3.1. Parameter calibration
In practice, we need to calibrate the five design parameters (N, δ, θT, θL, θU) on the basis of the desired type I error rate and power in the trial. We first specify N, and then take a two-stage procedure to calibrate the main design parameters (δ, θT), and the early termination parameters (θL, θU) for equivalence or superiority.
In the first stage, we set θL = 0 and θU = 1, so that the trial would not be terminated early, to determine the threshold values of δ and θT. We performed a series of simulation studies with different values of δ and θT and compared the corresponding type I error rates and powers. Recall the neoadjuvant lung cancer trial that was mentioned in Section 1; in this phase II trial, we chose N to control both the type I error rate (10% or less) and the power (at least 80%). One of the two treatments (say, arm 1) under investigation was the standard chemotherapy with a known efficacy rate: p1 = 0.2. We assumed that the new treatment would double the response rate, i.e. p2 = 0.4.
The total sample size was set as N = 160, although the actual sample size could be much less owing to early termination of the trial. The first 40 patients (n1 = n2 = 20) were equally randomized to the two arms and thereafter patients were adaptively randomized on the basis of the posterior probabilities of comparing the response rates of the two treatments after observing every single outcome. The tuning parameter τ was taken as 0.5 (Thall and Wathen, 2007) and the randomization rates were restricted between 0.1 and 0.9 to prevent having very unbalanced randomization rates. To allow the likelihood to dominate the posterior distribution, we took a relatively non-informative prior distribution of beta(2, 2) for both p1 and p2. We varied δ from 0.02 up to 0.09, and θT from 0.70 up to 0.90. We carried out 10000 simulated clinical trials. For each of the paired values of (δ, θT), we obtained the type I error rate and power as listed in Table 1.
Type I error rates and power values under the null hypothesis of p1 = p2 = 0.4 and alternative hypothesis of p1 = 0.2 and p2 = 0.4 by varying the design parameters δ and θT†
Considering the null cases in the left-hand panel of Table 1, all entries of the type I error rates below the boundary line of the staircase curve are 10% or less, for which the paired values of (δ, θT) satisfy our requirement. Simultaneously, under the alternative cases, we need to find the paired values of (δ, θT) that lead to a power of 80% or higher. These correspond to the power values above the staircase curve in the right-hand panel of Table 1. The overlapping tinted area meets both the type I error and the power constraints. With a clinically meaningful range of equivalence of δ = 0.05, we chose θT = 0.85 for further study. It is worth noting that a higher power value corresponds to a higher type I error rate. The null cases cover p1 = p2 = p for p between 0.2 and 0.4, and we chose p = 0.4 to report as it corresponds to the case with the largest type I error rate.
In the second stage, fixing δ = 0.05 and θT = 0.85, we followed a similar procedure to calibrate (θL, θU), which determine the early termination of a trial due to equivalence or superiority respectively. Although the design allows monitoring after every outcome becomes available, from the computational and practical point of view, we opted to monitor the trial for early termination with a cohort size of 10. We explored method 1 by enumerating all the possibilities of the future sample sizes and method 2 by using the expected future sample sizes to compute the PPs. In Table 2, we can see that the type I error rates and powers obtained from methods 1 and 2 are very close, which implies that using the expected number of future subjects in method 2 gives a very good approximation of the outcomes from all possible future sample sizes. Our goal is still to maintain a type I error rate of 10% or lower and to achieve a power of 80% or higher when the trial is allowed to terminate early. There are multiple pairs of (θL, θU) that satisfy our design requirements, as indicated by the values in the tinted areas of Table 2, from which we selected θL = 0.05 and θU = 0.99.
Type I error rates and power values by varying the design parameters θL and θU using method 1 and method 2 (fixing δ = 0.05 and θT = 0.85)†
3.2. Selected scenarios
To examine the performance of the proposed design with the BARPP, we carried out a series of simulation studies under various scenarios. We varied the true response rate p1 from 0.1 to 0.4 and, for each fixed value of p1, we set p2 at a value from 0.01 to 0.8. In all the simulations, we fixed the design parameters as N = 160, δ = 0.05, θT = 0.85, θL = 0.05 and θU = 0.99 on the basis of the two-stage parameter calibration procedure that was described in the previous section. We replicated 10000 clinical trials for each configuration.
