Prognostic models: What the statistician wants the clinician to know.

Prognostic model building is a process that begins much earlier than data analysis and ends later than when a model is reached. It requires careful delineation of a clinical question, methodical planning of the approach and attentive exploration of the data before attempting model building. Once following these important initial steps, the researcher may postulate a model to describe the process of interest and build such model. Once built, the model will need to be checked, validated and the exercise may take the researcher back a few steps - for instance, to adapt the model to fit a variable that displays a 'curved' pattern - to then return to check and validate the model again. To interpret and report the results it is vital to relate the output to the original question, to be transparent in the methodology followed and to understand the limitations of the data and the approach.

Organ Transplants From Deceased Donors With Primary Brain Tumors and Risk of Cancer Transmission.

Importance: Cancer transmission is a known risk for recipients of organ transplants. Many people wait a long time for a suitable transplant; some never receive one. Although patients with brain tumors may donate their organs, opinions vary on the risks involved. Objective: To determine the risk of cancer transmission associated with organ transplants from deceased donors with primary brain tumors. Key secondary objectives were to investigate the association that donor brain tumors have with organ usage and posttransplant survival. Design, Setting, and Participants: This was a cohort study in England and Scotland, conducted from January 1, 2000, to December 31, 2016, with follow-up to December 31, 2020. This study used linked data on deceased donors and solid organ transplant recipients with valid national patient identifier numbers from the UK Transplant Registry, the National Cancer Registration and Analysis Service (England), and the Scottish Cancer Registry. For secondary analyses, comparators were matched on factors that may influence the likelihood of organ usage or transplant failure. Statistical analysis of study data took place from October 1, 2021, to May 31, 2022. Exposures: A history of primary brain tumor in the organ donor, identified from all 3 data sources using disease codes. Main Outcomes and Measures: Transmission of brain tumor from the organ donor into the transplant recipient. Secondary outcomes were organ utilization (ie, transplant of an offered organ) and survival of kidney, liver, heart, and lung transplants and their recipients. Key covariates in donors with brain tumors were tumor grade and treatment history. Results: This study included a total of 282 donors (median [IQR] age, 42 [33-54] years; 154 females [55%]) with primary brain tumors and 887 transplants from them, 778 (88%) of which were analyzed for the primary outcome. There were 262 transplants from donors with high-grade tumors and 494 from donors with prior neurosurgical intervention or radiotherapy. Median (IQR) recipient age was 48 (35-58) years, and 476 (61%) were male. Among 83 posttransplant malignancies (excluding NMSC) that occurred over a median (IQR) of 6 (3-9) years in 79 recipients of transplants from donors with brain tumors, none were of a histological type matching the donor brain tumor. Transplant survival was equivalent to that of matched controls. Kidney, liver, and lung utilization were lower in donors with high-grade brain tumors compared with matched controls. Conclusions and Relevance: Results of this cohort study suggest that the risk of cancer transmission in transplants from deceased donors with primary brain tumors was lower than previously thought, even in the context of donors that are considered as higher risk. Long-term transplant outcomes are favorable. These results suggest that it may be possible to safely expand organ usage from this donor group.

Solid Organ Transplantation From Deceased Donors With Infective Endocarditis: The UK Experience.

BACKGROUND: There is little evidence regarding the use of organs from deceased donors with infective endocarditis. We performed a retrospective analysis of the utilization, safety, and long-term survival of transplants from donors with infective endocarditis in the United Kingdom. METHODS: We studied deceased donor transplants over an 18-y period (2001-2018) using data from the UK Transplant Registry. We estimated the risk of infection transmission, defined as a microbiological isolate in the recipient matching the causative organism in the donor in the first 30 days posttransplant. We examined all-cause allograft failure up to 5 years in kidney and liver recipients, comparing transplants from donors with endocarditis with randomly selected matched control transplants. RESULTS: We studied 88 transplants from 42 donors with infective endocarditis. We found no cases of infection transmission. There was no difference in allograft failure between transplants from donors with infective endocarditis and matched control transplants, among either kidney (hazard ratio, 1.48; 95% CI, 0.66-3.34) or liver (hazard ratio, 1.14; 95% CI, 0.54-2.41) recipients. Compared with matched controls, donors with infective endocarditis donated fewer organs (2.3 versus 3.2 organs per donor; P < 0.001) and were less likely to become kidney donors (odds ratio, 0.29; 95% CI, 0.16-0.55). CONCLUSIONS: We found acceptable safety and long-term allograft survival in transplants from selected donors with infective endocarditis in the United Kingdom. This may have implications for donor selection and organ utilization.

