Economic and humanistic burden of HPV-related disease in Indonesia: A qualitative analysis.

The burden of human papillomavirus (HPV) and HPV-related cancers and genital warts is increasing in developing countries, including Indonesia. The objective of this study was to qualitatively explore the humanistic and economic burden of these HPV-related diseases in patients in Indonesia. In 2021, in-depth interviews and focus groups were conducted with patients (N = 18) with HPV-related diseases and healthcare professionals (HCPs; N = 10) specialised in treating these patients. Interviews explored the physical, mental, social, and economic burden of HPV-related diseases. Patients emphasised the psychological and social burden of HPV-related diseases, which negatively impacted their mental state and close relationships. Treatment for HPV-related diseases was also associated with a substantial cost, which health insurance only partially alleviated. HCPs understood the physical negative impact of HPV-related diseases, but some understated patients' social, psychological, and financial burden. This research underscores the substantial economic and humanistic burden of HPV-related diseases that could be prevented by vaccination. In addition, it highlights the need for novel interventions to reduce negative psychosocial consequences of HPV-related diseases in Indonesia. Increased HCP education of the broader humanistic impacts of HPV-related diseases may improve patient support and increase awareness for preventive strategy.

Health Impact and Cost-Effectiveness of Implementing Gender-Neutral Vaccination With the 9-Valent Human Papillomavirus Vaccine in Belgium.

Background: Routine human papillomavirus (HPV) immunization in Belgium is currently regionally managed, with school-aged girls receiving the 9-valent HPV (9vHPV) vaccine in Flanders and Wallonia-Brussels with a national catch-up program for females only. This study will assess whether expanding these programs to gender-neutral vaccination (GNV) with the 9vHPV vaccine is a cost-effective strategy in Belgium. Methods: A validated HPV-type transmission dynamic model estimated the potential health and economic impact of regional vaccination programs, comparing GNV versus female-only vaccination (FOV) with the 9vHPV vaccine in individuals aged 11-12 years in Flanders, GNV with the 9vHPV vaccine versus FOV with the 2-valent HPV (2vHPV) vaccine in individuals aged 12-13 years in Wallonia-Brussels, and national catch-up GNV versus FOV with the 9vHPV vaccine for those aged 12-18 years. Vaccination coverage rates of 90, 50, and 50% in both males and females were used in the base cases for the three programs, respectively, and sensitivity analyses were conducted. All costs are from the third-party payer perspective, and outcome measures were reported over a 100-year time horizon. Results: GNV with the 9vHPV vaccine was projected to decrease the cumulative incidence of HPV 6/11/16/18/31/33/45/52/58-related diseases relative to FOV in both Flanders and Wallonia-Brussels. Further reductions were also projected for catch-up GNV with the 9vHPV vaccine, including reductions of 6.8% (2,256 cases) for cervical cancer, 7.1% (386 cases) and 18.8% (2,784 cases) for head and neck cancer in females and males, respectively, and 30.3% (82,103 cases) and 44.6% (102,936 cases) for genital warts in females and males, respectively. As a result, a GNV strategy would lead to reductions in HPV-related deaths. Both regional and national catch-up GNV strategies were projected to reduce cumulative HPV-related disease costs and were estimated to be cost-effective compared with FOV with incremental cost-effectiveness ratios of €8,062, €4,179, and €6,127 per quality-adjusted life-years in the three programs, respectively. Sensitivity analyses were consistent with the base cases. Conclusions: A GNV strategy with the 9vHPV vaccine can reduce the burden of HPV-related disease and is cost-effective compared with FOV for both regional vaccination programs and the national catch-up program in Belgium.

The status of human papillomavirus vaccination recommendation, funding, and coverage in WHO Europe countries (2018-2019).

Background: There is a need to better understand HPV vaccination (HPVv) implementation in WHO Europe Region (WHO/ER), including recommendations, funding, and vaccination coverage rates (VCR). Methods: A targeted literature review (up to 31 January 2020) was conducted using national health ministry websites, WHO database, and published studies from WHO/ER countries (n = 53). HPVv recommendations and funding data (target age, gender, schedule, setting, target and monitored VCR) for primary and catch-up cohorts were collected. Results: National recommendations for HPVv exist in 46/53 (87%) countries, of which 38 (83%), 2 (4%), and 6 (13%) countries provided full, partial, or no funding, respectively, for the primary cohort. Fully or partially funded HPVv was provided for girls only in 25/53 (47%) countries and for both boys and girls in 15/53 (28%) countries. HPVv catch-up was fully or partially funded in 14/53 (26%) countries. Among 40 countries with a national immunization program (NIP), monitored VCRs ranged from 4.3% to 99% (n = 30). Of the 10 countries reporting VCR targets, only Portugal exceeded its target. Conclusion: Of the 53 WHO/ER countries, 40 have funded HPVv NIPs, among which 30 report VCRs. Additional efforts are required to ensure HPVv NIPs are fully funded and high VCRs maintained.

