A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networks

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k > log_2 log n+omega(1), where omega(1) is any function going to infinity with n, then the minimum bounded-depth spanning tree still has weight tending to zeta(3) as n -> infinity, and that if k < log_2 log n, then the weight is doubly-exponentially large in log_2 log n - k. It is NP-hard to find the minimum bounded-depth spanning tree, but when k < log_2 log n - omega(1), a simple greedy algorithm is asymptotically optimal, and when k > log_2 log n+omega(1), an algorithm which makes small changes to the minimum (unbounded depth) spanning tree is asymptotically optimal. We prove similar results for minimum bounded-depth Steiner trees, where the tree must connect a specified set of m vertices, and may or may not include other vertices. In particular, when m = const * n, if k > log_2 log n+omega(1), the minimum bounded-depth Steiner tree on the complete graph has asymptotically the same weight as the minimum Steiner tree, and if 1 <= k <= log_2 log n-omega(1), the weight tends to (1-2^{-k}) sqrt{8m/n} [sqrt{2mn}/2^k]^{1/(2^k-1)} in both expectation and probability. The same results hold for minimum bounded-diameter Steiner trees when the diameter bound is 2k; when the diameter bound is increased from 2k to 2k+1, the minimum Steiner tree weight is reduced by a factor of 2^{1/(2^k-1)}.Comment: 30 pages, v2 has minor revision

The paradox of verbal autopsy in cause of death assignment: symptom question unreliability but predictive accuracy

Background: We believe that it is important that governments understand the reliability of the mortality data which they have at their disposable to guide policy debates. In many instances, verbal autopsy (VA) will be the only source of mortality data for populations, yet little is known about how the accuracy of VA diagnoses is affected by the reliability of the symptom responses. We previously described the effect of the duration of time between death and VA administration on VA validity. In this paper, using the same dataset, we assess the relationship between the reliability and completeness of symptom responses and the reliability and accuracy of cause of death (COD) prediction. Methods: The study was based on VAs in the Population Health Metrics Research Consortium (PHMRC) VA Validation Dataset from study sites in Bohol and Manila, Philippines and Andhra Pradesh, India. The initial interview was repeated within 3-52 months of death. Question responses were assessed for reliability and completeness between the two survey rounds. COD was predicted by Tariff Method. Results: A sample of 4226 VAs was collected for 2113 decedents, including 1394 adults, 349 children, and 370 neonates. Mean question reliability was unexpectedly low (kappa = 0.447): 42.5 % of responses positive at the first interview were negative at the second, and 47.9 % of responses positive at the second had been negative at the first. Question reliability was greater for the short form of the PHMRC instrument (kappa = 0.497) and when analyzed at the level of the individual decedent (kappa = 0.610). Reliability at the level of the individual decedent was associated with COD predictive reliability and predictive accuracy. Conclusions: Families give coherent accounts of events leading to death but the details vary from interview to interview for the same case. Accounts are accurate but inconsistent; different subsets of symptoms are identified on each occasion. However, there are sufficient accurate and consistent subsets of symptoms to enable the Tariff Method to assign a COD. Questions which contributed most to COD prediction were also the most reliable and consistent across repeat interviews; these have been included in the short form VA questionnaire. Accuracy and reliability of diagnosis for an individual death depend on the quality of interview. This has considerable implications for the progressive roll out of VAs into civil registration and vital statistics (CRVS) systems

Impact of traffic, poverty and facility ownership on travel time to emergency care in Nairobi, Kenya

Background: In many low and middle-income countries (LMICs), timely access to emergency healthcare services is limited. In urban settings, traffic can have a significant impact on travel time, leading to life-threatening delays for time-sensitive injuries and medical emergencies. In this study, we examined travel times to hospitals in Nairobi, Kenya, one of the largest and most congested cities in the developing world. Methods: We used a network approach to estimate average minimum travel times to different types of hospitals (e.g. ownership and level of care) in Nairobi under both congested and uncongested traffic conditions. We also examined the correlation between travel time and socioeconomic status. Results: We estimate the average minimum travel time during uncongested traffic conditions to any level 4 health facility (primary hospitals) or above in Nairobi to be 4.5 min (IQR 2.5–6.1). Traffic added an average of 9.0 min (a 200% increase). In uncongested conditions, we estimate an average travel time of 7.9 min (IQR 5.1–10.4) to level 5 facilities (secondary hospitals) and 11.6 min (IQR 8.5–14.2) to Kenyatta National Hospital, the only level 6 facility (tertiary hospital) in the country. Traffic congestion added an average of 13.1 and 16.0 min (166% and 138% increase) to travel times to level 5 and level 6 facilities, respectively. For individuals living below the poverty line, we estimate that preferential use of public or faith-based facilities could increase travel time by as much as 65%. Conclusion: Average travel times to health facilities capable of providing emergency care in Nairobi are quite low, but traffic congestion double or triple estimated travel times. Furthermore, we estimate significant disparities in timely access to care for those individuals living under the poverty line who preferentially seek care in public or faith-based facilities

Revising the WHO verbal autopsy instrument to facilitate routine cause-of-death monitoring.

