The bingo model of survivorship: 1. probabilistic aspects

A "bingo" model is one in which the pattern of survival of a system is determined by whichever of several components, each with its own particular distribution for survival, fails first. The model is motivated by the study of lifespan in animals. A number of properties of such systems are discussed in general. They include the use of a special criterion of skewness that probably corresponds more closely than traditional measures to what the eye observes in casually inspecting data. This criterion is the ratio, r(h), of the probability density at a point an arbitrary distance, h, above the mode to that an equal distance below the mode. If this ratio is positive for all positive arguments, the distribution is considered positively asymmetrical and conversely. Details of the bingo model are worked out for several types of base distributions: the rectangular, the triangular, the logistic, and by numerical methods, the normal, lognormal, and gamma.

Risk adjusting community rated health plan premiums: a survey of risk assessment literature and policy applications

This paper surveys recent health care reform debates and empirical evidence regarding the potential role for risk adjusters in addressing the problem of competitive risk segmentation under capitated financing. We discuss features of health plan markets affecting risk selection, methodological considerations in measuring it, and alternative approaches to financial correction for risk differentials. The appropriate approach to assessing risk differences between health plans depends upon the nature of market risk selection allowed under a given reform scenario. Because per capita costs depend on a health plan's population risk, efficiency, and quality of service, risk adjustment will most strongly promote efficiency in environments with commensurately strong incentives for quality care.

Unguided clinical and actuarial assessment of re-offending risk: a direct comparison with sex offenders in Denmark

Meta-analyses suggest that actuarial risk assessments outperform unguided clinical judgment for prediction of recidivism in criminal offenders. However, there is a lack of direct comparisons of the predictive accuracy of clinical judgment and actuarial risk scales for sexual offenders. We followed up 121 male sex offenders (> or =18 years) subjected to pre-trial forensic psychiatric assessment in Denmark in 1978-1992 (mean post-detainment time = 16.4 years) to compare the predictive validity of unstructured clinical judgment of recidivism risk with that of the well-established Static-99 (Hanson and Thornton, Law and Human Behavior 24:119-136, 2000) and an extension of the Static-99, the Static-2002 (Hanson and Thornton, Notes on the development of Static-2002 (Rep. No. 2003-01), Public Safety and Emergency Preparedness Canada, Ottawa, Canada, 2003). The predictive accuracy of unguided judgment did not exceed chance for any sexual, severe sexual or any violent (sexual or non-sexual) reconviction (AUCs of the ROC curve = 0.52, 95%CI = 0.41-0.63; 0.50, 95%CI = 0.34-0.67; and 0.57, 95%CI = 0.40-0.73, respectively). In contrast, all three outcomes were predicted significantly better than chance by the Static-99 (AUC = 0.62, 95%CI = 0.52-0.72; 0.72, 95%CI = 0.59-0.84; and 0.71, 95%CI = 0.56-0.86) and the Static-2002 (AUC = 0.67, 95%CI = 0.57-0.77; 0.69, 95%CI = 0.56-0.83; and 0.70, 95%CI = 0.55-0.86). Static-99 outperformed clinical judgment for sexual recidivision (chi(2) = 5.11, df = 1, p < .05). The Static-2002 was significantly more accurate for the prediction of any sexual recidivism as compared to unguided clinical judgment but its advantage fell just short of statistical significance for severe sexual recidivism (chi(2) = 3.56, df = 1, p = 0.06). When tested for recidivism within 2 years, none of the three prediction methods yielded results significantly better than chance for any outcome. This direct trial of the unguided clinical method argues against its continued use for risk assessment of sexual offenders.

The parameters of death: a consideration of the quantity of information in a life table using a polynomial representation of the survivorship curve

How much unique information is contained in any life table? The logarithmic survivorship (lx) columns of 360 empirical life tables were fitted by a weighted fifth degree polynomial, and it is shown that six parameters are adequate to reproduce these curves almost flawlessly. However, these parameters are highly intercorrelated, so that a two-dimensional representation would be adequate to express the similarities and differences among life tables. It is thus concluded that a life table contains but two unique pieces of information, these being the level of mortality in the population which it represents, and the relative shape of the underlying mortality curve.

Comparison of two risk assessment instruments for sexual offenders

The current research examines the predictive validity of the Static-99 and the SORAG in predicting sexual and violent recidivism among a sample of 258 treated high-risk sexual offenders. While the SORAG was found to have moderate predictive accuracy for both sexual and violent recidivism over a 5-year follow-up period, the Static-99 was found to only predict sexual recidivism. As well, the actual recidivism rates in the current sample were compared to the published risk percentages for each of the instruments. For both the Static-99 and the SORAG the current sample re-offended at a lower rate than expected. Possible explanations for this finding are discussed.

