
    COLORADO DEPARTMENT OF SOCIAL SERVICES, Plaintiff-Appellant, v. UNITED STATES DEPARTMENT OF HEALTH AND HUMAN SERVICES; Donna Shalala, in her official capacity as Secretary of the Department of Health and Human Services; Judith A. Ballard, Cecilia Sparks Ford, and Donald F. Garrett, in their official capacities as members of the Departmental Appeals Board of the Department of Health and Human Services, Defendants-Appellees.
    No. 93-1145.
    United States Court of Appeals, Tenth Circuit.
    June 22, 1994.
    Joyce K. Herr, Sr. Asst. Atty. Gen., Human Resources Section (Gale A. Norton, Atty. Gen., Raymond T. Slaughter, Chief Deputy Atty. Gen., Timothy M. Tymkovich, Sol. Gen., Paul Farley, Deputy Atty. Gen., and Wade Livingston, First Asst. Atty. Gen., with her on the briefs), Denver, CO, for plaintiff-appellant.
    Patricia L. Bossert, Asst. Regional Counsel, Dept, of Health and Human Services (James R. Allison, Interim U.S. Atty., Chalk S. Mitchell, Asst. U.S. Atty., of counsel: Ronald S. Luedemann, Chief Counsel, Region VIII, Dept, of Health and Human Services; and Jay A. Swope, Associate Chief Counsel, Dept, of Health and Human Services, with her on the brief), Denver, CO, for defendants-appellees.
    Before WHITE, Associate Justice (Ret.), LOGAN and EBEL, Circuit Judges.
    
      
       The Honorable Byron R. White, Associate Justice of the United States Supreme Court (Ret.), sitting by designation, pursuant to 28 U.S.C. § 294(a).
    
   LOGAN, Circuit Judge:

I

The Colorado Department of Social Services (Colorado) appeals the district court order affirming the final agency action of the Department of Health and Human Services (HHS). That action sustained in part and remanded in part disallowances of Colorado’s revised claims for federal reimbursement of its administrative costs incurred in a foster care and adoption assistance program under Title IV-E of the Social Security Act, 42 U.S.C. §§ 670-679a. Although there is a jurisdictional problem with the remanded claim, the principal issue on appeal is whether the Health and Human Services Departmental Appeals Board was arbitrary and capricious in denying the revised claims.

The Social Security Act provides for federal reimbursement of a percentage of state payments under certain approved public assistance programs. In addition to reimbursement of direct payments, states are entitled to partial reimbursement for the expenses of administering such federal programs, including Title IV-E. Administrative expenses often are associated with more than one federally-funded program; therefore, states are required to develop a cost allocation plan (CAP) — “a narrative description of the procedures that the State agency will use in identifying, measuring, and allocating all State agency costs incurred in support of all programs administered or supervised by the State agency.” 45 C.F.R. § 95.505. The CAP must

[cjontain sufficient information in such detail to permit the Director, Division of Cost Allocation, after consulting with the Operating Divisions, to make an informed judgment on the correctness and fairness of the State’s procedures for identifying, measuring, and allocating all costs to each of the programs operated by the State agency.

Id. § 95.507(a)(4). The CAP must be approved by the HHS Division of Cost Allocation (DCA) as a prerequisite to obtaining reimbursement. Id. § 95.511; 42 U.S.C. § 671(a). A state must amend its CAP if the procedures shown in the existing CAP become outdated, a material defect in the plan is discovered, or other changes occur that make the allocation basis or procedures in the previously approved CAP invalid. 45 C.F.R. § 95.509. A CAP amendment is effective on the first day of the calendar quarter after that event, unless “[ajn earlier date is needed to avoid a significant inequity to either the State or the Federal Government.” Id. § 95.515(a).

Because Colorado participates in several federal programs, each year Colorado submits its CAP, which includes a Time Analysis Reporting System (TARS) to record the time county social workers spend on each federal program. The TARS uses “cluster sampling” of randomly-selected three-day periods each quarter, and the data collected in each quarter is used to claim federal funds for the following quarter.

Colorado participates in both Title IV-E and Title XX programs. The Title IV-E program deals with social services for children who would be entitled to financial assistance from the Aid to Families With Dependent Children (AFDC) program except that they have been placed in foster or certain adoptive homes. In its Title XX program Colorado provides similar services to children in foster care who are not eligible for the AFDC program. Federal reimbursement to states for Title XX programs is subject to a ceiling but reimbursement for Title IV-E is not. The ceiling limited Colorado’s reimbursements under Title XX.

