Conditional Probability Of Death Research Articles

Conditional Relative Survival of Exocrine Pancreatic Cancer: A Population-Based Study.

Adjusted prognostic information is important for treatment decisions, especially in elderly patients or survivors of exocrine pancreatic cancer (EPC). This study aims to investigate conditional relative survival (CS) rates and conditional probabilities of death in patients with EPC. Data of 77,975 individuals diagnosed with EPC between 1999 and 2019 were obtained from the Korea Central Cancer Registry. CS was analyzed across strata including histology groups (ductal adenocarcinoma excluding cystic or mucinous [group I, PDAC] and ductal adenocarcinoma specified as mucinous or cystic adenocarcinoma [group II]), and age. For PDAC, the overall 5-year relative survival (RS) rate at diagnosis, 3-year CS of 2-year survivors, and 5-year CS of 5-year survivors were 8.5%, 50.1%, and 77.6%, respectively. Overall conditional probabilities of death were 85.2% (≥ 80 years), 73.5% (70-79 years), and 62.0% (60-69 years) in year 1 after diagnosis. Among patients with localized or regional stage who underwent surgery, conditional probabilities of death of ≥ 80, 70-79, and 60-69 years were 37.7%, 32.5%, and 22.6% in the first year, and 26.6%, 27.2%, and 26.0% in year 2 after diagnosis. Half of patients with EPC who survived for 2 years survived for an additional 3 years. However, 5-year PDAC survivors require follow-up as more than 20% do not survive for a further 5 years. Elderly patients should not be excluded from active treatment for localized or regional-stage PDAC, as the CS of elderly patients who are fit enough to undergo surgery is not inferior to that of younger patients.

Conditional relative survival of patients with endometrial cancer: a Korean National Cancer Registry study.

ObjectiveThe purpose of this study was to estimate 5-year conditional relative survival (5Y CRS) rates of endometrial cancer (EC) in Korea accounting for time already survived. Subgroup-specific estimates stratified by various patient characteristics were also presented.MethodsUsing the data from the Korean Central Cancer Registry, 5Y CRS rates were calculated in patients who were diagnosed with EC between 1998 and 2017. The CRS rates were presented by year of diagnosis, age at diagnosis, histology, cancer stage, and treatment received.ResultsThe 5-year relative survival rate at the time of diagnosis was 89.0% for all cases. The probability of surviving an additional 5 years (i.e., 5Y CRS), if the patient survived 1, 2, 3, 4, and 5 years after diagnosis was 91.8%, 94.1%, 95.6%, 96.5%, and 97.3%, respectively. Patients with poor initial prognoses, i.e., those who were older, had non-endometrioid histology, and high stage, showed the largest improvements in 5Y CRS, reaching >90% for most subgroups, except those with serous histology (88.4%) and distant stage (77.7%). Patients aged ≥70 years had the highest probability of death in the 1st and 2nd years after diagnosis (13.8 and 11.0%), but the conditional probability of death in the 3rd, 4th, and 5th years declined rapidly to 7.3%, 4.5%, and 3.7%, respectively.ConclusionThe CRS rates for patients with EC improved with increased time elapsed from diagnosis. The greatest improvements in 5Y CRS were observed among patients who were older, those with non-endometrioid histology, and those with more advanced disease.

Conditional Relative Survival of Ovarian Cancer: A Korean National Cancer Registry Study.

ObjectiveConditional relative survival (CRS) rates, which take into account changes in prognosis over time, are useful estimates for survivors and their clinicians as they make medical and personal decisions. We aimed to present the 5-year relative conditional survival probabilities of patients diagnosed with ovarian cancer from 1997–2016.MethodsThis nationwide retrospective cohort study used data from the Korean Central Cancer Registry. Patients diagnosed with ovarian cancer between 1997 and 2016 were included. CRS rates were calculated stratified by age at diagnosis, cancer stage, histology, treatment received, year of diagnosis, and social deprivation index.ResultsThe 5-year relative survival rate at the time of diagnosis was 61.1% for all cases. The probability of surviving an additional 5 years, conditioned on having already survived 1, 2, 3, 4, and 5 years after diagnosis was 65.0, 69.5, 74.6, 79.3, and 83.9%, respectively. Patients with poorer initial survival estimates (older, distant stage, serous histology) generally showed the largest increases in CRS over time. The probability of death was highest in the first year after diagnosis (11.8%), and the conditional probability of death in the 2nd, 3rd, 4th, and 5th years declined to 9.4%, 7.9%, 6.1%, and 5.2%, respectively.ConclusionCRS rates for patients with ovarian cancer increased with each year they survived, but this did not reach the level of ‘no excess mortality’ even 5 years after diagnosis. The largest improvements in CRS were observed in patients with poorer initial prognoses. Our findings provide updated prognosis to ovarian cancer survivors and clinicians.

