Interventions to control nosocomial infections : study designs and statistical issues

There is a wide range of potential study designs for intervention studies to decrease nosocomial infections in hospitals. The analysis is complex due to competing events, clustering, multiple timescales and time-dependent period and intervention variables. This review considers the popular pre-post quasi-experimental design and compares it with randomized designs. Randomization can be done in several ways: randomization of the cluster [intensive care unit (ICU) or hospital] in a parallel design; randomization of the sequence in a cross-over design; and randomization of the time of intervention in a stepped-wedge design. We introduce each design in the context of nosocomial infections and discuss the designs with respect to the following key points: bias, control for nonintervention factors, and generalizability. Statistical issues are discussed. A pre-post-intervention design is often the only choice that will be informative for a retrospective analysis of an outbreak setting. It can be seen as a pilot study with further, more rigorous designs needed to establish causality. To yield internally valid results, randomization is needed. Generally, the first choice in terms of the internal validity should be a parallel cluster randomized trial. However, generalizability might be stronger in a stepped-wedge design because a wider range of ICU clinicians may be convinced to participate, especially if there are pilot studies with promising results. For analysis, the use of extended competing risk models is recommended.

Estimating the burden of disease attributable to four selected environmental risk factors in South Africa

INTRODUCTION: The first South African National Burden of Disease study quantified the underlying causes of premature mortality and morbidity experienced in South Africa in the year 2000. This was followed by a Comparative Risk Assessment to estimate the contributions of 17 selected risk factors to burden of disease in South Africa. This paper describes the health impact of exposure to four selected environmental risk factors: unsafe water, sanitation and hygiene; indoor air pollution from household use of solid fuels; urban outdoor air pollution and lead exposure. METHODS: The study followed World Health Organization comparative risk assessment methodology. Population-attributable fractions were calculated and applied to revised burden of disease estimates (deaths and disability adjusted life years, [DALYs]) from the South African Burden of Disease study to obtain the attributable burden for each selected risk factor. The burden attributable to the joint effect of the four environmental risk factors was also estimated taking into account competing risks and common pathways. Monte Carlo simulation-modeling techniques were used to quantify sampling, uncertainty. RESULTS: Almost 24 000 deaths were attributable to the joint effect of these four environmental risk factors, accounting for 4.6% (95% uncertainty interval 3.8-5.3%) of all deaths in South Africa in 2000. Overall the burden due to these environmental risks was equivalent to 3.7% (95% uncertainty interval 3.4-4.0%) of the total disease burden for South Africa, with unsafe water sanitation and hygiene the main contributor to joint burden. The joint attributable burden was especially high in children under 5 years of age, accounting for 10.8% of total deaths in this age group and 9.7% of burden of disease. CONCLUSION: This study highlights the public health impact of exposure to environmental risks and the significant burden of preventable disease attributable to exposure to these four major environmental risk factors in South Africa. Evidence-based policies and programs must be developed and implemented to address these risk factors at individual, household, and community levels.

Studies on Wage Differentials and Labour Market Transitions

This thesis consists of four studies. The first study examines wage differentials between women and men in the Finnish manufacturing sector. A matched employer-employee data set is used to decompose the overall gender wage gap into the contributions of sex differences in human capital, labour market segregation, and residual within-job wage differentials. The topic of the second study is the relationship between the extended unemployment benefits and labour market transitions of older workers. The analysis exploits a quasi-experimental setting caused by a change in the law that raised the eligibility age of workers benefiting from extended benefits. Roughly half of the unemployed workers with extended benefits are estimated to be effectively withdrawn from labour market search. The risk of unemployment declined and the re-employment probability increased among the age groups directly affected by the reform. The third study provides an empirical analysis of a structural equilibrium search model. Estimation results from various model specifications are compared and discussed. The last study is a methodological study where the difficulties of interpreting the results of competing risks hazard models are discussed and a solution for a particular class of models is proposed. It is argued that a common practice of reporting the results of qualitative response models in terms of marginal effects is also useful in the context of competing risks duration models.