Fig. 1 illustrates the decision and sample size distributions with various values of p1 and p2. The colour and the co-ordinates of each point indicate the final decision and the number of patients assigned to each arm respectively. For a better view, the points are slightly jittered to break the ties and only 1000 trials are presented. When p1 = p2, the green points (shown in circles with a decision of p1 = p2) take a dominant role, indicating that the two treatments are equivalent; the red points (shown in plus symbols with a decision of p1 = p2) and the blue points (shown in crosses with a decision of p1 > p2) take roughly symmetric positions at the two corners. The small numbers of red and blue points depict that the stochastic nature of the responses may result in an imbalance of sample allocation between the two arms, and also lead to incorrect final conclusions. When the difference between p1 and p2 is large (e.g. p1 = 0.2 and p2 = 0.7, or p1 = 0.4 and p2 = 0.01), AR assigns most of the patients to the superior arm and almost all the simulated trials were terminated early. When the difference between p1 and p2 is small (e.g. p1 = 0.2 and p2 = 0.3, or p1 = 0.4 and p2 = 0.3), the treatments were claimed to be either equivalent or different and many trials used a large number of patients.
Sample size and decision distributions for various values of p1 and p2, with the BARPP designs. (the value of p2 varies from 0.01 to 0.7 whereas the value of p1 is fixed at (a) 0.2 and (b) 0.4; for each p1 and p2 combination, 1000 trials were simulated;...
We illustrate the percentages of rejecting the null hypothesis under various scenarios in Fig. 2. The value of p1 is fixed and the value of p2 varies from 0.01 to 0.8. The curves that were obtained from methods 1 and 2 are indistinguishable; hence, only one curve for the BARPP design is shown. The minimum percentage of rejecting the null case is always located at p1 = p2 for each scenario, which corresponds to the type I error rate. Our method yielded a minimum rejection rate of 0.014, 0.049, 0.082 and 0.097 at the null cases with p1 = 0.1, 0.2, 0.3, 0.4 respectively. The power curves typically have a ‘V’ shape because the power increases as p2 moves away from p1 to either the left-hand or the right-hand side.
To compare our design with the frequentist approach, in Fig. 2 we also present the corresponding power values calculated from the group sequential (GS) design by using the R package gsDesign (http://gsdesign.r-forge.r-project.org/). Given a significance level of 0.1 and a power of 80% under the alternative case with p1 = 0.2 and p2 = 0.4, the upper and lower boundary values at each group sequential test were calculated with the the Hwang–Shih–DeCani spending function (Hwang et al., 1990), for which the upper design parameter λ = −4 yielded the O’Brien–Fleming type of boundary (O’Brian and Felming, 1979) for efficacy stopping and the lower design parameter λ = −2 was taken for futility stopping. Both futility (or equivalence) and efficacy stopping were considered in the GS design to make it comparable with the BARPP method. The number of patients in each group under the GS design was also set as 10 with five patients in each arm. Equal randomization is applied throughout with the maximum number of patients at 140. No early termination was allowed for the first 40 patients and thereafter the GS boundaries were applied. On the basis of 10000 simulations, the GS method also produced a V-shaped power curve similar to that using the BARPP. In scenarios with p1 = 0.3 or p1 = 0.4, the curves of the BARPP and GS designs are almost identical. However, for scenarios with p1 = 0.1 or p1 = 0.2, the power values by using the GS design are higher than those by using the BARPP design. This is because the BARPP design takes a more conservative approach to controlling type I errors across different null response rates and thus the BARPP has lower type I error rates.
Fig. 3 illustrates the numbers of patients who were allocated to arm 1 and arm 2, and the total sample sizes under various scenarios. It can be seen that more patients were randomized to a more efficacious treatment arm by using the BARPP method. When p1 = p2, patients were essentially equally randomized to the two arms by using AR. When the difference between the two response rates was substantially large, early stopping took place very quickly in the AR stage, which led to small sample sizes in both arms. When p2 increases while fixing p1 at a certain value, the number of patients who were assigned to arm 2 increases and, as a result, the overall percentage of patient responses increases. The total sample size of the BARPP method is slightly larger than that of the GS design, which is mainly caused by AR in the BARPP method. Owing to the provision allowing for early stopping, both the BARPP and the GS design are more efficient and more ethical than the fixed sample size design. Allowing for early stopping is an important design consideration for randomized phase II trials (Lee and Feng, 2005).