INCIDENCE, RISK FACTORS AND SURVIVAL OF CRITICALLY-ILL PATIENTS WITH ACUTE KIDNEY INJURY

Objective: to analyze the incidence, risk factors and survival of critically-ill patients with acute kidney injury. Method: a concurrent cohort study, conducted with 126 participants between May and September 2019 in a public Intensive Care Unit of the state of Acre. The Kaplan-Meier method was used to estimate the probability of death (log-rank 95% test) and the Cox regression model was employed to determine the prognostic factors of death. Results: the incidence of acute kidney injury was 37.3 per 1,000 individuals admitted to the intensive Care Unit. Disease recovery was the outcome in 36.7% of the patients, and 42.9% evolved to death. The conditional probability of death was higher in the female gender and in those who did not use mechanical ventilation, with glomerular filtration rate at admission < 60 ml/min/1.73 m2 and sepsis diagnosis. Regardless of the acute kidney injury diagnosis, the risk factors associated with death in the population of critically-ill patients were serum creatinine above 1.2 mg/dl at admission and glomerular filtration rate < 60 ml/min/1.73 m2 at admission. Conclusion: in this population, survival is aggravated by gender dimorphism and by the reduction of the glomerular filtration rate.

Extending Inferences from a Cluster‐Randomized Trial to a Target Population

Research ObjectiveIn cluster‐randomized trials, participating clusters are not necessarily representative of the target population of trial‐eligible clusters where the experimental treatments might be applied. To the extent that participating and nonparticipating clusters differ in terms of covariates that are modifiers of the treatment effect, the average treatment effect in the trial may not apply to the entire target population. We describe analyses that extend (generalize or transport) causal inferences from cluster‐randomized trials to a target population of clusters, under a general nonparametric model that allows for arbitrary within‐cluster dependence.Study DesignWe consider study designs where a subset of a cohort of clusters are invited and agree to participate in a randomized trial with cluster‐level treatment assignment (ie, nested trial designs). Treatment and outcome data need only be collected from clusters participating in the trial, but data on baseline covariates must be collected from the entire cohort. We propose doubly robust estimators of potential outcome means in the target population that exploit individual‐level data on covariates and outcomes to improve efficiency and are appropriate for use with machine learning methods.Population StudiedWe illustrate the methods using a 2 × 2 factorial cluster‐randomized trial of influenza vaccination strategies conducted in 818 nursing homes nested in a cohort of 4,475 trial‐eligible Medicare‐certified nursing homes. To be eligible for the trial, nursing homes had to be free‐standing facilities (ie, not hospital based) within 50 miles of a CDC‐reporting city, have a minimum of 50 long‐stay residents, and at least 80% of residents aged 65 years or older.Principal FindingsWe applied the methods to estimate the potential outcome means for the four vaccination strategies in the target population of trial‐eligible nursing homes. We estimated the conditional probability of trial participation (nursing home level) and the conditional probability of death from any cause (individual level, separately for each treatment group) using different methods to illustrate that our approach can easily accommodate them. One set of analyses used logistic regression models estimated by maximum likelihood methods. For comparison, we also estimated probabilities using various machine learning methods. Overall, the doubly robust estimator produced similar point estimates for the potential outcome mean under each treatment across all approaches for estimating the conditional probabilities of trial participation and death. Point estimates for generalizability analyses were largely similar to those from the randomized trial, suggesting that the trial‐only estimates were applicable to the broader population of trial‐eligible nursing homes for the outcome of all‐cause death.ConclusionsRecent work on extending causal inferences from individually randomized trials to a target population can be extended to the cluster trial setting, under a general causal model that allows for arbitrary within‐cluster dependence.Implications for Policy or PracticeWhen cluster‐randomized trials are embedded in large health care systems, investigators can use the methods we describe to extend causal inferences from the trials to the broader health care system.Primary Funding SourcePatient‐Centered Outcomes Research Institute.