Healthcare utilization and associated costs following initiation of perampanel in patients with epilepsy.

PURPOSE: We compared health service utilization and costs for patients with epilepsy before and after initiation of perampanel and compared with matched controls. METHOD: Patients were selected from the Clinical Practice Research Datalink (CPRD). Patients initiating perampanel were matched to controls initiating an alternate add-on therapy for the same underlying epilepsy subtype. First prescription defined index date. Primary and secondary care contacts and associated costs were aggregated in the 12 months before and after index date. Secondary care contacts were available for a subset (~60%) of patients. RESULTS: Three hundred and forty-three patients treated with perampanel were identified. One hundred and eighty-three (53.4%) were male, mean age was 39.1 (sd: 16.0). Mean epilepsy duration was 21.1 (standard deviation (sd): 13.3) years. Two hundred and eighty-seven (83.7%) were matched to controls. Inpatient admissions with a primary diagnosis of epilepsy (0.5 versus 0.2 per patient-year (ppy), p = 0.002) and neurology specific outpatient appointments (3.2 versus 2.9 ppy, p = 0.041) were significantly reduced following initiation with perampanel. Total costs attributable to epilepsy (£1889 to 1477 ppy) and overall secondary costs (£2593 to £2102) were also significantly reduced. There was no significant difference in primary care, outpatient, or general inpatient admissions. Compared with controls, there was a significant reduction in primary epilepsy admissions (incidence rate ratio (IRR): 0.423; 95% Confidence intervals (CI): 0.198-0.835) but a significant increase in outpatient appointments (1.306; 95% CI: 1.154-1.478) and accident and emergency contacts (1.603; 95% CI: 1.081-2.390) for patients treated with perampanel. CONCLUSION: Treatment with perampanel is associated with reduced epilepsy-related inpatient admissions and accident and emergency contacts.

The Impact of Price Reductions After Loss of Exclusivity in a Cost-Effectiveness Analysis: Fingolimod Versus Interferon Beta-1a for the Treatment of Relapsing-Remitting Multiple Sclerosis.

BACKGROUND: Cost-effectiveness analyses tend not to take into account the availability of lower-priced generics following loss of exclusivity (LOE) of branded products. By not considering these generics, which are typically adopted quickly, total costs are likely to be overestimated and may be unreflective of real-world payer conditions in the United States. OBJECTIVE: To assess the impact of including future price reductions following LOE on the cost-effectiveness of fingolimod versus intramuscularly administered interferon beta-1a (IM IFNß-1a) as treatments for multiple sclerosis. METHODS: This model was adopted from a previously published Markov model and was conducted from a U.S. payer perspective over a 10-year time horizon. Patients with relapsing-remitting multiple sclerosis entered the model and received either fingolimod (an oral therapy) or IM IFNß-1a (an injectable). These treatments reflect the interventions studied in the TRANSFORMS randomized clinical trial. Clinical, cost, and utility inputs were based on a recent cost-effectiveness review of therapies for multiple sclerosis. To model LOE, price reductions and the proportion of patients switching to generic versions following LOE were based on published estimates. Price reductions varied to reflect the difference in product types (oral vs. large molecule injectable). Assumptions were also made around the proportion of patients switching to generic versions over time following LOE and the projected date of LOE. Outcomes included per-patient total direct costs (medication, administration and monitoring, and disease-related costs including relapses), quality-adjusted life-years, and the incremental cost per quality-adjusted life-year. RESULTS: Assuming no price reductions following LOE, fingolimod was considered cost-effective versus IM IFNß-1a ($118,434 per quality-adjusted life-year), despite having higher total direct costs over 10 years ($475,740 vs. $446,792). When including future price reductions following LOE, total direct costs were reduced with fingolimod and were lower than those accrued with IM IFNß-1a over the model time horizon ($308,570 vs. $442,653). Cost-effectiveness results were sensitive to changes in both clinical parameters and medication costs. Scenario analyses demonstrated that an earlier date of LOE was associated with lower total costs. CONCLUSIONS: Health economic models may predict higher total costs when the price reductions following LOE are not considered. Here, oral fingolimod was seen to be cost-saving versus IM IFNß-1a over the model time horizon when such price reductions were included. The cost implications of not accounting for future price changes may determine whether an intervention is considered cost-effective and as such may influence reimbursement decisions based on cost-effectiveness thresholds. Multiple product types (e.g., oral, injectable, and infused agents) have been approved for use as treatments for multiple sclerosis in the United States, and LOE is likely to have a different effect on each of these therapies. DISCLOSURES: This study was funded by Novartis Pharmaceuticals Corporation. Hua and Hersh report consulting fees from Novartis for work on this study. Hua also reports speaking, advisory board, and consulting fees from Biogen, Genzyme, Teva, EMD Serono, Genentech, TG Therapeutics, and Novartis for activities outside of this study. Hersh also reports speaking and consulting fees from Novartis, Biogen, Genzyme, Genentech, and EMD Serono for activities outside of this study, and research grants from PCORI and Biogen. At the time of this research, Morten and Kusel were paid employees of Costello Medical, which was contracted by Novartis to undertake some of this study's work. Lin, Cave, Herrera, and Ko were paid employees of Novartis at the time of this research. Cave, Herrera, and Ko also report owning stock in Novartis Pharmaceuticals. Varga provided services to Novartis at the time of this research and has nothing further to disclose. This research was presented as a poster at the AMCP Managed Care & Specialty Pharmacy Annual Meeting 2017; March 27-30, 2017; Denver, CO.

