The study evaluated the performance of PSD in determining the **probability** of **survival** in adult subjects with TBI. It highlighted some complexities in determining the **probability** of **survival**. An issue is related to the interrelationships of injury parameters and other factors such as age, sex, pre-existing medical conditions that can influence the **probability** of **survival** [41]. AIS, GCS, age, respiration rate, pulse rate and systolic blood pressure play an important role in determining the **probability** of **survival** in TBI cases. We are currently working on improving the performance of models for injury outcome analysis. In this study PSD was compared with Ps14. The newer version of Ps14, i.e., Ps17, is similar to Ps14 but its coefficients were changed slightly. In this study we did not have access to Ps17 values from the TARN database but in future we will compare its performance with PSD when Ps17 values become available to us.

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The FIS provides likelihood rather than **probability** (i.e. measure of chance). Although **probability** and likelihood could be related, they are not the same measure. To illustrate the point, if for a person the **probability** of being frail is 0.5, that person has a 50% chance of being frail (i.e. he or she may not fail at all or be completely frail. However, if the same person (in fuzzy logic domain processing) has the likelihood of being frail equal to 0.5 (from maximum of 1), that person is definitely frail to an extent represented by 0.5. In the next sections a brief overview of a number of existing methods for determining the **probability** of **survival** is provided, study's methodology and its results are then explained.

Trauma injury is an important cause of death and disability [1]. Determining the **probability** or likelihood of **survival** in trauma injuries is important for triage, setting treatment priorities and research and management audit [2]. Numerous parameters influence the **probability** of **survival** that include extent, type and location of body injuries, pre-existing medical conditions (such as a heart illness), physiological parameters (such as heart rate, blood pressure and respiration rate), age, gender, frailty and neurological parameters that indicate the level of conscious state. A complicating factor is the manner and extent of interaction and interrelations of these parameters on the **probability** of **survival**.

Abstract: Hemodialysis patients are highly exposed to infections because the blood has to circulate out of the body through a cleaning machine. Usually an apparatus such as fistula or catheter is used to manipulate the blood access. Grafts and blood factors are thought to be m ajor causes of morbidity and mortality. In this paper, sixty patients are considered, the whole population of the infected hemodialysis patients who came to the infectious service of Hedi Chaker hospital in Sfax Tunisia over 10 years period. The data are not available on all the patients. Statistics on: (1) Clinical factors such as age and gender and (2) Blood factors such as type and resistance of the germs are computed. A univariate analysis for each factor and its effects on the **probability** of **survival** are presented. A multivariate analysis is performed in which the **probability** of **survival** is found to be related to the non-presence of prosthesis, higher hemoglobin level and stable heart beats per minute. Monte Carlo methodology helped to refine the result by making inferences on the global population of the infected hemodialysis patients.

In this chapter the operations and the results for the three methods (PSD, IRCC and combing IRCC with FL) for determining **probability** of **survival** are explained and their merits and limitations are analyzed against the exiting Ps14 method. The study mainly evaluated the performance of the methods for determining the **probability** of **survival** in adult subjects with traumatic brain injuries as TBI represented most trauma cases. A number of other body regions were also included in the analyses but the numbers associated with them were much smaller. In this chapter two probabilities of **survival** models were developed. One was based on Bayesian statistics that accommodated PSD and the other was a novel approach called IRCC. There were 4124 TBI cases (age: mean = 67.9 years, standard deviation = 21.6 years). In total, 86.2% of cases were survivors and 13.8% of cases were not survivors. The parameters considered for input to PSD and IRCC were age, AIS, GCS, PR, SBP and RR. PSD was used as the statistical method while IRCC is an iterative method. These two models were calibrated on randomly selected, roughly 2/3 (number 2676), of the trauma cases and their performances were validated on the remaining cases (number 1448, i.e. validation dataset). The effectiveness of the two models in determining the **probability** of **survival** was compared with Ps14 method that uses regression operation to predict **probability** of **survival** Ps14 is the method developed by the Trauma and Research Audit Network. Fuzzy inference system was further adopted as part of IRCC to further improve its operation.