The Impact of Cold Ischaemia Time on Outcomes of Living Donor Kidney Transplantation in the UK Living Kidney Sharing Scheme.

OBJECTIVE: To assess the impact of CIT on living donor kidney transplantation (LDKT) outcomes in the UKLKSS versus outside the scheme. BACKGROUND: LDKT provides the best treatment option for end-stage kidney disease patients. end-stage kidney disease patients with an incompatible living donor still have an opportunity to be transplanted through Kidney Exchange Programmes (KEP). In KEPs where kidneys travel rather than donors, cold ischaemia time (CIT) can be prolonged. METHODS: Data from all UK adult LDKT between 2007 and 2018 were analysed. RESULTS: 9969 LDKT were performed during this period, of which 1396 (14%) were transplanted through the UKLKSS, which we refer to as KEP. Median CIT was significantly different for KEP versus non-KEP (339 versus 182 minutes, P < 0.001). KEP LDKT had a higher incidence of delayed graft function (DGF) (2.91% versus 5.73%, P < 0.0001), lower 1-year (estimated Glomerular Filtration Rate (eGFR) 57.90 versus 55.25 ml/min, P = 0.04) and 5-year graft function (eGFR 55.62 versus 53.09 ml/min, P = 0.01) compared to the non-KEP group, but 1- and 5-year graft survival were similar. Within KEP, a prolonged CIT was associated with more DGF (3.47% versus 1.95%, P = 0.03), and lower graft function at 1 and 5-years (eGFR = 55 vs 50 ml/min, P = 0.02), but had no impact on graft survival. CONCLUSION: Whilst CIT was longer in KEP, associated with more DGF and lower graft function, excellent 5-year graft survival similar to non-KEP was found.

Convalescent plasma therapy for the treatment of patients with COVID-19: Assessment of methods available for antibody detection and their correlation with neutralising antibody levels.

INTRODUCTION: The lack of approved specific therapeutic agents to treat coronavirus disease (COVID-19) associated with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection has led to the rapid implementation of convalescent plasma therapy (CPT) trials in many countries, including the United Kingdom. Effective CPT is likely to require high titres of neutralising antibody (nAb) in convalescent donations. Understanding the relationship between functional neutralising antibodies and antibody levels to specific SARS-CoV-2 proteins in scalable assays will be crucial for the success of a large-scale collection. We assessed whether neutralising antibody titres correlated with reactivity in a range of enzyme-linked immunosorbent assays (ELISA) targeting the spike (S) protein, the main target for human immune response. METHODS: Blood samples were collected from 52 individuals with a previous laboratory-confirmed SARS-CoV-2 infection. These were assayed for SARS-CoV-2 nAbs by microneutralisation and pseudo-type assays and for antibodies by four different ELISAs. Receiver operating characteristic (ROC) analysis was used to further identify sensitivity and specificity of selected assays to identify samples containing high nAb levels. RESULTS: All samples contained SARS-CoV-2 antibodies, whereas neutralising antibody titres of greater than 1:20 were detected in 43 samples (83% of those tested) and >1:100 in 22 samples (42%). The best correlations were observed with EUROimmun immunoglobulin G (IgG) reactivity (Spearman Rho correlation coefficient 0.88; p < 0.001). Based on ROC analysis, EUROimmun would detect 60% of samples with titres of >1:100 with 100% specificity using a reactivity index of 9.1 (13/22). DISCUSSION: Robust associations between nAb titres and reactivity in several ELISA-based antibody tests demonstrate their possible utility for scaled-up production of convalescent plasma containing potentially therapeutic levels of anti-SARS-CoV-2 nAbs.