The Impact of Disease-Modifying Therapy Access Barriers on People With Multiple Sclerosis: Mixed-Methods Study.

BACKGROUND: In the United States, people with relapsing-remitting multiple sclerosis (RRMS) can face difficulty accessing disease-modifying therapies (DMTs) because of insurance, pharmacy, or provider policies. These barriers have been associated with poor adherence and negative health outcomes. OBJECTIVE: The goals of this study were to describe the overall occurrence of difficulties and delays associated with gaining access to DMTs among people with RRMS, to assess DMT adherence during periods of reduced access, and to contextualize the patients' journey from receipt of a prescription for DMT to obtaining and taking their medication when faced with access barriers. METHODS: We recruited US-based adults self-reporting RRMS from a Web-based health data-sharing social network, PatientsLikeMe. Individuals were invited to complete a Web-based survey if they reported a diagnosis of RRMS and were prescribed a DMT for MS. Follow-up phone interviews were conducted with 10 respondents who reported experiencing an MS-related relapse during the time they had experienced challenges accessing DMTs. RESULTS: Among 507 survey completers, nearly half were either currently experiencing an issue related to DMT assess or had difficulty accessing a DMT in the past (233/507, 46.0%). The most frequently reported reasons for access difficulty were authorization requirements by insurance companies (past issues: 78/182, 42.9%; current issues: 9/42, 21%) and high out-of-pocket costs (past issues: 54/182, 29.7%; current issues: 13/42, 31%). About half (20/39, 51%) of participants with current access issues and over a third (68/165, 41.2%) of those with past issues went without their medication until they could access their prescribed DMT. Relapses were reported during periods of reduced DMT access for almost half (56/118, 47.5%) of those with past issues and nearly half (22/45, 49%) of those with current issues. Resolving access issues involved multiple stakeholder agents often coordinated in a patient-led effort. Among those who had resolved issues, about half (57/119, 47.9%) reported that doctors or office staff were involved, under half (48/119, 40.3%) were involved themselves, and about a third (39/119, 32.8%) reported the drug manufacturer was involved in resolving the issue. Follow-up interviews revealed that the financial burden associated with obtaining a prescribed DMT led to nonadherence. Additionally, participants felt that DMT treatment delays and stress associated with obtaining the DMT triggered relapses or worsened their MS. CONCLUSIONS: This study expands current research by using a patient-centered, mixed-methods approach to describe barriers to MS treatment, the process to resolve barriers, and the perceived impact of treatment barriers on outcomes. Issues related to DMT access occur frequently, with individuals often serving as their own agents when navigating access difficulties to obtain their medication(s). Support for resolution of DMT access is needed to prevent undue stress and nonadherence.

Cost-Effectiveness of Aspirin Adherence for Secondary Prevention of Cardiovascular Events.