Fig. 4 shows a comparison of the percentages of patient responses between the BARPP and the GS methods. It can be seen that the overall response rate of the BARPP method is higher than that of the GS method when the values of p1 and p2 are different. When p1 = p2, the percentages of response are the same between the two methods because patients are also equally randomized by using the BARPP method. When the value of |p1 − p2| lies around 0.3, we observe the biggest difference in the overall response rate between the two methods. For p1 = 0.1 and p2 = 0.3, the overall response rates of the BARPP and the GS methods were 0.233 and 0.203 respectively, and, for p1 = 0.2 and p2 = 0.4, the corresponding response rates were 0.33 and 0.301. Despite the substantial difference in sample size between the two arms (for example, the averaged sample sizes of treatments 1 and 2 are 43 and 79 respectively, for the latter case; Fig. 1), AR achieves only a modest 10% gain in the overall response rate compared with ER.
When the difference between p1 and p2 is larger than 0.3, early termination occurs very quickly after ER of the first 40 patients, and thus the number of patients who were assigned in the AR stage becomes very small. This would in turn lead to a small difference in the percentage of response between the BARPP and the GS methods. For example, in Fig. 3(a), when p1 = 0.1 and p2 = 0.7 or p2 = 0.8, i.e. treatment 2 is overwhelmingly superior to treatment 1, the trial is stopped soon after the initial ER stage to claim superiority of treatment 2, and the total sample size is very small (41.1 and 40.1 for the cases of p2 = 0.7 and p2 = 0.8 respectively). Comparing Figs 2 and 3, it is interesting that the power still increases even when the sample size decreases. Because of trial early termination based on the PP, the sample size can be substantially reduced if a decision can be made in the middle of the trial.
As suggested by the Associate Editor, we can measure the number of lost responses due to treating patients with the worse treatment, i.e. the number of patients who were assigned to the worse treatment arm multiplied by |p2 − p1|. In Fig. 5, we can see that the lost responses in the BARPP design are lower than that in the GS design, mainly because of AR. Moreover, we also explored the BARPP design without equivalence stopping and the findings are quite similar, except that the trials may run until reaching the maximum sample size when p1 and p2 are close to each other. The added feature of AR in the BARPP design assigns more patients to the better treatment arm, leading to more imbalance between the two arms. The imbalance in allocation of patients may result in a loss of statistical power. Hence, the sample size that is required for the BARPP is typically larger than that for the GS design. In addition, we also observed more variability in the sample size of the BARPP design. Overall, the BARPP design performed very well in terms of frequentist properties, such as maintaining the type I error rate and achieving the power desired.
~ February 13, 2015 ~
AOB’s Have Been Valid Since 1917 And
If You Like Your Health-Care Plan, You Can Keep It
David J. Salmon, Esq. & Andrew A. Labbe, Esq.
What is an Assignment of Benefits?
An Assignment of Benefits (“AOB”) is a document utilized by water mitigation companies and other vendors to extract payment from insurance companies for services they allegedly provide. AOBs in the context of homeowner’s policies have become prevalent in Florida only within the last few years, but have become the largest cost-driver in the insurance industry and are having a widespread, detrimental effect on consumers throughout the state.
In practical application, an AOB works like this:
An insured has a pipe burst in his home and calls a plumber to come fix it. The plumber fixes the pipe, and then refers a water mitigation company to the insured to dry out the home. The water mitigation company comes to the insured’s home and tells him it needs to be dried immediately, but he will need to sign an AOB or they cannot begin work. Typically, the AOB will be explained to the insured as allowing the vendor to “bill the insurance company directly.” The insured, under the stress of the event, with no knowledge of the legal implications of what he is signing, and wanting to get his house dried immediately, invariably complies. The vendor then takes the position that it “owns” the insured’s claim, oftentimes preventing the insured from maintaining a separate lawsuit for other portions of the claim. All this occurs before there is any agreement as to cost or scope of repairs. At this point, rather than restoring the property to its pre-loss condition and making the insured whole, the focus of the claim becomes vendor’s profit.
The Law of Assignments
Plaintiffs’ attorneys like to argue that the assignment of post-loss benefits have been recognized in Florida since 1917, a reference to the Florida Supreme Court’s decision in West Florida Grocery Co. v. Teutonia Fire Ins. Co., 77 So. 209 (Fla. 1917). However, the fact is that there has never been a case in Florida in the context of property insurance holding that the post-loss assignment of an unaccrued right to payment is valid. To assess the validity of AOBs in this context, we need to start at the beginning.