Colorado noted that its reported administrative costs for Title IV-E were significantly lower per case than for Title XX, even though it believed the time spent by social workers on each Title IV-E case was at least as much as for a Title XX case. See R. 1363-71, 1605. Colorado officials thought that caseworkers were erroneously recording time spent on Title IV-E cases as time spent on Title XX cases. In an attempt to improve accuracy of TARS data, in June 1986 Colorado submitted to the DCA modifications in its TARS, including changes in the coding procedure that employees use to report their time. The TARS modifications eliminated some of the social services codes and provided new descriptions for others. Also, the reporting form for county employees was condensed substantially. Colorado also revised its procedures handbook for county employees, including the instructions on how to complete the coding form. See R. 1393. Colorado informed DCA that it planned to implement the new procedures for the quarter ending December 31, 1986. The DCA director treated the state’s submission as a request for an amendment of its CAP. In June 1988, DCA approved the amendment to apply retroactively to July 1, 1987.

In March 1988, Colorado made revised claims for Title IV-E administrative costs for the period from October 1, 1985, to June 30, 1987. The revised claims employed data collected during the first three quarters in 1987 under the revised TARS, and applied this data retroactively. See R. 451-52. The revised claims had the effect of shifting approximately $6.6 million in administrative costs from Title XX to Title IV-E. For example, Colorado’s Title IV-E administrative claim jumped from $5,250 based on the approved CAP for the first quarter of 1987 to $594,019 for the second quarter of 1987, more than a hundredfold increase. Because Colorado had substantially exceeded its Title XX cap the reallocations did not reduce Colorado’s Title XX claims. R. 1436-37; Appellant’s App. 15 n. 4 (Departmental Appeals Board Decision).

Within HHS the Title IV-E program is operated by the Administration for Children, Youth and Families (ACYF). The ACYF commissioner disallowed the revised claims, finding that they did not conform to Colorado’s CAP approved for the applicable time period, see 45 C.F.R. § 95.517(a), and that the methodology used to calculate the revised claims was flawed. Colorado appealed the disallowance to the Departmental Appeals Board (Board), which conducted a hearing. The Board upheld the ACYF commissioner’s decision to disallow Colorado’s revised claims for October 1, 1985, to March 31, 1987, for $3,327,162 and remanded the state’s revised claim for the second quarter of 1987 of $594,-019 to ACYF for further consideration and consultation with the DCA.

Colorado then appealed to the district court, alleging that the final administrative decision of the Board was arbitrary, capricious, an abuse of discretion, and contrary to law. The district court referred the case to a magistrate judge. That judge’s detailed report stated that the revised claims for October 1, 1985, through March 31, 1987, were made pursuant to a proposed TARS which had not yet been approved under the CAP. The magistrate judge treated 45 C.F.R. § 95.515 as creating a presumption against retroactive CAP adjustments. He determined that Colorado could not use the data from its sample period because it failed to show the data was reliable and that the “Title IV-E program remained essentially the same in the sample period as it was during the earlier” quarters. Appellant’s App. 45. He also questioned Colorado’s assumption that county employees had accounted for time spent on Title IV-E programs using Title XX codes. Thus, he recommended upholding the final administrative decision disallowing Colorado’s revised claims for January 1, 1986, to March 31, 1987. He would find that the revised claim for April 1, 1987, to June 30, 1987 was not properly before the court because there was not a final administrative decision on that claim. The district court adopted the magistrate judge’s recommendation, and it is from that judgment that Colorado has appealed.

II

A

We agree that the district court properly declined to address the validity of the revised claim for the second quarter of 1987. The Board remanded that claim to ACYF for further consideration. Even if the Board’s remand to ACYF is in effect the agency reserving to itself the right to reconsider, as Colorado argues, there is no final agency determination of the claim. Neither do we agree with Colorado’s argument that somehow the government is estopped from reconsidering this issue, or must be deemed to have approved the claim by its delay. Colorado has been paid the whole amount of its claim, and the issue before ACYF is whether all or some part of that $594,019 is to be repaid or credited against future payments due to Colorado. We agree with the district court that there is no federal court jurisdiction to address the claim for the second quarter of 1987. See 5 U.S.C. § 706.