BACKGROUND: Suboptimal adherence to aspirin therapy for secondary prevention of cardiovascular (CV) events is an important public health problem. Prior studies have demonstrated non-adherent patients are at higher risk of experiencing CV events. OBJECTIVES: This study aimed to estimate the clinical and economic outcomes of aspirin non-adherence in patients with a prior primary CV event. METHODS: We developed a Markov model to estimate the cost-effectiveness of aspirin adherence from a generic US managed care payer perspective over a 5-year time horizon. Costs, utilities and rates of aspirin adherence, CV events and adverse events were gathered from published literature to populate the model. Outcomes were quality-adjusted life years (QALYs), costs (US$) and incremental cost-effectiveness ratios (ICERs). We applied the model separately to a population without type II diabetes as a comorbidity (non-diabetic model) and a population with type II diabetes (type II diabetes model). A one-way sensitivity analysis was performed to assess the model uncertainty. RESULTS: The base case showed adherent patients lived 0.25 and 0.36 QALYs longer than non-adherent patients in the non-diabetic model and type II diabetes model, respectively. Adherence to aspirin had an ICER of US$25/QALY in the non-diabetic population, while it saved US$297 per patient over a 5-year period in the type II diabetes population. One-way sensitivity analysis showed the models were most sensitive to rates of non-fatal events in non-adherent patients. CONCLUSION: This study suggests aspirin adherence may improve QALYs for patients with a prior primary CV event. Further, it may decrease costs in patients with type II diabetes. While additional research is needed to validate these results, payers may wish to increase strategies to promote adherence in order to improve population health. TRIAL REGISTRATION: Not applicable.

Communication: Renormalization method for infinite lattice sums revisited: Lattice sums with Bloch phase factors.

An infinite lattice summation scheme based on the idea of renormalization is generalized to enable the evaluation of infinite lattice sums with Bloch phase factors which can occur when treating long-range interactions in infinite periodic systems. The scheme is fast, with easily adjustable accuracy and is not limited to any choice of special points in the Brillouin zone. Illustrative calculation for a first few contributions for a simple cubic lattice is presented.

Evaluating Oncology Value-Based Frameworks in the U.S. Marketplace and Challenges in Real-World Application: A Multiple Myeloma Test Case.

BACKGROUND: With the continuous rise in costs for oncology drugs, the American Society of Clinical Oncology (ASCO), the Institute for Clinical and Economic Review (ICER), the Memorial Sloan Kettering Cancer Center's Drug Abacus (DrugAbacus), and the National Comprehensive Cancer Network (NCCN) have developed value-based frameworks (VBFs) to assist stakeholders in formulary and treatment decision-making processes. Since emerging VBFs have the potential to affect available treatment options for patients, it is important to understand the differences associated with these VBFs within various therapeutic areas. OBJECTIVES: To (a) compare VBFs across 3 therapeutic options for relapsed or refractory multiple myeloma (RRMM) and (b) identify challenges and limitations associated with real-world decision making using VBFs in the U.S. marketplace. METHODS: The values of regimens carfilzomib (CFZ), elotuzumab (ELO), and ixazomib (IX) were generated using the ASCO, NCCN, ICER, and DrugAbacus VBFs. These regimens, used for second- or third-line treatment of RRMM, shared a common comparator in clinical trials: lenalidomide + dexamethasone (LEN + DEX). ASCO's 2016 VBF, which incorporated clinical benefit, toxicity, and bonus points, was used to generate a net health benefit score, along with the drug wholesale acquisition cost, for each regimen compared with LEN + DEX. Results of the 2016 NCCN Evidence Blocks for multiple myeloma and the ICER 2016 report of treatment options for RRMM were extracted to generate the value of CFZ, ELO, and IX. No output was generated from DrugAbacus because of the lack of regimens included in the test case. Shortcomings associated with running the test case in RRMM for each VBF were also identified. RESULTS: Among the 3 therapeutic agents, CFZ, in combination with LEN + DEX, was the most valued. ASCO and ICER VBFs suggested that CFZ + LEN + DEX may be the most valued, followed by ELO + LEN + DEX and IX + LEN + DEX. NCCN suggested that LEN + DEX may be the most valued followed by CFZ + LEN + DEX, IX + LEN + DEX, and ELO + LEN + DEX. A number of shortcomings were noted across each VBF, such as complexities of drug evidence evaluation with the ASCO VBF, the inability to adjust the ICER and NCCN VBFs to specific populations, and subjectivity associated with the NCCN VBF and DrugAbacus. CONCLUSIONS: Although the test case provided some consensus on treatment decisions, there is much nuance and limitations with the VBFs available for RRMM. Clearer objectivity and better adaptability to specific treatment decisions are warranted. DISCLOSURES: No outside funding supported this study. The authors have nothing to disclose. All authors contributed to study concept and design, as well data collection and interpretation. Djatche and Goble wrote and revised the manuscript, along with Chun and Varga. Portions of this work have previously been presented at the AMCP Managed Care and Specialty Pharmacy Annual Meeting 2017 in Denver, Colorado, March 27-30, 2017, and at the ISPOR 22nd Annual International Meeting in Boston, Massachusetts, May 20-24, 2017.