PIN82 EXTENDING INFERENCES FROM A CLUSTER RANDOMIZED TRIAL TO A TARGET POPULATION

The clusters participating in cluster randomized trials are not necessarily representative of the target population of trial-eligible clusters where the experimental treatments might be applied. To the extent that participating and non-participating clusters differ in terms of covariates that are modifiers of the treatment effect, the average treatment effect in the trial may not apply to the entire target population. We describe analyses that extend (generalize or transport) causal inferences from cluster randomized trials to a target population of clusters, under a general nonparametric model that allows for arbitrary within-cluster dependence. We consider study designs where a subset of a cohort of clusters are invited and agree to participate in a randomized trial with cluster-level treatment assignment (i.e., nested trial designs). Treatment and outcome data need only be collected from clusters participating in the trial, but data on baseline covariates must be collected from the entire cohort. We propose doubly robust estimators of potential outcome means in the target population that exploit individual- level data on covariates and outcomes to improve efficiency and are appropriate for use with machine learning. We illustrate the methods using a 2x2 factorial cluster randomized trial of influenza vaccination strategies in 818 nursing homes that were nested in a cohort of 4,475 trial- eligible Medicare-certified nursing homes. We used machine learning methods to estimate the conditional probability of participation and the conditional probability of death, to obtain the potential outcome means for the vaccination strategies in the target population of trial-eligible nursing homes. Point estimates from generalizability analyses using different methods were similar, suggesting that the trial-only estimates were applicable to the broader population of trial-eligible nursing homes for the outcome of all-cause death. When cluster randomized trials are embedded in large health-care systems, investigators can use the methods to extend causal inferences.

Risk factors for death in patients with sepsis in an intensive care unit

Objective: to determine the main risk factors for death in patients with sepsis in an intensive care unit. Methods: it is a retrospective cohort study, wich included 126 patient chorts lhat had clinical and clinical and laboratory diagnosis of sepsis were considered eligible. The conditional probability of death was calculated through the Kaplan-Meier method and the risk of death was estimated by the hazard ratio, using a Cox regression model with p<0.050. Results: a total of 124 patients were included in the study. The main focus of infection was the respiratory system. Regarding the outcome, 40.3% patients with sepsis, 73.9% with severe sepsis and 69.2% with septic shock died. Patients with abdominal sepsis and using vasopressors were at higher risk of death. Conclusion: septic patients with abdominal source of infection and using vasopressor agents had a higher risk of dying, while patients who were tracheostomized had a better chance of living.

Fatores de risco para morte em pacientes com sepse em uma unidade de terapia intensiva

Objetivo: determinar os principais fatores de risco para a morte em pacientes com sepse em uma unidade de terapia intensiva. Métodos: trata-se de uma coorte retrospectiva, onde foram incluídos 124 prontuários de pacientes que tiveram diagnóstico clínico e laboratorial de sepse. A probabilidade condicional de morte foi calculada através do método de Kaplan-Meier; o risco de morte foi estimado pela razão de risco, utilizando modelo de regressão de Cox com p&lt;0,050. Resultados: o foco principal da infecção foi o sistema respiratório. Em relação ao desfecho, morreram 40,3% pacientes com sepse, 73,9% com sepse grave e 69,2% com choque séptico. Os pacientes com sepse abdominal e que utilizaram vasopressores apresentaram maior risco de morte. Conclusão: pacientes sépticos com fonte abdominal de infecção e fazendo uso de agentes vasopressores apresentaram maior risco de morte, enquanto que pacientes traqueostomizados tiveram melhores chances de sobreviver.