B

The issue that we properly have before us on the merits is whether the Board acted in an arbitrary and capricious manner in denying Colorado’s revised claims for the five quarters spanning January 1, 1986, to March 31, 1987. Colorado argues that the Board erred in determining that the revised TARS constituted a CAP amendment precluding reimbursement of its claims and that the state failed to prove its claims. It further asserts that if the revised TARS was a CAP amendment, the Board should have approved an earlier effective date to avoid a significant inequity to the state.

We review the agency action to determine if it is “arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law.” See Administrative Procedure Act, 5 U.S.C. § 706(2); Lewis v. Babbitt, 998 F.2d 880, 881-82 (10th Cir.1993). Our review is narrow and deferential; we must uphold the agency’s action if it has articulated a rational basis for the decision and has considered relevant factors. See Motor Vehicle Mfrs. Ass’n v. State Farm Mutual Auto. Ins. Co., 463 U.S. 29, 43, 103 S.Ct. 2856, 2866, 77 L.Ed.2d 443 (1983). When, as here, a dispute concerns an agency’s interpretation and application of its own regulations, we give substantial deference to the agency. See Downtown Medical Ctr. v. Bowen, 944 F.2d 756, 768 (10th Cir.1991). We will affirm if we find that the agency considered “all relevant factors and articulate[d] a rational connection between the facts found and the choice made.” Action, Inc. v. Donovan, 789 F.2d 1453, 1457 (10th Cir.1986). We review the administrative record independently, giving the district court determination no deference. Thomas Brooks Chartered v. Burnett, 920 F.2d 634, 644 (10th Cir.1990).

Colorado acknowledges that federal financial reimbursement for administrative costs is allowed only in accordance with an approved CAP. 45 C.F.R. § 95.517. It asserts, however, that the revised claims were in accord with its prior approved CAP. Colorado argues that although the revised claims were retrospective projections of data collected under the revised TARS, the revised TARS did not constitute a CAP amendment requiring DCA approval; therefore, the revised claims were allowable regardless of the effective date of the CAP amendment. It argues that the revised claims were significantly higher because of improved training and not because of any changes in the TARS system, the CAP, or the Title IV-E program itself.

The record supports the Board’s finding that the revised TARS, on which the revised claims were calculated, constituted an amendment to the CAP. See, e.g., R. 1369, 1373, 1413, 1795. The TARS is, by definition, an integral part of the CAP. See 45 C.F.R. § 95.505; see also R. 1566. In submitting its CAP the state included the changes in the TARS. See R. 1682. Although the revised TARS did not change the Title IV-E code combinations, the revised procedures handbook added definitions for each of the code combinations. These definitions effectively changed the procedures referred to because they facilitated allocation of costs pertaining to specific programs. The coding changes for programs other than the Title IV-E program potentially affected Title IV-E figures; for example, the Board pointed to the deletion of several codes related to Title XX activities that might have caused an increase in the use of codes for Title IV-E activities. In other words, because parts of the reporting procedures for some of the programs involved were changed, the overall CAP was in fact amended. The Board did not act arbitrarily, capriciously, or contrary to the evidence in finding that the revised TARS constituted an amendment to the CAP, requiring HHS approval.

C

Colorado urged before the Board and on appeal that if the revised claims were based on an amended CAP, that an effective date earlier than July 1, 1987 is needed. Colorado argues that it has shown by a preponderance of the evidence that its initial claims for the quarters in question were inadequate, and that a retroactive application of the amended CAP is required “to avoid a significant inequity” to the state. See 45 C.F.R. § 95.515. Colorado seeks to apply the amended CAP because the data collected under that CAP provides the only means to redetermine its claims for the earlier period. Those claims allegedly were too low because Colorado’s social workers were inadequately trained in how to report their time.

The Board declined to decide whether to allow the retroactive application of the CAP, because “the [revised] claims were not based on the methodology in the amendment and because the methodology actually used was seriously flawed.” Appellant’s App. 18. Colorado revised the time spent administering various programs by using data from sample periods, and “backcasting” from what it considered more accurate figures, to the earlier period. The Board’s criteria for allowing revised claims are that the state show that (1) the original figures were inaccurate; (2) the data is reliable; and (3) circumstances relating to the sampled and unsampled periods are such that the data can be used for the unsampled period. See Missouri Dep’t of Social Servs., Doc. No. 87-188, Dec. No. 1021, (Dep’t HHS Feb. 21, 1989) (Appellant’s Opening Brief, Add. 3).