Patient and Provider Characteristics Associated With Optimal Post-Fracture Osteoporosis Management.

Despite an estimated 2 million osteoporosis (OP)-related fractures annually, quality of care for post-fracture OP management remains low. This study aimed to identify patient and provider characteristics associated with achieving or not achieving optimal post-fracture OP management, as defined by the current HEDIS quality measure. The study included women 67 to 85 years of age, with ≥1 fracture, and continuous enrollment in a Humana insurance plan. The study identified a higher percentage of black women in the not achieved group (6.2% vs 5.4%; P < .0001) and Hispanic women in the achieved group (3.0% vs 1.3%; P < .0001). The not achieved group largely included patients residing in the South and urban and suburban areas. The majority of providers were primary care or OP-related specialty, and 66% did not achieve the 4-star OP rating. The study findings can guide development of predictive models to identify at-risk women to improve post-fracture OP management.

Hospitalization rates during potentially inappropriate medication use in a large population-based cohort of older adults.

BACKGROUND AND AIMS: The temporal relationship between potentially inappropriate medication (PIM) use and hospitalization remains uncertain. We examined whether current PIM use increases the rate of hospitalization and estimated the rate of hospitalization during exposure to individual PIMs. METHODS: A retrospective population-based cohort study of 1 480 137 older adults was conducted using the 2003-2013 Italian Emilia-Romagna Regional administrative healthcare database (~4.5 million residents), which includes demographic, hospital and outpatient prescription information. Each day of follow-up was defined as exposed/unexposed to PIMs that 'should always be avoided', according to the Maio criteria, an Italian modified version of the Beers criteria. The study outcome was all-cause hospitalizations. Crude PIM-related hospitalization rates were calculated for individual PIMs. Repeated-events Cox proportional hazards models with time-dependent covariates estimated adjusted hazard ratios for hospitalization during PIM exposure, as defined by three versions of the Maio criteria (v2007, v2011, v2014). RESULTS: During >10 million person-years of follow-up, 54.2% of individuals used ≥1 PIM and 10.9% of all person-time was exposed to v2014 PIMs. Among 1 604 901 hospitalizations, 15.6% occurred during v2014 PIM exposure. Crude hospitalization rates during v2014 PIM-exposed and unexposed person-time were 228.1 and 152.1 per 1000 person-years, respectively. The PIM with the highest rate of hospitalization was ketorolac, while nonsteroidal anti-inflammatory drugs had the most exposure time. The hazard of hospitalization was 16% greater (hazard ratio = 1.16; 95% confidence interval 1.14, 1.18) among patients exposed to v2014 PIMs. The v2007 and v2011 estimates were similar. CONCLUSIONS: In this large population-based cohort of older adults, we found a 16% increased hospitalization risk associated with PIM exposure.

A Review of US Drug Costs Relevant to Medicare, Medicaid, and Commercial Insurers Post-Affordable Care Act Enactment, 2010-2016.

Since passage of the Affordable Care Act (ACA) in 2010, US stakeholders are increasingly being held accountable for the value of healthcare services and drugs administered to patients. Pharmacoeconomic analyses offer one method of demonstrating a product's value, yet there is a lack of resources specific to US drug costs relevant to each stakeholder. The aim of this study was to review current US drug costs (post-ACA). A literature review aimed at finding evidence on outpatient prescription drug costs was performed using the following sources: PubMed, governmental agencies, news websites, the Academy of Managed Care Pharmacy (AMCP) website, and Google Scholar. Articles were limited to those published in the years "2010-2016" and the "English" language, and those that described drug acquisition costs, reimbursement costs, and rebates or discounting for Medicare, Medicaid, and commercial payors. The Drug Cost Focus Group (DCFG) was convened to supplement the literature review; the DCFG provided their expertise on US drug costs and emerging issues affecting drug costs. ACA legislation increased drug rebates for manufacturers participating in the Medicaid Drug Rebate Program. Acquisition costs commonly referred to in the literature include the wholesale acquisition cost and average manufacture price. Drugs reimbursed by Medicaid are currently based on the actual acquisition cost and ACA-Federal Upper Limit. Evidence suggests that reimbursement methods in the public market are varied. Current gaps in the literature regarding commercial insurers' drug costs (post-ACA) present barriers to the application of relevant drug costs to pharmacoeconomic analyses.