Failure-to-rescue after injury is associated with preventability: The results of mortality panel review of failure-to-rescue cases in trauma

Failure-to-rescue is defined as the conditional probability of death after a complication, and the failure-to-rescue rate reflects a center's ability to successfully "rescue" patients after complications. The validity of the failure-to-rescue rate as a quality measure is dependent on the preventability of death and the appropriateness of this measure for use in the trauma population is untested. We sought to evaluate the relationship between preventability and failure-to-rescue in trauma. All adjudications from a mortality review panel at an academic level I trauma center from 2005-2015 were merged with registry data for the same time period. The preventability of each death was determined by panel consensus as part of peer review. Failure-to-rescue deaths were defined as those occurring after any registry-defined complication. Univariate and multivariate logistic regression models between failure-to-rescue status and preventability were constructed and time to death was examined using survival time analyses. Of 26,557 patients, 2,735 (10.5%) had a complication, of whom 359 died for a failure-to-rescue rate of 13.2%. Of failure-to-rescue deaths, 272 (75.6%) were judged to be non-preventable, 65 (18.1%) were judged potentially preventable, and 22 (6.1%) were judged to be preventable by peer review. After adjusting for other patient factors, there remained a strong association between failure-to-rescue status and potentially preventable (odds ratio 2.32, 95% confidence interval, 1.47-3.66) and preventable (odds ratio 14.84, 95% confidence interval, 3.30-66.71) judgment. Despite a strong association between failure-to-rescue status and preventability adjudication, only a minority of deaths meeting the definition of failure to rescue were judged to be preventable or potentially preventable. Revision of the failure-to-rescue metric before use in trauma care benchmarking is warranted.

Age and preexisting conditions as risk factors for severe adverse events and failure to rescue after injury

BackgroundFailure to rescue (FTR: the conditional probability of death after complication) has been studied in trauma cohorts, but the impact of age and preexisting conditions (PECs) on risk of FTR is not well known. We assessed the relationship between age and PECs on the risk of experiencing serious adverse events (SAEs) subsequent FTR in trauma patients with the hypothesis that increased comorbidity burden and age would be associated with increased FTR. Materials and methodsWe performed a retrospective cohort analysis at an urban level 1 trauma center in Pennsylvania. All patients aged ≥16 y with minimum Abbreviated Injury Scale score ≥2 from 2009 to 2013 were included. Univariate logistic regression models for SAE and FTR were developed using age, PECs, demographics, and injury physiology. Variables found to be associated with the end point of interest (P ≤ 0.2) in univariate analysis were included in separate multivariable logistic regression models for each outcome. ResultsSAE occurred in 1136 of 7533 (15.1 %) patients meeting inclusion criteria (median age 42 [interquartile range 26-59], 53% African-American, 72% male, 79% blunt, median ISS 10 [interquartile range 5-17]). Of those who experienced an SAE, 129 of 1136 patients subsequently died (FTR = 11.4%). Development of SAE and FTR was associated with age ≥ 70 y (odds ratio 1.58-1.78, 95% confidence interval 1.13-2.82). Renal disease was the only preexisting condition associated with both SAE and FTR. ConclusionsTrauma patients with renal disease are mostly at increased risk for both SAE and FTR, but other PECs associated with SAE are not necessarily those associated with FTR. Future interventions designed to reduce FTR events should target this high-risk cohort.

Conditional relative survival of cancer patients and conditional probability of death

Little information is available on the conditional probabilities of death among patients who survive for >5 years after a diagnosis with cancer. The objective of this study was to estimate the conditional probabilities of death for breast cancer, prostate cancer, colorectal cancer, and lung cancer in France. The study included data from the French Network of Cancer Registries from 205,562 patients aged <75 years who were diagnosed with cancer between 1989 and 1997. The conditional probabilities of death were calculated by using a relative survival regression model in which age was included as a covariate. After the first year and until 10 years after diagnosis, the annual probability of death decreased dramatically for colorectal cancer: It was the same in all age groups after 3 years, and it was approximately 1% at 10 years. For prostate cancer, the decrease was not as great, and the conditional probability of death remained higher among younger patients at >4% at 10 years. During the 3 years after diagnosis, the probability of death was greater for older patients with breast cancer; then, it decreased less for younger patients compared with older patients, leading to a greater conditional probability of death among younger patients at 4 years and up to 10 years. The annual probability of death in patients with lung cancer decreased for both sexes but remained substantially higher for men than for women, reaching approximately 8% and 5%, respectively, at 10 years. Further studies would facilitate a better understanding of the observed differences in relative survival within European countries.