Convalescent plasma treatment for SARS-CoV-2 infection: analysis of the first 436 donors in England, 22 April to 12 May 2020.

Serological reactivity was analysed in plasma from 436 individuals with a history of disease compatible with COVID-19, including 256 who had been laboratory-confirmed with SARS-CoV-2 infection. Over 99% of laboratory-confirmed cases developed a measurable antibody response (254/256) and 88% harboured neutralising antibodies (226/256). Antibody levels declined over 3 months following diagnosis, emphasising the importance of the timing of convalescent plasma collections. Binding antibody measurements can inform selection of convalescent plasma donors with high neutralising antibody levels.

Inequity in Access to Transplantation in the United Kingdom.

BACKGROUND AND OBJECTIVES: Despite the presence of a universal health care system, it is unclear if there is intercenter variation in access to kidney transplantation in the United Kingdom. This study aims to assess whether equity exists in access to kidney transplantation in the United Kingdom after adjustment for patient-specific factors and center practice patterns. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS: In this prospective, observational cohort study including all 71 United Kingdom kidney centers, incident RRT patients recruited between November 2011 and March 2013 as part of the Access to Transplantation and Transplant Outcome Measures study were analyzed to assess preemptive listing (n=2676) and listing within 2 years of starting dialysis (n=1970) by center. RESULTS: Seven hundred and six participants (26%) were listed preemptively, whereas 585 (30%) were listed within 2 years of commencing dialysis. The interquartile range across centers was 6%-33% for preemptive listing and 25%-40% for listing after starting dialysis. Patient factors, including increasing age, most comorbidities, body mass index >35 kg/m2, and lower socioeconomic status, were associated with a lower likelihood of being listed and accounted for 89% and 97% of measured intercenter variation for preemptive listing and listing within 2 years of starting dialysis, respectively. Asian (odds ratio, 0.49; 95% confidence interval, 0.33 to 0.72) and Black (odds ratio, 0.43; 95% confidence interval, 0.26 to 0.71) participants were both associated with reduced access to preemptive listing; however Asian participants were associated with a higher likelihood of being listed after starting dialysis (odds ratio, 1.42; 95% confidence interval, 1.12 to 1.79). As for center factors, being registered at a transplanting center (odds ratio, 3.1; 95% confidence interval, 2.36 to 4.07) and a universal approach to discussing transplantation (odds ratio, 1.4; 95% confidence interval, 1.08 to 1.78) were associated with higher preemptive listing, whereas using a written protocol was associated negatively with listing within 2 years of starting dialysis (odds ratio, 0.7; 95% confidence interval, 0.58 to 0.9). CONCLUSIONS: Patient case mix accounts for most of the intercenter variation seen in access to transplantation in the United Kingdom, with practice patterns also contributing some variation. Socioeconomic inequity exists despite having a universal health care system.

Recipient Comorbidity and Survival Outcomes After Kidney Transplantation: A UK-wide Prospective Cohort Study.

