indicator, 33 in total labeled 1-33
Table 1 – continued from the previous page Name Description
Team dummy variable indicating the team of RTW coordinators, either team 1 (RTW coordinators 3-9,11,13,15,18,23,24,26,29,31) or team 2 (RTW coordinators 1,2,10,12,14,16,17,19,20-22,25,27,28,30,32,33)
Arbodienst11 city that locates the office of the arbodienst:
1 Alkmaar 2 Amersfoort 3 Amsterdam 4 Arnhem 5 Breda 6 Eindhoven 7 Enschede 8 Goes 9 Groningen 10 Haarlem 11 Heerlen 12 Nijmegen 13 Rotterdam 14 Tilburg 15 Utrecht 16 Venlo 17 Voorburg 18 Zaandam 19 Zwolle
Continues on the next page
11The Dutch arbodienst is an independent organization that supports employers/companies with the
Table 1 – continued from the previous page Name Description
Sector12 sector in which the company operates:
A agriculture, forestry & fishing B mining & quarrying
C manufacturing
D electricity, gas, steam and air conditioning supply
E water supply; sewerage; waste management and remediation activities F construction
G wholesale and retail trade; repair of motor vehicles and motorcycles H transporting & storage
I accommodation and food service activities J information & communication
K financial and insurance activities L real estate activities
M professional, scientific and technical activities N administrative & support service activities
O public administration & defense; compulsory social security
P education
Q human health & social work activities R art, entertainment & recreation S other services activities
T activities of households as employers; undifferentiated goods - and ser-vices - producing activities of households for own use
U activities of extra-territorial organizations and bodies Start of disability:
Start 2011 dummy variable for disability spells started in 2011 (or else 2010) Continues on the next page