Assessment of the use of the age- and sex-specific United States population as a control group for analysis of survival in coronary artery disease

The use of the age- and sex-specific U.S. population as a control group for analysis of survival in coronary artery disease was assessed. Population-based survival rates were calculated for nonsurgically treated patients evaluated for coronary artery disease at Duke University Medical Center. Survival of the overall group of medically treated patients with significant coronary artery disease was lower than the corresponding age- and sex-specific U.S. population rates. However, survival of patients with significant disease who had normal left ventricular contraction and stable chest pain was similar to the age- and sex-specific population survival rates. Both the observed survival and the population-based survival estimates for patients with normal left ventricular contraction and stable pain were lower than the survival of patients with normal coronary arteriograms. Even after deaths from ischemic heart disease are eliminated from the population rates, survival of patients with normal coronary arteries exceeded the age-and sex-specific population survival. Because of biases inherent in the selection of patients for cardiac catheterization and the presence of other serious diseases in persons in the general population is not an adequate control group for rigorous analysis of the effect of therapy in coronary artery disease.

The analysis of survival data from a central cancer registry with passive follow-up

We present analyses for survival data obtained from a central cancer registry with passive follow-up. This method of data collection has the potential to produce unknown random losses which would affect estimates of survival. We show that non-parametrically estimated conditional distributions remove any effect of these unknown losses and that a compound mixture model estimates their magnitude. Lung cancer data are used to illustrate the procedures.

Risk and safety assessment in child welfare: instrument comparisons

The assessment of risk is a critical part of child welfare agency practice. This review of the research literature on different instruments for assessing risk and safety in child welfare focuses on instrument reliability, validity, outcomes, and use with children and families of color. The findings suggest that the current actuarial instruments have stronger predictive validity than consensus-based instruments. This review was limited by the variability in definitions and measures across studies, the relatively small number of studies examining risk assessment instruments, and the lack of studies on case decision points other than the initial investigation.

Sex offenders and actuarial risk assessments: ethical considerations

When assessing the recidivism risk of previously convicted sex offenders, the relevant ethical standards and practice guidelines obligate psychologists to acknowledge numerous limits related to their data and conclusions. For the actuarial instruments used in these assessments, the highest rates of classification accuracy are associated with greater specificity compared with sensitivity. Selecting cut-off scores to maximize sensitivity results in an inordinate frequency of false positive classifications. Attempts at maximizing specificity create an undesirable frequency of false negative classifications.Unfortunately, adjusted actuarial assessment cannot remedy these problems created by the sensitivity-specificity tradeoff. As an unstandardized procedure, the accuracy of adjusted actuarial assessment is severely limited. Consequently, civil proceedings for previously convicted sexual offenders rely on assessments of very limited accuracy. Undertaking these assessments, therefore, may be inconsistent with relevant ethical standards and practice guidelines.

A modified life table method to study congenital genetic disorders: an application in sickle cell anemia

A modified life table procedure is introduced designed to study the survival of patients with congenital genetic disorders with the endpoint defined by a complication or death. It uses the ages of the patients as the time axis as in "population' or "current' life tables, and it allows patients to enter and exit the study as in survival life tables. The procedure uses the exact length of time that each patient is observed in the study to determine the conditional probabilities of developing the complication. The proposed procedure is especially helpful in studying recurrent complications or events that occur frequently. The proposed life table procedure is demonstrated in the study of the conditional probability of developing a sickle cell crisis in 509 patients with sickle cell anemia (SS) with different number of prior crises. The demonstration is intended to illustrate the use of the proposed method and not to investigate the clinical severity of sickle cell anemia. It was found that the risk of crisis was to investigate the clinical severity of sickle cell anemia. It was found that the risk of crisis was positively related to the number of prior crises in SS patients (P less than 0.001). This trend was significant in the first three decades of life.

ANTEROCOD: actuarial survival curves applied to medical coding support for chronic diseases

For the practitioner, choosing diagnosis codes is a non-intuitive operation. Mistakes are frequent, causing severe consequences on healthcare performance evaluation and funding. French physicians have to assign a code to all their activities and are frequently prone to these errors. Given that most of the time and particularly for chronic diseases indexed information is already available, we propose a tool named AnterOcod, in order to support the medical coding task. It suggests the list of most relevant plausible codes, predicted from the patient's earlier hospital stays, according to a set of previously utilized diagnosis codes. Our method applies the estimation of code reappearance rates, based on an equivalent approach to actuarial survival curves. Around 33% of the expected correct diagnosis codes were retrieved in this manner, after evaluating 998 discharge abstracts, significantly improving the coding task.

The design and use of a simple database for head and neck cancer

A simple database for head and neck cancer using a simple coding system is described. New patients and follow-up data can be added easily at the terminal. Interactive data-analysis can easily be performed by anyone who understands the coding system; specific skills in computer programming and system handling are not needed.

Formulae for cause-deleted life tables

The medical and demographic literature contain two popular formulae for the construction of cause-deleted life table lx values, one developed for applications in follow-up studies and the other for cross-sectional studies. It turns out that for both types of applications one of the two formulae is virtually always of better quality than the other. A formula developed by Keyfitz and Frauenthal is usually better than either.