BACKGROUND: Comorbidity is increasingly common in kidney transplant recipients, yet the implications for transplant outcomes are not fully understood. We analyzed the relationship between recipient comorbidity and survival outcomes in a UK-wide prospective cohort study-Access to Transplantation and Transplant Outcome Measures (ATTOM). METHODS: A total of 2100 adult kidney transplant recipients were recruited from all 23 UK transplant centers between 2011 and 2013. Data on 15 comorbidities were collected at the time of transplantation. Multivariable Cox regression models were used to analyze the relationship between comorbidity and 2-year graft survival, patient survival, and transplant survival (earliest of graft failure or patient death) for deceased-donor kidney transplant (DDKT) recipients (n = 1288) and living-donor kidney transplant (LDKT) recipients (n = 812). RESULTS: For DDKT recipients, peripheral vascular disease (hazard ratio [HR] 3.04, 95% confidence interval [CI]: 1.37-6.74; P = 0.006) and obesity (HR 2.27, 95% CI: 1.27-4.06; P = 0.006) were independent risk factors for graft loss, while heart failure (HR 3.77, 95% CI: 1.79-7.95; P = 0.0005), cerebrovascular disease (HR 3.45, 95% CI: 1.72-6.92; P = 0.0005), and chronic liver disease (HR 4.36, 95% CI: 1.29-14.71; P = 0.018) were associated with an increased risk of mortality. For LDKT recipients, heart failure (HR 3.83, 95% CI: 1.15-12.81; P = 0.029) and diabetes (HR 2.23, 95% CI: 1.03-4.81; P = 0.042) were associated with poorer transplant survival. CONCLUSIONS: The key comorbidities that predict poorer 2-year survival outcomes after kidney transplantation have been identified in this large prospective cohort study. The findings will facilitate assessment of individual patient risks and evidence-based decision making.

Estimating Health-State Utility Values in Kidney Transplant Recipients and Waiting-List Patients Using the EQ-5D-5L.

OBJECTIVES: To report health-state utility values measured using the five-level EuroQol five-dimensional questionnaire (EQ-5D-5L) in a large sample of patients with end-stage renal disease and to explore how these values vary in relation to patient characteristics and treatment factors. METHODS: As part of the prospective observational study entitled "Access to Transplantation and Transplant Outcome Measures," we captured information on patient characteristics and treatment factors in a cohort of incident kidney transplant recipients and a cohort of prevalent patients on the transplant waiting list in the United Kingdom. We assessed patients' health status using the EQ-5D-5L and conducted multivariable regression analyses of index scores. RESULTS: EQ-5D-5L responses were available for 512 transplant recipients and 1704 waiting-list patients. Mean index scores were higher in transplant recipients at 6 months after transplant surgery (0.83) compared with patients on the waiting list (0.77). In combined regression analyses, a primary renal diagnosis of diabetes was associated with the largest decrement in utility scores. When separate regression models were fitted to each cohort, female gender and Asian ethnicity were associated with lower utility scores among waiting-list patients but not among transplant recipients. Among waiting-list patients, longer time spent on dialysis was also associated with poorer utility scores. When comorbidities were included, the presence of mental illness resulted in a utility decrement of 0.12 in both cohorts. CONCLUSIONS: This study provides new insights into variations in health-state utility values from a single source that can be used to inform cost-effectiveness evaluations in patients with end-stage renal disease.

Barriers to living donor kidney transplantation in the United Kingdom: a national observational study.

BACKGROUND: Living donor kidney transplantation (LDKT) provides more timely access to transplantation and better clinical outcomes than deceased donor kidney transplantation (DDKT). This study investigated disparities in the utilization of LDKT in the UK. METHODS: A total of 2055 adults undergoing kidney transplantation between November 2011 and March 2013 were prospectively recruited from all 23 UK transplant centres as part of the Access to Transplantation and Transplant Outcome Measures (ATTOM) study. Recipient variables independently associated with receipt of LDKT versus DDKT were identified. RESULTS: Of the 2055 patients, 807 (39.3%) received LDKT and 1248 (60.7%) received DDKT. Multivariable modelling demonstrated a significant reduction in the likelihood of LDKT for older age {odds ratio [OR] 0.11 [95% confidence interval (CI) 0.08-0.17], P < 0.0001 for 65-75 years versus 18-34 years}; Asian ethnicity [OR 0.55 (95% CI 0.39-0.77), P = 0.0006 versus White]; Black ethnicity [OR 0.64 (95% CI 0.42-0.99), P = 0.047 versus White]; divorced, separated or widowed [OR 0.63 (95% CI 0.46-0.88), P = 0.030 versus married]; no qualifications [OR 0.55 (95% CI 0.42-0.74), P < 0.0001 versus higher education qualifications]; no car ownership [OR 0.51 (95% CI 0.37-0.72), P = 0.0001] and no home ownership [OR 0.65 (95% CI 0.85-0.79), P = 0.002]. The odds of LDKT varied significantly between countries in the UK. CONCLUSIONS: Among patients undergoing kidney transplantation in the UK, there are significant age, ethnic, socio-economic and geographic disparities in the utilization of LDKT. Further work is needed to explore the potential for targeted interventions to improve equity in living donor transplantation.