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This work was motivated by increased attention in the medical literature on conditional **survival**. We distinguish between two types of conditional **survival** probabilities. The first refers to those proba- bilities that condition on fixed covariates at time of diagnosis (e.g., Xu and O’Quigley, 2000). The second, which we refer to as time-conditional **survival** probabilities, condition on time survived and will be the focus of the work here. With earlier detection, better therapies for diseases, and more systematic tracking, patients in recent years have been surviving longer and information on their long-term follow-up is more readily available. With patients living longer, there is interest in estimat- ing the **probability** of **survival** not from a patient’s time of diagnosis, but rather from her/his present state sometime after diagnosis. Time-conditional **survival** **probability** is defined as the **probability** of surviving at least an additional ∆ years given that a patient has already survived a years. As described in further detail in Chapter 2, this **probability** can be estimated by the ratio of the a- and (∆ + a)-year estimated **survival** probabilities from a single Kaplan-Meier survivor function (Kaplan and Meier, 1958).

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characteristic (ROC) curve analysis was used to find the overall predictivity of parameters and the best cutoff value for detection, along with sensitivity and specificity, and uni- variate analysis was performed for each variable followed by multivariate analysis to detect factors’ predictors for poor **survival**. The Mann–Whitney U-test was used to compare two nonparametric quantitative variables. **Survival** curve analysis was carried out to detect the **probability** of **survival** according to VEGF and endocan levels among HCC group and the prognostic values, and P < 0.05 was considered sta- tistically significant.

All analyses of plasma C-peptide concentrations (in quartiles) were controlled for baseline age and time since last meal, and subsequent analyses controlled for baseline BMI, or clinical stage and Gleason grade to assess the independent association of C-peptide. Tests for trend were conducted by treating median concentration of quartiles as a continuous variable. We also examined the joint association between BMI (<25 kg/m 2 vs. ≥25 kg/m 2 ) and quartile of C- peptide concentration and tested the significance of the interaction by including a product term of the two variables with the main exposures. Because excluding 11 men with history of diabetes at baseline did not change the results materially, we presented data including all men with plasma C-peptide levels. We used Cox proportional hazards regression models adjusting for age at diagnosis and smoking categories to produce plots of prostate cancer-specific **survival** curves for the three BMI categories or for the quartiles of C-peptide concentration. In addition, we conducted log rank tests controlling for age at diagnosis and smoking status to test if the **survival** curves estimated via Kaplan-Meier method for the three BMI categories or for the quartiles of C-peptide concentration are equal. All statistics were calculated using SAS (version 9.1.3; SAS Institute Inc, Cary, NC), with a two-sided significance level of 0.05.

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In recent years, the quantum walk on the trapped lattice has been intensively investigated due to importance ap- plications in quantum information and computing. Therefore, many theoretical and experimental studies have been carried out to understand the effect of the trapping states on the quantum walk. For example, Agliari [1] considered a continuous-time quantum walk propagating on Erdos-Renyi random graphs in the pres- ence of a random distribution of traps, and showed that the **survival** **probability** exhibits an exponential character which fluctuates depending on the trap concentration. Zahringer et al. [2] implemented a quantum walk using trapped ions. They used an experimental technique to determine the **probability** distribution along a line in phase space. It is shown that instabilities in the trapping frequency leads to decoherence and by change in the coupling strength due to high phonon numbers. Schimitz et al. [3] implemented the proof of principle for the quantum walk of one ion in a linear ion trap. It is shown that quantum interference enforces asymmetric, non- classical distributions in the highly entangled degrees of freedom (of coin and position states). Xue et al. [4] im- plemented a multi-step quantum walk for a single trapped ion with interpolation between quantum and random walk by randomizing the generalized Hadamard coin flip phase. It is shown that the distribution of the

In studies of **survival** time, we graph the Kaplan-Meier estimator of the **survival** function for each of the subgroups. That is, plotting the corresponding estimates of the two survivor functions on the same axes of Kaplan Meier estimator. Generally if the plot shows that the pattern of one **survival** function lies above another, it would mean the group defined by the upper curve lived longer, or had a more favorable **survival** experience than the group defined by the lower curve. However, the statistical question is whether the observed difference seen on the plot is significant. This can be answered using an appropriate statistical test (Hosmer et al, 1999). The general form of test statistic that deal with this issue is given as

Data from this analysis validate the significant and positive contribution of the FTA with the EU for Israeli export advantage, in the majority of sectors. At the outset, we note that the median duration for the whole sample of exports to the EU is 13 years, compared to 10 years for Israeli exports to the rest of the world. Furthermore, the gap between the **survival** rates, differentiated by the type of destination, is notably larger as time progresses, meaning that the **probability** of maintaining the Israeli export RCA is significantly higher after 15 years compared to after 5 years. At the end point of the analysis, the **survival** rates are especially higher for exports to the EU in traditional labor-intensive sectors, such as wood, textiles and clothing, footwear, and hides and skins.