Benefit and Risk of Mammography Screening – Considerations from an Epidemiological Viewpoint: Stage-Dependent Lethality

Becker and Junkermann’s article on the benefits and risks of mammography screening is heralded on the title page with the words, Mammography: Screening Lowers Breast Cancer by 35%. This statement, which is also one of the authors’ three main conclusions, is misleading in two respects: (1) The authors are speaking, not of mortality in the usual epidemiological sense of the specific probability of death in a defined population group, but rather of lethality, i.e., the conditional probability of death over a certain period of observation after a particular diagnosis has been made and (in the normal situation) followed up with treatment (1). (2) The authors attempt to circumvent the statistical problem of lead-time bias, i.e., earlier diagnosis in the screened than in the unscreened population, by measuring the effect of screening in terms of mortality/lethality. They write: Mortality is the only variable quantifiable without bias for studies on the effectiveness of early detection activities. Yet the endpoint that they consider, i.e., lethality after the diagnosis of breast cancer of any type, is variable depending on the stage of the tumor (according to the WHO tumor classification) at the time the diagnosis is made. The distribution of cases in the screened population is selected in favor of earlier and prognostically more favorable stages, and a slower course of disease, in comparison to the unscreened population. Thus, a consideration of mortality/lethality after the disease is diagnosed does not eliminate lead-time bias. To do this, the authors would have had to present and discuss stage-dependent lethality rates over a defined period of time.

The risk of death associated with delayed coronary artery bypass surgery

BackgroundThe detrimental effect of delaying surgical revascularization has been estimated in randomized trials and observational studies. It has been argued that the Kaplan-Meier method used in quantifying the hazard of delayed treatment is not appropriate for summarizing the probability of competing outcomes. Therefore, we sought to improve the estimates of the risk of death associated with delayed surgical treatment of coronary artery disease.MethodsPopulation-based prospective study of 8,325 patients registered to undergo first time isolated coronary artery bypass grafting (CABG) in any of the four tertiary hospitals that provide cardiac care to adult residents of British Columbia, Canada. The cumulative incidence of pre-operative death, the cumulative incidence of surgery, and the probability that a patient, who may die or undergo surgery, dies if not operated by certain times over the 52-week period after the decision for CABG were estimated. The risks were quantified separately in two groups: high-severity at presentation were patients with either persistent unstable angina or stable angina and extensive coronary artery disease, and low-severity at presentation were stable symptomatic patients with limited disease.ResultsThe median waiting time for surgery was 10 weeks (interquartile range [IQR] 15 weeks) in the high-severity group and 21 weeks (IQR 30 weeks) in the low-severity group. One percent of patients died before surgery: 54 in the high-severity and 26 in the low-severity group. For 58 (72.5%) patients, death was related to CVD (acute coronary syndrome, 33; chronic CVD, 16; other CVD, 4; and sudden deaths, 5). The overall death rate from all causes was 0.61 (95% CI 0.48-0.74) per 1,000 patient-weeks, varying from 0.62 (95% CI 0.45-0.78) in the high-severity group to 0.59 (95% CI 0.37-0.82) in the low-severity group. After adjustment for age, sex, and comorbidity, the all-cause death rate in the low-severity group was similar to the high-severity group (OR = 1.02, 95% CI 0.64-1.62). The conditional probability of death was greater in the high-severity group than in the low-severity group both for all-cause mortality (p = 0.002) and cardiovascular deaths (p <0.001).ConclusionThe probability of death conditional on not having undergone a required CABG increases with time spent on wait lists.