Variation in hospital utilization at the end of life for patients with cancer in the Emilia-Romagna region of Italy.

INTRODUCTION: Despite the preference of many patients to die at home, high proportions of patients with advanced cancer undergo major procedures, receive intensive care, and die in the hospital. The goal of this study is to examine variation in hospital utilization and site of death for patients dying with poor-prognosis cancer in the Regione Emilia-Romagna (RER), Italy. METHODS: We conducted a retrospective, population-level study using administrative data. Patients were included if they died in 2012 and had at least one hospital admission for metastatic or poor-prognosis cancer within 180 days of death. Variations in the use of the hospital, intensive care, and procedures performed were evaluated. RESULTS: 11,470 patients died with metastatic or poor-prognosis cancer in 2012. Seventy-eight percent of patients were hospitalized in the last month of life while 50.7% of patients died in the hospital. Results varied by local health authority from 38.3% to 69.3%. Of patients who had an ICU stay, 55.1% in the community hospitals and 59.8% in the teaching hospitals were admitted to the ICU on the day of death or the day before death. 7.5% of patients underwent a major procedure in the last 30 days of life. CONCLUSIONS: The overall high rate, and substantial variation, in hospital care at the end of life offers the RER the opportunity to evaluate if increasing availability of palliative care, along with provider and patient education, could reduce utilization of high-cost hospital care and increase patient and family satisfaction.

Cost-of-Illness Studies: An Updated Review of Current Methods.

INTRODUCTION: Cost-of-illness (COI) studies provide policy-relevant information for cross-country, longitudinal, and other cost comparisons. Prior studies have called for standardization in COI methods. We investigated trends, identified factors associated with variation in COI estimation methods, and characterized reporting of heterogeneity in COI estimates. METHODS: The review of COI studies was implemented following (i) a structured search of PubMed, SCOPUS and EMBASE; (ii) a review of abstracts; (iii) a full-text review; and (iv) classification of articles according to six COI estimation methods: Sum_All Medical, Sum_Diagnosis Specific, Matched, Regression, Other_Total and Other_Incremental. Descriptive and multivariable regression analyses were conducted. RESULTS: Of the 993 studies included in the full-text review, 186 (18.7 %) were Sum_All Medical, 458 (46.1 %) were Sum_Diagnosis Specific, 96 (9.7 %) were Matched, 97 (9.8 %) were Regression, 70 (7.1 %) were Other_Incremental, and 68 (6.9 %) were Other_Total. Compared with the early period, publications in the middle and late period were associated with lower odds of using Sum_All Medical compared with Sum_Diagnosis Specific (adjusted odds ratio [AOR]middle 0.14; 95 % CI 0.07-0.28; AORlate 0.44; 95 % CI 0.29-0.67). Overall, 640 articles (64 %) reported COI estimates across patient groups defined by patient-level factors, while 247 articles (25 %) reported COI estimates across patient groups defined by non-patient-level factors. CONCLUSION: The disease-specific total costing method (Sum_Diagnosis Specific) was most commonly used and its use increased over the time period covered by this review. The investigation of subgroup heterogeneity in COI estimates represents an area for future research.

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition.

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k(1)(1)k(2)(1)|g(1)(2)g(2)(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion.

Grid-free density functional calculations on periodic systems.

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Density fitting of two-electron integrals in extended systems with translational periodicity: the Coulomb problem.

Density fitting approach to Coulomb integrals for infinite systems with translational periodicity is reformulated in direct space. Despite of the Coulomb infinite decay of some integrals, direct-space calculation is shown to be feasible. Moreover, we show that the direct-space ansatz is completely equivalent to our previous formulation in reciprocal space. Computational demands scale linearly with the number of unit cells. In addition, direct-space treatment has some practical advantages over the reciprocal-space formulation. The efficiency of our scheme is demonstrated on systems with translational periodicity in one dimension. Computation time takes only a small fraction of the conventional calculation with exact integrals. We show that for infinite systems auxiliary basis sets of equally good quality as for molecules can be constructed in a systematic way.