Unless a specific statutory exception applies, an “assignment” is the transfer of a complete and present right from one person to another. SeeContinental Cas. Co. v. Ryan Inc. E., 974 So. 2d 368, 376 (Fla. 2008). In order to be “complete,” the assignment must transfer a complete interest in the thing assigned. In order to be “present,” the assigned right must have accrued and vested in the assignor.
So the first step in the analysis of any assignment is whether it is complete. In the first party property context, there is often a mortgagee. A homeowner simply cannot enter into a subsequent assignment with a restoration company for services to a house, which is the collateral for the mortgagee’s loan, and then assign away the insurance proceeds to a third-party after having entered into an agreement with the mortgagee over the same insurance proceeds and after having entered into an agreement with the insurance company that the mortgagee will be listed as a loss payee in the policy. Furthermore, any assignment of a policy with a mortgagee holding an interest in the insurance proceeds is never valid because it is not a complete assignment.
At the time of a loss, the insured does not yet have any rights to insurance proceeds; the insured has duties following a loss under the policy that must be met before any benefits accrue, which include adjusting the loss with the insurer. Additionally, before any benefits accrue, the insurer must first make a determination that coverage exists under the policy and has various other contractual rights, such as the option to repair, it may avail itself of. Hence, there is no present right that may be transferred at the time of the loss because nothing has yet accrued. All the homeowner possesses is an expectation.
Despite the universal reliance by Plaintiffs’ attorneys on West Florida Grocery, a plain reading of that case demonstrates the invalidity of AOBs in this context. In that case, the Florida Supreme Court stated that the insurance company had waived its right to challenge the assignment when it filed the interpleader, and emphasized that it was not ruling on the validity of the assignment. Id. at 211. However, the court’s analysis on the validity of the writs of garnishment would also have applied to the assignment, as the court focused on whether the right to insurance claim proceeds had accrued at the time the writs were issued. Id. at 211-212. The court stated that “until the conditions of the insurance policy have been complied with by the insured, or compliance . . . waived by the insurer, and until it has exercised its option to replace or restore the property,” the writs were invalid. Id. “If the amount of the claim is not capable of being ascertained, if there may never be any indebtedness, if there are certain things unperformed upon the performance of which liability depends,” the writs were not effective because there was not a complete and present right. Id. Accordingly, the court held that the writs were “premature and ineffectual.” Id. at 212.
In the context of homeowner’s insurance, virtually every policy includes post-loss duties of the insured, post-loss rights of the insurer, and conditions precedent to the accrual of a right to receive benefits. Pursuant to the holding in West Florida Grocery, until post-loss duties are complied with, there is a coverage determination, and a right to payment accrues, there is nothing for the insured to assign and an AOB is invalid as a matter of law. The assignment is not a “present” transfer, because the right to payment has not accrued, nor is it “complete,” as both the insured and mortgagee maintain an interest in the claim and policy. Moreover, as in West Florida Grocery,benefits under these policies are contingent and may never accrue.
This is consistent with the general rule in Florida, that a policy may be assignable, or not assignable, as provided by its terms. See Fla. Stat. §627.422. Unless an exception exists, this is the rule of law. The insurance contract governs the parties’ actions from the moment of loss until final resolution of a claim. When the right to the payment has fully accrued under the policy and vested in the insured, notwithstanding the terms and conditions of a policy, an assignment may be valid. SeeAldana v. Colonial Palms Plaza, Ltd., 591 So. 2d 953, 955 (Fla. 3d DCA 1991). Under this scenario¸ where there are no contingencies to payment and no third parties with priority interests, an insured can direct the insurer to pay a third party, as the money belongs to the insured regardless of whether the funds have been paid.
Plaintiffs’ attorneys rely on case law under life, health, or automobile policies to support their arguments. However, these situations are distinguishable from assignments in the property context because there are statutory exceptions as respects health, life, and automobile policies. See §§627.422, 627.736, Fla. Stat. (2012). These exceptions affect both the definition of assignment and an insurer’s right to restrict same. Unlike other policies, the onlyexception with regard to property insurance policies relates to assignment of proceeds due under the policy. The justification behind this exception is that there is no effect on the rights of the insurer or the risk it undertook to insure. SeeInt’l Sch. Servs. v. AAUG Ins. Co., Ltd., 2012 U.S. Dist. LEXIS 153683, *25 (S.D. Fla. 2012) (“[A]llowing [post-loss assignment of insurance proceeds] hurts the insurer not at all. . .The assignment does not increase or decrease the financial exposureof the company in any way”) (emphasis added). In fact, the Restatement (Second) of Contracts §317 provides that a contractual right cannot be assigned if inter alia, it would materially increase the risk imposed on the obligor.