Iodine Brachytherapy for Large Uveal Melanomas

Uveal melanoma is the most common primary intraocular malignancy in adults. Vision in the affected eye is threatened by both the tumor and side-effects from the treatments currently available. Poor prognosis for saving vision increases with tumor size and, consequently, enucleation has been the treatment of choice for large uveal melanomas in most centers. However, increasing evidence suggests that no survival benefit is gained (nor lost) by enucleation as compared to eye-conserving methods. The Helsinki University Eye Hospital has since 1990 offered episcleral iodine-125 plaque brachytherapy (IBT) for all patients unwilling to undergo enucleation for a large uveal melanoma. The primary aim of this study was to assess survival, local tumor recurrence and preservation of the eye and vision after IBT in a population-based series of 97 patients with uveal melanomas classified as large by the Collaborative Ocular Melanoma Study (COMS) criteria. Further aims included reporting the incidence of side-effects and assessing the role of intraocular dose distribution and clinical risk factors in their development. Finally, means to improve the current treatment were investigated by using computer models to compare existing plaques with collimating ones and by comparing the outcome of a subgroup of 54 IBT patients with very thick tumors with 33 patients with similarly-sized tumors managed with transscleral local resection (TSR) in Liverpool, United Kingdom. Kaplan-Meier estimates of all-cause and melanoma-specific survival at 5 years after IBT were 62% and 65%, respectively, and visually comparable with the survival experience of patients reported after enucleation by the COMS. Local recurrence developed in 6% of eyes and 84% of eyes were conserved at 5 years. Visual prognosis was guarded with 11% avoiding loss of 20/70 vision and 26% avoiding loss of 20/400 vision in the tumor eye at 2 years. Large tumor height and short distance from the posterior pole were independently associated with loss of vision. Using cumulative incidence analysis to account for competing risks, such as enucleation and metastatic death, the 5-year incidence of cataract after IBT was 79%, glaucoma 60%, optic neuropathy 46%, maculopathy 52%, persistent or recurring retinal detachment (RD) 25%, and vitreous hemorrhage 36%. In multivariate competing risks regression models, increasing tumor height was associated with cataract, iris neovascularization and RD. Maculopathy and optic neuropathy were associated with distance from the tumor to the respective structure. Median doses to the tumor apex, macula and optic disc were 81 Gy (range, 40-158), 79 Gy (range, 12-632), and 83 Gy (range, 10-377), respectively. Dose to the optic disc was independently associated with optic neuropathy, and both dose to the optic disc and dose to the macula predicted vision loss after IBT. Simulated treatment using collimating plaques resulted in clinically meaningful reduction in both optic disc (median reduction, 30 Gy) and macular (median reduction, 36 Gy) doses as compared to the actual treatment with standard plaques. In the subgroup of patients with uveal melanomas classified as large because of tumor height, cumulative incidence analysis revealed that while long-term preservation of 20/70 vision was rare after both IBT and TSR, preservation of 20/400 vision was better after TSR (32% vs. 5% at 5 years). In multivariate logistic regression models, TSR was independently associated with better preservation of 20/400 vision (OR 0.03 at 2 years, P=0.005) No cases of secondary glaucoma were observed after TSR and optic neuropathy was rare. However, local tumor recurrence was more common after TSR than it was after IBT (Cumulative incidence 41% vs. 7% at 5 years, respectively). In terms of survival, IBT seems to be a safe alternative to enucleation in managing large uveal melanomas. Local tumor control is no worse than with medium-sized tumors and the chances of avoiding secondary enucleation are good. Unfortunately, side-effects from radiotherapy are frequent, especially in thick tumors, and long-term prognosis of saving vision is consequently guarded. Some complications can be limited by using collimating plaques and by managing uveal melanomas that are large because of tumor height with TSR instead of IBT. However, the patient must be willing to accept a substantial risk of local tumor recurrence after TSR and it is best suited for cases in which the preservation of vision in the tumor eye is critical.

Cesarean section and rate of subsequent stillbirth, miscarriage and ectopic pregnancy: a Danish register-based cohort study