Spatial decomposition of predation risk using resource selection functions: an example in a wolf–elk predator–prey system

Predation is a fundamental ecological and evolutionary process that varies in space, and the avoidance of predation risk is of central importance in foraging theory. While there has been a recent growth of approaches to spatially model predation risk, these approaches lack an adequate mechanistic framework that can be applied to real landscapes. In this paper we show how predation risk can be decomposed into encounter and attack stages, and modeled spatially using resource selection functions (RSF) and resource selection probability functions (RSPF). We use this approach to compare the effects of landscape attributes on the relative probability of encounter, the conditional probability of death given encounter, and overall wolf and elk resource selection to test whether predation risk is simply equivalent to location of the predator. We then combine the probability of encounter and conditional probability of death into a spatially explicit function of predation risk following Lima and Dill's reformulation of Holling's functional response. We illustrate this approach in a wolf–elk system in and adjacent to Banff National Park, Alberta, Canada. In this system we found that the odds of elk being encountered by wolves was 1.3 times higher in pine forest and 4.1 times less in grasslands than other habitats. The relative odds of being killed in pine forests, given an encounter, increased by 1.2. Other habitats, such as grasslands, afforded elk reduced odds (4.1 times less) of being encountered and subsequently killed (1.4 times less) by wolves. Our approach illustrates that predation risk is not necessarily equivalent to just where predators are found. We show that landscape attributes can render prey more or less susceptible to predation and effects of landscape features can differ between the encounter and attack stages of predation. We conclude by suggesting applications of our approach to model predator–prey dynamics using spatial predation risk functions in theoretical and applied settings.

Converting Clinical Literature to an Insured Population: A Comparison of Models Using Nhanes

The use of clinical literature to set risk classification standards for life insurance underwriting stems from the need to set the most accurate standards using the best available information. A necessary hurdle in this process is converting any excess mortality observed in a clinical study to the appropriate rating for use in underwriting. A widely accepted model in the insurance industry, the Excess Death Rate model, treats the excess as additive to the conditional probability of death for an insurance company’s unimpaired class. In this paper we test the validity of that model versus other common predictive models of excess mortality in an insured population. Applying these models to National Health and Nutrition Examination Survey (NHANES) data, we derive estimates for excess mortality from three commonly seen underwriting impairments in what could be considered a clinical population. These estimates are added to an estimate of an insurance company’s unimpaired mortality class and then used to predict deaths in an “insurable” subset of that clinical population. The Excess Death Rate model performed the best of all models, having the smallest cumulative difference of actual to predicted deaths. The use of publicly available data, such as that in NHANES, could help bridge the gap between clinical literature and its application in insurance underwriting if insurable cohorts can be reliably identified from these generally healthy, ambulatory groups.

Identification of poor prognostic features among patients requiring mechanical ventilation after hematopoietic stem cell transplantation

AbstractPatients who develop respiratory failure requiring mechanical ventilation after hematopoietic stem cell transplantation (HSCT) have very high mortality. Several investigators have identified prognostic features that can be used to identify a subset of these patients who are virtually certain to die, yet these have never been prospectively assessed. The objectives of this study were to determine the accuracy of published prognostic features for mortality and to determine the survival of patients who recover from respiratory failure. A systematic review of the literature was undertaken to identify reported poor prognostic features and survival rates. The study validated the reported poor prognostic features on a prospective, multicenter inception cohort of 226 patients with respiratory failure requiring mechanical ventilation after HSCT. The main outcome measures were determination of a baseline probability of death, drawn from literature review; likelihood ratio of mortality for each prognostic feature determined from the validation cohort; conditional probability of death in the presence of each feature; and 6-month survival of those who recover. Patients requiring mechanical ventilation after HSCT have a baseline probability of death of 82% to 96%. In the setting of combined hepatic and renal dysfunction, the probability of death rises to 98% to 100%. Other previously reported prognostic features are less strongly associated with mortality. For patients who recover from respiratory failure, the proportion surviving 6 months or longer ranges from 27% to 88%. It was concluded that in patients requiring mechanical ventilation after HSCT, the presence of combined hepatic and renal dysfunction is highly predictive of death. The presence of this feature may justify the recommendation to withdraw life-sustaining measures.