Predicting patient survival after deceased donor kidney transplantation using flexible parametric modelling.

BACKGROUND: The influence of donor and recipient factors on outcomes following kidney transplantation is commonly analysed using Cox regression models, but this approach is not useful for predicting long-term survival beyond observed data. We demonstrate the application of a flexible parametric approach to fit a model that can be extrapolated for the purpose of predicting mean patient survival. The primary motivation for this analysis is to develop a predictive model to estimate post-transplant survival based on individual patient characteristics to inform the design of alternative approaches to allocating deceased donor kidneys to those on the transplant waiting list in the United Kingdom. METHODS: We analysed data from over 12,000 recipients of deceased donor kidney or combined kidney and pancreas transplants between 2003 and 2012. We fitted a flexible parametric model incorporating restricted cubic splines to characterise the baseline hazard function and explored a range of covariates including recipient, donor and transplant-related factors. RESULTS: Multivariable analysis showed the risk of death increased with recipient and donor age, diabetic nephropathy as the recipient's primary renal diagnosis and donor hypertension. The risk of death was lower in female recipients, patients with polycystic kidney disease and recipients of pre-emptive transplants. The final model was used to extrapolate survival curves in order to calculate mean survival times for patients with specific characteristics. CONCLUSION: The use of flexible parametric modelling techniques allowed us to address some of the limitations of both the Cox regression approach and of standard parametric models when the goal is to predict long-term survival.

Stochastic cellular fate decision making by multiple infecting lambda phage.

Bacteriophage lambda is a classic system for the study of cellular decision making. Both experiments and mathematical models have demonstrated the importance of viral concentration in the lysis-lysogeny decision outcome in lambda phage. However, a recent experimental study using single cell and single phage resolution reported that cells with the same viral concentrations but different numbers of infecting phage (multiplicity of infection) can have markedly different rates of lysogeny. Thus the decision depends on not only viral concentration, but also directly on the number of infecting phage. Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network. Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated. We find that interplay between the level of intrinsic noise and viral protein decision threshold is a major factor that produces dependence on multiplicity of infection. However, simulations suggest spatial segregation of phage particles does not play a significant role. Cellular image processing is used to re-analyse the original time-lapse movies from the recent study and it is found that higher numbers of infecting phage reduce the cell elongation rate. This could also contribute to the observed phenomena as cellular growth rate can affect transcription rates. Our model further predicts that rate of lysogeny is dependent on bacterial growth rate, which can be experimentally tested. Our study provides new insight on the mechanisms of individual phage decision making. More generally, our results are relevant for the understanding of gene-dosage compensation in cellular systems.

Imputing unobserved values with the EM algorithm under left and right-truncation, and interval censoring for estimating the size of hidden populations.

Capture­recapture techniques have been used for considerable time to predict population size. Estimators usually rely on frequency counts for numbers of trappings; however, it may be the case that these are not available for a particular problem, for example if the original data set has been lost and only a summary table is available. Here, we investigate techniques for specific examples; the motivating example is an epidemiology study by Mosley et al., which focussed on a cholera outbreak in East Pakistan. To demonstrate the wider range of the technique, we also look at a study for predicting the long-term outlook of the AIDS epidemic using information on number of sexual partners. A new estimator is developed here which uses the EM algorithm to impute unobserved values and then uses these values in a similar way to the existing estimators. The results show that a truncated approach ­ mimicking the Chao lower bound approach ­ gives an improved estimate when population homogeneity is violated.