HHS does not seriously contend that the figures in Colorado’s original claims were in fact accurate. The Board, however, found Colorado failed to meet the other two requirements: it concluded that the revised claims were based on a statistically unsound application of data to quarters for which Colorado could not show the data would properly apply. We now review those findings.

Colorado compiled the data for its revised claims by first calculating the mean Title IVE time from the revised TARS data collected during the last three quarters of 1987. It next determined the percentage of administrative costs attributed to Title IV-E, and then refigured the Title IV-E costs for the quarters at issue. See R. 1627-28. The record shows that the number of Title IV-E hours reported using the amended TARS for quarters ending March 31, 1987, June 30, 1987, and September 30, 1987, were 1748, 1143, and 1007 respectively. See Ex. U. According to a statistician, this substantial variation could be due to “nonsampling error” such as errors in measurement, reporting, editing, coding and databasing. Ex. W at 2. One of Colorado’s witnesses testified that the variation might reflect a decline in accuracy of reporting Title IV-E hours as the effects of training provided during the first quarter faded. ACYF agreed that training could have had an impact on the hours reported, but suggested the training emphasis on increasing Title IV-E claims might also have caused initial over-reporting of Title IV-E hours.

Colorado argues that the average of the first three quarters in which it used revised TARS was a reasonable basis for calculating prior quarter claims because the three-quarter average was similar to the average of thirteen quarters ending March 1990. See R. 1615-16, 1640. But the Board noted that the data for the additional ten quarters also showed a marked variation within the time periods, R. 1639-40; it found that this variation could be attributed to any number of factors, and that the similarity between the averages was not persuasive evidence that the calculations were sound for retroactive application.

The Board further questioned the accuracy of the studies on which the underlying assumption for the revised claims was based. See infra fn. 2. It noted that Colorado’s revised claim for each of the quarters beginning October 1, 1985, and ending June 30, 1987, was larger than the claim submitted for any of the five succeeding quarters, even though ACYF showed that the average number of Title IV-E children in each category except voluntary foster care increased annually from fiscal year 1986 to fiscal year 1988. Exs. 20-25; R. 1763-69. The logical assumption would be that Title IV-E administrative costs would be directly related to the number of Title IV-E children; here the costs decreased when they should have increased. Thus the revised claims might have been inflated.

In response Colorado pointed out that by October 1, 1988, its claims had risen to the level of those it sought for the contested periods. It argued that this was because reporting under the amended TARS had become more accurate -by this time. But the Board found that this merely confirmed that the revised claims were overstated; the revised earlier claims should have been lower than the later claims. Although Colorado argues that its original claims were too low, and that the Board offered no alternative method to retroactively identify Title IV-E administrative costs, the state, not the agency, has the burden to substantiate its claims based on reliable data.

Finally, the Board also found that Colorado did not meet its burden to show that the Title IV-E program remained constant during the quarters at issue compared to the three quarters upon which the retroactive calculations were made. Colorado argues that the Board stated only that “the testimony does not rule out program changes,” Appellant’s App. 22; it asserts that it provided testimony that there were no program changes, and that HHS did not provide any evidence of changes. The record, however, contains some evidence of program changes, see R. 1763 (rise in overall Title IV-E program cases); and the fluctuations in data from sampling periods discussed above also suggest change in the Title IV-E program during the period in question.

The Board determined that Colorado failed to prove that the data for the sampled periods was reliable or that the program was unchanged. Based on our review of the entire record, this determination is not clearly erroneous. Colorado complains that HHS unfairly denied its revised claims; however, Colorado must shoulder the consequences of its admitted fault, even if it is only failure to train its employees to report properly. An agency is entitled to require rather strict proof when considering a state’s retroactive claims under federal entitlement programs. A principal reason for requiring prior approval of CAPs, and making CAP amendments function prospeetivély, is because Congress must budget for these program costs. Here Colorado’s estimate for the time periods was dramatically lower than the revised claims. See R. 1857-59.