Background: With cesarean section rates increasing worldwide, clarity regarding negative effects is essential. This study aimed to investigate the rate of subsequent stillbirth, miscarriage, and ectopic pregnancy following primary cesarean section, controlling for confounding by indication. Methods and Findings: We performed a population-based cohort study using Danish national registry data linking various registers. The cohort included primiparous women with a live birth between January 1, 1982, and December 31, 2010 (n = 832,996), with follow-up until the next event (stillbirth, miscarriage, or ectopic pregnancy) or censoring by live birth, death, emigration, or study end. Cox regression models for all types of cesarean sections, sub-group analyses by type of cesarean, and competing risks analyses for the causes of stillbirth were performed. An increased rate of stillbirth (hazard ratio [HR] 1.14, 95% CI 1.01, 1.28) was found in women with primary cesarean section compared to spontaneous vaginal delivery, giving a theoretical absolute risk increase (ARI) of 0.03% for stillbirth, and a number needed to harm (NNH) of 3,333 women. Analyses by type of cesarean section showed similarly increased rates for emergency (HR 1.15, 95% CI 1.01, 1.31) and elective cesarean (HR 1.11, 95% CI 0.91, 1.35), although not statistically significant in the latter case. An increased rate of ectopic pregnancy was found among women with primary cesarean overall (HR 1.09, 95% CI 1.04, 1.15) and by type (emergency cesarean, HR 1.09, 95% CI 1.03, 1.15, and elective cesarean, HR 1.12, 95% CI 1.03, 1.21), yielding an ARI of 0.1% and a NNH of 1,000 women for ectopic pregnancy. No increased rate of miscarriage was found among women with primary cesarean, with maternally requested cesarean section associated with a decreased rate of miscarriage (HR 0.72, 95% CI 0.60, 0.85). Limitations include incomplete data on maternal body mass index, maternal smoking, fertility treatment, causes of stillbirth, and maternally requested cesarean section, as well as lack of data on antepartum/intrapartum stillbirth and gestational age for stillbirth and miscarriage. Conclusions: This study found that cesarean section is associated with a small increased rate of subsequent stillbirth and ectopic pregnancy. Underlying medical conditions, however, and confounding by indication for the primary cesarean delivery account for at least part of this increased rate. These findings will assist women and health-care providers to reach more informed decisions regarding mode of delivery.

Influence of sex on the survival of patients with esophageal cancer

PURPOSE: The prognostic value of sex for esophageal cancer survival is currently unclear, and growing data suggest that hormonal influences may account for incidence disparities between men and women. Therefore, moving from the hypothesis that hormones could affect the prognosis of patients with esophageal cancer, we investigated the primary hypothesis that sex is associated with survival and the secondary hypotheses that the relationship between sex and survival depends, at least in part, on age, histology, and race/ethnicity.

PATIENTS AND METHODS: By using the SEER databases from 1973 to 2007, we identified 13,603 patients (34%) with metastatic esophageal cancer (MEC) and 26,848 patients (66%) with locoregional esophageal cancer (LEC). Cox proportional hazards model for competing risks were used for analyses.

RESULTS: In the multivariate analysis, women had longer esophageal cancer-specific survival (ECSS) than men in both MEC (hazard ratio [HR], 0.949; 95% CI, 0.905 to 0.995; P = .029) and LEC (HR, 0.920; 95% CI, 0.886 to 0.955; P < .001) cohorts. When age and histology were accounted for, there was no difference for ECSS between men and women with adenocarcinoma. In contrast, women younger than age 55 years (HR, 0.896; 95% CI, 0.792 to 1.014; P = .081) and those age 55 years or older (HR, 0.905; 95% CI, 0.862 to 0.950; P < .001) with squamous cell LEC had longer ECSS than men. In the squamous cell MEC cohort, only women younger than age 55 years had longer ECSS (HR, 0.823; 95% CI, 0.708 to 0.957; P = .011) than men.

CONCLUSION: Sex is an independent prognostic factor for patients with LEC or MEC. As secondary hypotheses, in comparison with men, women age 55 years or older with squamous cell LEC and women younger than age 55 years with squamous cell MEC have a significantly better outcome. These last two findings need further validation.

The Impact of income support programs on transitions to employment

The income support programs are created with the purpose of fighting both, the poverty trap and the inactivity trap. The balance between both is fragile and hard to find. Thus, the goal of this work is to contribute to solve this issue by finding how income support programs, particularly the Portuguese RSI, affect transitions to employment. This is made through duration analysis, namely using Cox and Competing Risks models. A particular feature is introduced in this work as it incorporates the possibility of Defective Risks. The estimated hazard elasticity with respect to the amount of RSI received for individuals who move to employment is -0,41. More than a half of RSI receivers stays for more than a year and the probability of never leaving to employment is 44%. The results appear to indicate that RSI has affected negatively transitions to employment.

Influence of noninjecting and injecting drug use on mortality, retention in the cohort, and antiretroviral therapy, in participants in the Swiss HIV Cohort Study.