Clearly the exception in this context only applies to the post-loss assignment of an accrued right to payment, where the assignee has no influence over the amount of the proceeds. If the only issue is whose name to write on the check, these cases would not be flooding courts throughout Florida. However, a vendor’s ability to influence the claim amount has a distinct, cognizable effect on an insurer’s rights, and clearly increases its financial exposure. The Florida legislature has recognized the inherent dangers of such a conflict with the 2011 Florida bill once entitled, “Contractors Adjusting Claims,” making it a third degree felony for a contractor to act as an unlicensed public adjuster. See §626.8738, Fla. Stat. (2011).
An insurer enters into a contract with a homeowner, providing coverage and setting premiums based on information gathered about that individual. In adjusting a loss, the insurer should not then be forced to deal with a different party that routinely makes insurance claims and files suit if their unilateral demand is not paid by the insurer. An insured’s interest is to restore the property to its pre-loss condition and receive only those proceeds sufficient to do so; a contractor’s interest is maximizing its profit from the loss. This represents a fundamental change in the risk bargained-for by the insurer. The purpose of insurance is to restore an insured to their pre-loss condition, not to provide profit on such loss, as this would increase moral hazard and undermine the entire concept of insurance. SeeDeCespedes v. Prudence Mut. Cas. Co., 193 So. 2d 224, 227 (Fla. 3d DCA 1966).
Vendors and their attorneys try to couch AOBs as a way to protect insureds. In reality, insureds receive no benefit from these AOBs and, in fact, can be severely prejudiced. The only people that benefit are the vendors and their attorneys.
A recent lawsuit handled by our office helps demonstrate the abuse that occurs through use of AOBs. The insureds, a couple in their 70s, suffered a water loss at their home and retained a vendor to perform water mitigation and restoration services. The vendor provided a verbal quote of $8,000.00-$9,000.00, but never put anything in writing. The vendor subsequently submitted 3 invoices totaling over $31,500.00. When the insureds received these invoices, they noticed numerous discrepancies and duplicate billing entries, and contacted their insurer. After inspecting the property, it was discovered that the invoices did, in fact, contain numerous fraudulent charges, such as charging for replacing the entire kitchen ceiling when only a small portion was performed, performing work in rooms that were not affected, removal of furniture from an office (the furniture was built-in and could not be removed), and cleaning the property though the insureds were forced to clean the property themselves. It was determined that the actual amount due for work performed by the vendor was about half of what was billed.
Despite being made aware of these issues, the vendor still brought suit against the insurer and placed a lien on the insureds’ home. The 3 invoices were attached to the Complaint and relied on by Plaintiff for settlement negotiations. However, once the insurer moved to dismiss the lawsuit for fraud on the court, the vendor asserted that the documents were merely estimates, which is why they included charges for work that was never performed. However, they could not explain why they sought payment for these services both before and after filing suit. The lawsuit was ultimately dismissed for fraud.
AOBs have a significant negative impact on the insurance industry. They are “cost drivers,” which increase premiums without any benefit to insureds. AOBs have spurred a “cottage industry” in which vendors and attorneys carry out a “litigation for profit” scheme through a network of referrals and exploitation of insureds, insurers, and the judicial system. Not only do these AOBs drive up insurance premiums, this litigation scheme has flooded courts throughout Florida with these unmeritorious claims, at the cost of judicial resources and taxpayer dollars. The situation is akin to the crisis experienced in Florida as a result of PIP claims except, unlike PIP, AOBs abridge the rights of third parties, are unregulated, and have a prejudicial effect on insureds.
 Generally in exchange for a referral fee.
 In addition to potentially preventing an insured from maintaining his or her own lawsuit, these AOBs can have other detrimental effects on insureds with respect to underwriting.
 Despite the attempts of the vendor’s attorney to withdraw the invoice the day prior to the hearing and claim it was attached to the Complaint in error.