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to the form or distribution of the baseline hazard, this can be regarded as the nonparametric part of the Cox proportional hazards model. However, the Cox model assumes a parametric form with respect to the effect of the predictors on the hazard. In particu- lar, as seen in equation 4, the predictors are assumed to multiply hazard at any point in time. This is an important assumption of the Cox model referred to as the assumption of proportional hazards. It means that the hazard functions for any two individuals at any point in time should be proportional. In other words, if a certain individual has a risk of the event at some initial point in time that is twice as high as that of another individual, then, under the proportional hazards assumption the risk remains twice as high also at all later times. There are a variety of different graphical and goodness-of-fit based procedures that can be used to evaluate the proportional hazards as- sumption for **survival** data (see Kleinbaum and Klein (2005) for an overview.).

C- ART is based on the association of three anti-viral drugs that inhibit the HIV replication. It was introduced in the care of HIV patients in 1997 and has improved the **survival** of these patients on renal replacement ther- apy (RRT) [15]. Reported results on **survival** of HIV positive patients compared to HIV negative one on haemodialysis are conflicting. In the USA **survival** of HIV patients with ESKD was lower compared to HIV negative patients [10, 16], while 2-year **survival** of treated HIV positive patients on haemodialysis was comparable to HIV-negative ones in France [17]. Despite the burden of HIV and the improve access to RRT and c-ART in most countries in sub Saharan Africa (SSA), data on sur- vival of HIV patients on RRT are rare. A recent study in South Africa reported a similar **survival** between HIV positive and negative patients [18].

A further consideration is how the fate of these mutations in temperate phage might compare with similar mutations in an obligately lytic bacteriophage. To compare these cases, we consider a temperate phage in the lysogeny-advantage pa- rameter regime (Table 1), such that the temperate phage has no advantage a priori during the lytic cycle of replication. As a comparison, we consider an obligately lytic phage with burst size B ¼ 100 and attachment **probability** A ¼ 1=100; such that both wild-type phage have the same burst size and ﬁt- ness. We then compare the fate of mutations increasing either B or A for lineages ﬁrst occurring in (a) free temperate phage, (b) prophage, or (c) the obligately lytic phage. Not surpris- ingly, mutations ﬁrst occurring in the lytic phage fare simi- larly to mutations that ﬁrst occur in the lytic cycle of the temperate phage, as shown in the left-hand panels of Figure 5. In the panels on the right of Figure 5, we plot the same results vs. the selective advantage, s. In the top panel, we see that for both traits, mutations ﬁrst occurring in the lytic phage or the lytic cycle of the temperate phage fare similarly. In contrast, if we compare mutations ﬁrst occurring in prophage to the same mutations occurring in the lytic phage, the pro- phage mutations are far more likely to survive drift when rare.

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overall dataset was 31% (s.d. 3; range 26–35). The misclassi- fication rate for men was 34% (6; 26– 40), and for females was 26% (3; 23–31: p ¼ 0.04). The prediction of implant **survival** based on age at surgery and annual wear rate for male and female subjects are shown in figure 4a,b, respectively. The sex-specific **probability** density estimation for both control and revision groups are also shown in figure 5. The inferior performance for males can be attributed to the long-tailed den- sity of the control group (figure 5a) compared to its female counterpart (figure 5c). There are also fewer data points with high wear rate in the male revision group (figure 5b) compared with the female revision group (figure 5d). This perhaps resulted in a better training of the model over the region with high annual wear rate where only female subjects were used.