OBJECTIVES: We studied the influence of noninjecting and injecting drug use on mortality, dropout rate, and the course of antiretroviral therapy (ART), in the Swiss HIV Cohort Study (SHCS). METHODS: Cohort participants, registered prior to April 2007 and with at least one drug use questionnaire completed until May 2013, were categorized according to their self-reported drug use behaviour. The probabilities of death and dropout were separately analysed using multivariable competing risks proportional hazards regression models with mutual correction for the other endpoint. Furthermore, we describe the influence of drug use on the course of ART. RESULTS: A total of 6529 participants (including 31% women) were followed during 31 215 person-years; 5.1% participants died; 10.5% were lost to follow-up. Among persons with homosexual or heterosexual HIV transmission, noninjecting drug use was associated with higher all-cause mortality [subhazard rate (SHR) 1.73; 95% confidence interval (CI) 1.07-2.83], compared with no drug use. Also, mortality was increased among former injecting drug users (IDUs) who reported noninjecting drug use (SHR 2.34; 95% CI 1.49-3.69). Noninjecting drug use was associated with higher dropout rates. The mean proportion of time with suppressed viral replication was 82.2% in all participants, irrespective of ART status, and 91.2% in those on ART. Drug use lowered adherence, and increased rates of ART change and ART interruptions. Virological failure on ART was more frequent in participants who reported concomitant drug injections while on opiate substitution, and in current IDUs, but not among noninjecting drug users. CONCLUSIONS: Noninjecting drug use and injecting drug use are modifiable risks for death, and they lower retention in a cohort and complicate ART.

Sector-Specific on-the-Job Training: Evidence from U.S. Data.

Using data from the National Longitudinal Survey of Youth (NLSY), we re-examine the effect of formal on-the-job training on mobility patterns of young American workers. By employing parametric duration models, we evaluate the economic impact of training on productive time with an employer. Confirming previous studies, we find a positive and statistically significant impact of formal on-the-job training on tenure with the employer providing the training. However, the expected net duration of the time spent in the training program is generally not significantly increased. We proceed to document and analyze intra-sectoral and cross-sectoral mobility patterns in order to infer whether training provides firm-specific, industry-specific, or general human capital. The econometric analysis rejects a sequential model of job separation in favor of a competing risks specification. We find significant evidence for the industry-specificity of training. The probability of sectoral mobility upon job separation decreases with training received in the current industry, whether with the last employer or previous employers, and employment attachment increases with on-the-job training. These results are robust to a number of variations on the base model.

Évaluation de l'impact clinique et économique du développement d'un traitement pour la schizophrénie

Contexte : Les stratégies pharmacologiques pour traiter la schizophrénie reçoivent une attention croissante due au développement de nouvelles pharmacothérapies plus efficaces, mieux tolérées mais plus coûteuses. La schizophrénie est une maladie chronique présentant différents états spécifiques et définis par leur sévérité. Objectifs : Ce programme de recherche vise à: 1) Évaluer les facteurs associés au risque d'être dans un état spécifique de la schizophrénie, afin de construire les fonctions de risque de la modélisation du cours naturel de la schizophrénie; 2) Développer et valider un modèle de Markov avec microsimulations de Monte-Carlo, afin de simuler l'évolution naturelle des patients qui sont nouvellement diagnostiqués pour la schizophrénie, en fonction du profil individuel des facteurs de risque; 3) Estimer le coût direct de la schizophrénie (pour les soins de santé et autres non reliés aux soins de santé) dans la perspective gouvernementale et simuler l’impact clinique et économique du développement d’un traitement dans une cohorte de patients nouvellement diagnostiqués avec la schizophrénie, suivis pendant les cinq premières années post-diagnostic. Méthode : Pour le premier objectif de ce programme de recherche, un total de 14 320 patients nouvellement diagnostiqués avec la schizophrénie ont été identifiés dans les bases de données de la RAMQ et de Med-Echo. Les six états spécifiques de la schizophrénie ont été définis : le premier épisode (FE), l'état de dépendance faible (LDS), l’état de dépendance élevée (HDS), l’état stable (Stable), l’état de bien-être (Well) et l'état de décès (Death). Pour évaluer les facteurs associés au risque de se trouver dans chacun des états spécifiques de la schizophrénie, nous avons construit 4 fonctions de risque en se basant sur l'analyse de risque proportionnel de Cox pour des risques compétitifs. Pour le deuxième objectif, nous avons élaboré et validé un modèle de Markov avec microsimulations de Monte-Carlo intégrant les six états spécifiques de la schizophrénie. Dans le modèle, chaque sujet avait ses propres probabilités de transition entre les états spécifiques de la schizophrénie. Ces probabilités ont été estimées en utilisant la méthode de la fonction d'incidence cumulée. Pour le troisième objectif, nous avons utilisé le modèle de Markov développé précédemment. Ce modèle inclut les coûts directs de soins de santé, estimés en utilisant les bases de données de la Régie de l'assurance maladie du Québec et Med-Echo, et les coûts directs autres que pour les soins de santé, estimés à partir des enquêtes et publications de Statistique Canada. Résultats : Un total de 14 320 personnes nouvellement diagnostiquées avec la schizophrénie ont été identifiées dans la cohorte à l'étude. Le suivi moyen des sujets était de 4,4 (± 2,6) ans. Parmi les facteurs associés à l’évolution de la schizophrénie, on peut énumérer l’âge, le sexe, le traitement pour la schizophrénie et les comorbidités. Après une période de cinq ans, nos résultats montrent que 41% des patients seront considérés guéris, 13% seront dans un état stable et 3,4% seront décédés. Au cours des 5 premières années après le diagnostic de schizophrénie, le coût direct moyen de soins de santé et autres que les soins de santé a été estimé à 36 701 $ canadiens (CAN) (95% CI: 36 264-37 138). Le coût des soins de santé a représenté 56,2% du coût direct, le coût de l'aide sociale 34,6% et le coût associé à l’institutionnalisation dans les établissements de soins de longue durée 9,2%. Si un nouveau traitement était disponible et offrait une augmentation de 20% de l'efficacité thérapeutique, le coût direct des soins de santé et autres que les soins de santé pourrait être réduit jusqu’à 14,2%. Conclusion : Nous avons identifié des facteurs associés à l’évolution de la schizophrénie. Le modèle de Markov que nous avons développé est le premier modèle canadien intégrant des probabilités de transition ajustées pour le profil individuel des facteurs de risque, en utilisant des données réelles. Le modèle montre une bonne validité interne et externe. Nos résultats indiquent qu’un nouveau traitement pourrait éventuellement réduire les hospitalisations et le coût associé aux établissements de soins de longue durée, augmenter les chances des patients de retourner sur le marché du travail et ainsi contribuer à la réduction du coût de l'aide sociale.