The efficiency of a group-specific mandated benefit revisited: the effect of infertility mandates

This paper examines the labor market effects of state health insurance mandates that increase the cost of employing a demographically identifiable group. State mandates requiring that health insurance plans cover infertility treatment raise the relative cost of insuring older women of child-bearing age. Empirically, wages in this group are unaffected, but their total labor input decreases. Workers do not value infertility mandates at cost, and so will not take wage cuts in exchange, leading employers to decrease their demand for this affected and identifiable group. Differences in the empirical effects of mandates found in the literature are explained by a model including variations in the elasticity of demand, moral hazard, ability to identify a group, and adverse selection.

Extension of life-table methodology to allow for left-censoring in survival studies of pacing devices followed by commercial monitoring services

The actuarial life-table is commonly used to describe lifetime data of living subjects and manufactured products. The life-table method allows subjects to come under observation at different times and, thus, to have differing lengths of follow-up, by assuming all subjects begin their lifetimes relative to the outcome of interest at some common point in time. As time progresses, subjects are withdrawn from the life-table when their period of observation has elapsed. This pattern of follow-up is often termed "right-censoring." An important feature of the classical life table approach is that the time at which the subject is placed at risk is known, and the status relative to the outcome of interest is known for the entire time at risk. Sometimes, however, subjects cannot be observed for some period after the beginning of their lifetimes. The example to be considered involves follow-up data collected by a commercial pacemaker monitoring service, to which patients subscribe, generally at some point following the actual implant of the pacemaker. Since the outcome of interest is device failure after implant, some means of dealing with the lack of information between implant and initiation of follow-up is needed. The extension of the actuarial life-table to accommodate this "left-censoring" will be described in this paper.

A time series modeling approach in risk appraisal of violent and sexual recidivism

For over half a century, various clinical and actuarial methods have been employed to assess the likelihood of violent recidivism. Yet there is a need for new methods that can improve the accuracy of recidivism predictions. This study proposes a new time series modeling approach that generates high levels of predictive accuracy over short and long periods of time. The proposed approach outperformed two widely used actuarial instruments (i.e., the Violence Risk Appraisal Guide and the Sex Offender Risk Appraisal Guide). Furthermore, analysis of temporal risk variations based on specific time series models can add valuable information into risk assessment and management of violent offenders.

Clinical-economic appropriateness of drug treatments: designing a method that combines evidence-based information and cost assessments to construct league tables accounting for the potential number of patients

This paper presents a method to assess drug treatment appropriateness, based on an original combination of economic analysis, pharmacoepidemiological techniques and evidence-based information. This method generates an index of clinical-economic appropriateness for the treatment under examination, by comparing the theoretically expected health gain (EHG) to the yearly national expenditure (EXPEND) on that drug and the amount of health that is thought to be gained in the 'real' patients (RHG). This paper reviews all the analyses conducted so far using this method, and discusses their main results. The primary aim of this article is to suggest a ranking approach for allocating the drug budgets of national health systems.

Life-span of amalgam restorations in primary molars: some results and comments on statistical analyses

The life-span of amalgam restorations placed in primary molars by three general dental practitioners is investigated. Two methods of analysis have been carried out. In the analysis of "non-independent" restorations (i.e. using several restorations from each mouth), the median survival time was 52.8 months with an apparent standard error of 2.1 months. In the analysis of "independent" restorations (i.e. only using one restoration from each mouth), three random samples were chosen and their median survival times were 68.2 months (s.e. = 6.9), 60.5 months (s.e. = 6.9), and 56.8 months (s.e. = 3.7). The two methods are compared and discussed. It is concluded that the analysis of "independent" restorations should be the method of choice in studying the life-span of restorations.

The application of a modified follow-up life table technique to the study of outpatient clinic services for sickle-cell patients

A cohort of 60 matched pairs of sickle-cell anaemia (SS) patients from Ibadan, Nigeria and Oakland, California, were compared in a follow-up study. The null hypothesis tested was that there was no significant difference in the morbidity associated with sickle-cell anaemia among Ibadan SS patients receiving antimalarial prophylaxis and Oakland SS patients. Proportions of all clinic visits during which the patients had crises or infections associated with sickle cell anaemia (SSINF) were used as measures of morbidity. A modification of the follow-up life table was used for the analysis. Plots of PX and its confidence bands against frequency of clinic visits due to crises and SSINF were drawn. The Kruskal Wallis test was used to determine any significant differences in the probability of SS patients from either of the two centres visiting the clinic because of crises or SSINF. The results showed no significant differences in these probabilities.

Predictive medical information and underwriting

Medical underwriting involves the application of actuarial science by analyzing medical information to predict the future risk of a claim. The objective is that individuals with like risk are treated in a like manner so that the premium paid is proportional to the risk of future claim.