Model selection results suggest that the location in which an individual oystercatcher spends the breeding season is more important in determining its **survival** and recruitment than its natal site. However, models that included an effect of natal site suggest that place of origin may influence some age classes more than others (Table 3.2; Figures 3.4 & 3.5). Estimates for juvenile **survival**, transition to adult, and immature **survival** rates were all higher than rates assumed in a recent demographic model of American Oystercatchers in North Carolina based largely on parameters estimated for the Eurasion Oystercatcher (Felton et al. 2017). This finding supports statewide surveys of breeding pairs that suggest that North Carolina’s breeding population may be growing (Schweitzer 2016, Schweitzer et al. 2017). However, differences in vital rates across natal sites indicates that sites may not be equal in their contributions to overall population viability.

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frequency percentages for categorical variables. Char- acteristics were compared between groups using the 2- sample t -test, rank sum test, Chi square test, or Fisher’s exact test. Logistic regression was used to as- sess whether hospital **survival** was associated with epoch after adjusting for POS score. In order to assess for trends in **survival** over time, before and after the introduction of the protective ventilation, logistic regression analyses was performed for each time period with hospital **survival** as the dependent variable and calendar year as the continuous explana- tory variable. To explore the association between local vs. remote transfer on **survival** we focused on neonates with early presentation of symptoms during Epoch II. **Survival** was compared using the Chi square test. In all cases 2-tailed P values <0.05 were considered statistically significant. Data were analyzed using SAS version 9.3 (SAS Institute Inc, Cary, NC).

Our aim is to provide an overview of different time- to-event measures that can be used to summarize **survival** data in both the overall **survival** setting and the “relative **survival**” setting and to introduce them in a way they can be interpreted and estimated by applied researchers. In the overall **survival** setting, these measures are the overall sur- vival, the conditional **survival** (CS) and the restricted mean **survival** time (RMST). In the “relative **survival**” setting, the measures detailed below are the net **survival** (NS), the con- ditional net **survival** (CNS), the restricted mean net **survival** time (RMNST), the crude probabilities of death (CPD) due to each competing cause and the number of life years lost (NLYL) due to each competing cause. We illustrate their use and interpretation using a cancer epidemiology example with public health policy implications, where we display **survival** socioeconomic disparities after the diagnosis of colon cancer. We discuss their usefulness distinguishing clinical perspective from population health perspective. For reproducibility, we also provide R code for the derivation and the computation of all the measures introduced in the Supplementary materials.

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acceptance guideline or criterion . . . For most regulatory applications, that value is specified to be the mean [. . . ] The mean values referred to are the arithmetic means of the **probability** distributions that result from the propagation of the uncertainties on the input parameters. Uncertainty propagation methods will in theory produce accurate results for any given distri- bution; but their application is hard: apart from computational complexity, their fundamental drawbacks are in delivering numerical results rather than insight on how the various aspects of parameter uncertainty may affect the results, and in requiring a complete description of the pa- rameters’ distribution, which in practice may be hard to specify with any degree of soundly based consensus (especially if we consider that the uncertainties on the various parameters are not sta- tistically independent – a concern called sometimes “epistemic correlation”). When the problem is to extract a distribution for the parameters in question from detailed failure data about multiple similar systems, typical approaches to modelling and inference use hierarchical or empirical Bayes [3, Ch.8],[42, Ap.A],[11],[40, §6],[31].

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Seedling germination and establishment rates are known to vary significantly with local above- and below-ground micro- environmental conditions, and vegetation that ameliorates abiotic stress can have a beneficial (nurse) effect on newly establishing seedlings. Nurse effects may be particularly important in dry environments, where shrubs may have strong facilitative effects on **survival** and initial growth of seedlings because their canopy provides protection from temperature extremes and improves the water balance of the regenerating indigenous seedlings (Maestre et al. 2003; Gómez- Aparicio et al. 2005; Pugnaire et al. 2011). For example, in a Mediterranean savannah, seedling **survival** under living shrubs was more than double that in open microsites after 1 year (Gómez-Aparicio et al. 2004). Nurse effects can be disrupted by management treatments that alter existing vegetation cover and seedling establishment, whether directly (by changing temperature, light, humidity, soil moisture and disturbance regimes), indirectly (through altering plant competition and herbivory), or a combination of direct and indirect effects (Holmgren et al. 1997).

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