Analysis of a Toxicological Experiment Using a Generalized Linear Model with Nested Random Effects

This paper is concerned with the modeling and analysis of data collected in a large experiment designed to study the mortality in gypsy moths exposed to a mixture of two toxicants and observed over three time periods. The stochastic survival model employed is based on a pertinent biological model that describes the mode of action of synergism between the toxicants. Conditional probability of death in an interval, given survival up to that interval, is fitted by a binary response model with nested random effects added to fixed treatment effects. The random effects factors are used to account for intercorrelation and extravariation. Approximate maximum likelihood estimates of the parameters are evaluated by adapting the iteratively weighted least squares algorithm within GLIM. Results from the nested random effect model are compared with those from the quasi-likelihood procedure for overdispersed data. Analysis of the gypsy moth data suggests that the addition of an enzyme to an environmentally safe, but not very potent, microbial control agent produces a mixture that is a more effective toxicant for the gypsy moth than the microbial agent used alone.

Nonoperative observation therapy for splenic injuries: A safe therapeutic option?

Combining these reported and estimated incidences of mortality from overwhelming postsplenectomy infection, splenic salvage with nonoperative observation therapy and operative therapy, and the incidence of posttransfusion hepatitis and related mortality provides a conditional probability estimation of the risks of death with nonoperative observation therapy and operative therapy (Figure 4). The combined mortality rates for nonoperative observation and operative therapies are based on the following measured and estimated statistics: (1) The posttransfusion hepatitis death rate per unit of blood transfused is 0.14 percent. (2) Forty percent of children and 20 percent of adults who have successful nonoperative observation therapy receive an average of 2 units of blood. (3) One hundred percent of children and adults in whom nonoperative observation therapy is unsuccessful receive an average of 4 units of blood. (4) Twenty percent of children and adults who undergo operation initially receive an average of 2 units of blood. (5) Ten percent of observed children require laparotomy and 75 percent of these patients then undergo splenectomy. (6) Forty percent of adults who have nonoperative observation initially later require laparotomy, 93 percent of whom also require splenectomy. (7) Ten percent of children and adults treated with initial operation later require splenectomy. (8) Death from overwhelming postsplenectomy infection occurs in 0.026 percent of adults who undergo splenectomy and 0.052 percent of children who undergo splenectomy. Given these assumptions, the conditional probability of death in a child who initially undergoes nonoperative observation therapy is 0.17 percent compared with 0.06 percent for initial operative therapy. In adults, 0.26 percent of the observed patients die compared with 0.06 percent for those operated on initially. As stated, many of the percentages or probabilities listed are estimations based on the best available clinical data. The inability to establish a mortality rate from overwhelming postsplenectomy infection remotely resembling that reported for otherwise healthy patients required an unsubstantiated estimate. However, even when mortality rates from overwhelming postsplenectomy infection of 0.43 percent and 0.6 percent [3] were substituted, early laparotomy still produced lower mortality rates. This continues to be true if one assumes that early laparotomy will result in 50 percent or even 100 percent of patients undergoing splenectomy, although in these cases the statistical differences would be less. We acknowledge that these statistics may exceed or underestimate the true risk of either treatment plan. We also acknowledge that assignment of probabilities to an individual patient is a measure of the clinician or statistician's ignorance of the individual characteristics of any given patient [24]. One of the benefits of conditional probability models is that alternate probabilities can be substituted along the probability chain if there is disagreement with the percentages used for computation. We encourage physicians who disagree with our probabilities based on solid clinical data to substitute their figures in a similar model as a means to arrive at a logical approach to the management of a child or adult with an apparently isolated splenic injury.

Probabilistic Approaches to Current Life Table Estimation

"Two simple current life table estimators of conditional probabilities of death result from making either a uniform or exponential distributional assumption of time at death in the age interval. Each is compared with Chiang's estimator based on the concept of fraction of the last age interval of life. Graphical and numerical results are presented to assess the magnitude and direction of differences between estimators when the true value of Chiang's fraction takes on specific values."

Nonidentifiability of lethality in the survival experiment with serial sacrifice

This paper refers to the methodology of the survival experiment with serial sacrifice. In a finite-state, continuous-time model of this experiment, transitions between “illness states” are nonidentifiable. Turnbull and Mitchell proposed a methodology based on the “approximating assumption” A1 that changes in illness state can only occur at discrete times. This assumption identified lethality, i.e. the conditional probability of death in an interval of time, given that the experimental animal is alive in a specified illness state at the beginning of this interval. However, the TM-BT method of evaluating lethalities can lead to conclusions deviating substantially from reality when an animal has a high enough probability of contracting an illness and dying in an interval of time.