We hold the Board acted within its discretion in denying the revised claims, and hence AFFIRM the district court’s judgment denying relief. 
      
      . The effective date may also be earlier if "[t]he information provided by the State which was used to approve a previous plan or plan amendment is later found to be materially incomplete or inaccurate, or the previously approved plan is later found to violate a Federal statute or regulation. In either situation, the effective date of any required modification to the plan will be the same as the effective date of the plan or plan amendment that contained the defect.” 45 C.F.R. § 95.515(b).
     
      
      . This assumption was based on a study in one mid-sized county (Fremont) in which no Title IVE time was reported before training, see R. 1409-11; and in ten large counties, R. 1410, in which reporting of Title IV-E increased dramatically after training.
     
      
      . The new procedures and descriptions were designed in part to reduce the misuse of Code 1L04 "Child Welfare Foster Care,” a code intended to be used for Title XX cases. See R. 1363, 1379.
     
      
      . The revised reporting form contained an error: Code 1L02 was inadvertently omitted and Code 1L01 was inserted but was not described in the procedures manual. See Appellant’s App. 14; R. 1377, 1380.
     
      
      . The revised claim for the quarter which ended December 31, 1985, was not filed within the two-year period required by the statute and regulation and was denied for that reason as well. Colorado has not appealed this part of the district court’s decision.
     
      
      . Colorado's CAP provided for use of data in one quarter to determine the reimbursement for the subsequent quarter. Colorado began collecting data under its revised TARS beginning January 1, 1987, and, based on that data, claimed $594,-019 in federal funds for Title IV-E administrative expenses for the second quarter which ended June 30, 1987. ACYF disallowed the state’s claims for that quarter because the plan had not been approved to apply before July 1, 1987. The dispute over the claim for the second quarter of 1987 has been remanded to the agency.
     
      
      . On its appeal to the district court Colorado conceded its revised claim in the amount of $541,801 for the quarter ended December 31, 1985, was not submitted within the two-year period mandated by 45 C.F.R. § 95.7. This reduced the amount of the disputed disallowance to a revised claim of $2,785,361 in addition to $594,019 for the quarter ending June 30, 1987. Appellant's App. 43.
     
      
      . The Board also noted that the controller of the state agency submitted the TARS changes to DCA for its review and approval before the planned implementation date, an action that would not have been made unless the controller thought that the TARS changes were a CAP amendment.
     
      
      . "The general rule in the regulations is that a CAP amendment goes into effect prospectively following the event that gave rise to the amendment.” Missouri Dep't of Social Servs., Doc. No. 87-188, Dec. No. 1021 (Dep't HHS Feb. 21, 1989) (Appellant’s Opening Brief, Add. 3). The amendment is effective the first day of the calendar quarter following the event. Here, as in Missouri, the "event giving rise to the amendment is the State's discretionary decision to modify its methodology to maximize the allocation of costs to one of its programs.” Id. As in Missouri, Colorado appears to assert that when a state makes a discretionary change that may affect the costs allocated to programs, the change should be seen as rectifying an inequity, and thus should be applied retroactively. The Board in its Missouri decision rejected this approach, concluding that when action or inaction on the part of the agency was not the cause of the state failing to include all possible costs in the original claim, the agency was not under a mandate to allow the revised claim. Id. at 8-9. In Missouri, the Board noted that the mere assertion "that it would be inequitable not to apply the CAP amendment retroactively because it would stand to lose millions in [Title] IV-E funds" is not controlling, because "we simply do not know the impact of the CAP amendment for the retroactive period.” Id. at 9 & n. 4.
     
      
      . One of the individuals who did this calculation stated "that is the best that we can do with three data points if you want to have any precise estimate.” R. 1627-28. "[T]hree quarters of information was insufficient data to support a more sophisticated and precise analysis such as a linear regression." R. 1627.
     
      
      . Colorado argues that these revised claims are much more accurate because once the county employees were better trained on TARS reporting similar increases were shown and have been paid for by the federal government. It is logical to conclude that better training has produced more accurate recording of time. However, the revised handbook, the revised TARS coding procedures and the increase in numbers of Title IVE clients have also undoubtedly affected these figures. Further, Colorado has the responsibility for training employees to properly record their time and fairness dictates that it bear the consequences of inadequate training.
     