La néphrectomie partielle chez les patients atteints du cancer du rein de stade T1b

Objectif : La néphrectomie partielle est reconnue actuellement comme le traitement de choix des tumeurs de moins de 7 cm. Le but de notre étude est de comparer le taux de mortalité lié au cancer du rein suite au traitement par néphrectomie partielle ou radicale chez les patients de stade T1b, de présenter la tendance temporelle du taux d'intervention par néphrectomie partielle pour les tumeurs de stade T1b et d’identifier les facteurs sociodémographiques et tumoraux qui influencent le choix thérapeutique entre les deux types de traitement chirurgical. Méthode : Il s’agit d’une étude épidémiologique de type rétrospective. La population de patients provient de la base de donnée SEER (Surveillance, Epidemiology, and End Results) qui regroupe une grande proportion de la population nord-américaine. Dans notre étude, nous avons utilisé l’analyse par régression logistique pour identifier les facteurs sociodémographiques associés à l'intervention par néphrectomie partielle. Dans un deuxième temps, nous avons comparé la mortalité liée au cancer entre les deux options chirurgicales, après association par score de tendance pour diminuer les différences de base entre les deux populations. Nos critères étaient l’âge, la race, le sexe, l’état civil, le niveau socioéconomique, la taille tumorale, le grade nucléaire, l’histologie et la localité du centre hospitalier. L’analyse des données a été faite par le logiciel SPSS. Résultats : Le taux d'interventions par néphrectomie partielle a augmenté de 1,2% en 1988 à 15,9% en 2008 (p <0,001). Les jeunes patients, les tumeurs de petite taille, les patients de race noire, ainsi que les hommes sont plus susceptibles d'être traités par néphrectomie partielle (tous les p < 0,002). Parmi le groupe ciblé, le taux de mortalité lié au cancer à 5 ans et à 10 ans est de 4,4 et de 6,1% pour les néphrectomies partielles et de 6,0 et 10,4% pour les néphrectomies radicales (p = 0,03). Après ajustement de toutes les autres variables, les analyses de régression montrent que le choix entre les deux types de néphrectomie n’est pas associé à la mortalité lié au cancer (hazard ratio: 0,89, p = 0,5). Conclusion : Malgré un contrôle oncologique équivalent, le taux d'intervention par néphrectomie partielle chez les patients ayant un cancer du rein T1b est faible en comparaison à la néphrectomie radicale.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.