OBJECTIVE: Verbal autopsy (VA) is a systematic approach for determining causes of death (CoD) in populations without routine medical certification. It has mainly been used in research contexts and involved relatively lengthy interviews. Our objective here is to describe the process used to shorten, simplify, and standardise the VA process to make it feasible for application on a larger scale such as in routine civil registration and vital statistics (CRVS) systems. METHODS: A literature review of existing VA instruments was undertaken. The World Health Organization (WHO) then facilitated an international consultation process to review experiences with existing VA instruments, including those from WHO, the Demographic Evaluation of Populations and their Health in Developing Countries (INDEPTH) Network, InterVA, and the Population Health Metrics Research Consortium (PHMRC). In an expert meeting, consideration was given to formulating a workable VA CoD list [with mapping to the International Classification of Diseases and Related Health Problems, Tenth Revision (ICD-10) CoD] and to the viability and utility of existing VA interview questions, with a view to undertaking systematic simplification. FINDINGS: A revised VA CoD list was compiled enabling mapping of all ICD-10 CoD onto 62 VA cause categories, chosen on the grounds of public health significance as well as potential for ascertainment from VA. A set of 221 indicators for inclusion in the revised VA instrument was developed on the basis of accumulated experience, with appropriate skip patterns for various population sub-groups. The duration of a VA interview was reduced by about 40% with this new approach. CONCLUSIONS: The revised VA instrument resulting from this consultation process is presented here as a means of making it available for widespread use and evaluation. It is envisaged that this will be used in conjunction with automated models for assigning CoD from VA data, rather than involving physicians

Using Verbal Autopsy to Measure Causes of Death: the Comparative Performance of Existing Methods.

Monitoring progress with disease and injury reduction in many populations will require widespread use of verbal autopsy (VA). Multiple methods have been developed for assigning cause of death from a VA but their application is restricted by uncertainty about their reliability. We investigated the validity of five automated VA methods for assigning cause of death: InterVA-4, Random Forest (RF), Simplified Symptom Pattern (SSP), Tariff method (Tariff), and King-Lu (KL), in addition to physician review of VA forms (PCVA), based on 12,535 cases from diverse populations for which the true cause of death had been reliably established. For adults, children, neonates and stillbirths, performance was assessed separately for individuals using sensitivity, specificity, Kappa, and chance-corrected concordance (CCC) and for populations using cause specific mortality fraction (CSMF) accuracy, with and without additional diagnostic information from prior contact with health services. A total of 500 train-test splits were used to ensure that results are robust to variation in the underlying cause of death distribution. Three automated diagnostic methods, Tariff, SSP, and RF, but not InterVA-4, performed better than physician review in all age groups, study sites, and for the majority of causes of death studied. For adults, CSMF accuracy ranged from 0.764 to 0.770, compared with 0.680 for PCVA and 0.625 for InterVA; CCC varied from 49.2% to 54.1%, compared with 42.2% for PCVA, and 23.8% for InterVA. For children, CSMF accuracy was 0.783 for Tariff, 0.678 for PCVA, and 0.520 for InterVA; CCC was 52.5% for Tariff, 44.5% for PCVA, and 30.3% for InterVA. For neonates, CSMF accuracy was 0.817 for Tariff, 0.719 for PCVA, and 0.629 for InterVA; CCC varied from 47.3% to 50.3% for the three automated methods, 29.3% for PCVA, and 19.4% for InterVA. The method with the highest sensitivity for a specific cause varied by cause. Physician review of verbal autopsy questionnaires is less accurate than automated methods in determining both individual and population causes of death. Overall, Tariff performs as well or better than other methods and should be widely applied in routine mortality surveillance systems with poor cause of death certification practices

Performance of the Tariff Method: validation of a simple additive algorithm for analysis of verbal autopsies

<p>Abstract</p> <p>Background</p> <p>Verbal autopsies provide valuable information for studying mortality patterns in populations that lack reliable vital registration data. Methods for transforming verbal autopsy results into meaningful information for health workers and policymakers, however, are often costly or complicated to use. We present a simple additive algorithm, the Tariff Method (termed Tariff), which can be used for assigning individual cause of death and for determining cause-specific mortality fractions (CSMFs) from verbal autopsy data.</p> <p>Methods</p> <p>Tariff calculates a score, or "tariff," for each cause, for each sign/symptom, across a pool of validated verbal autopsy data. The tariffs are summed for a given response pattern in a verbal autopsy, and this sum (score) provides the basis for predicting the cause of death in a dataset. We implemented this algorithm and evaluated the method's predictive ability, both in terms of chance-corrected concordance at the individual cause assignment level and in terms of CSMF accuracy at the population level. The analysis was conducted separately for adult, child, and neonatal verbal autopsies across 500 pairs of train-test validation verbal autopsy data.</p> <p>Results</p> <p>Tariff is capable of outperforming physician-certified verbal autopsy in most cases. In terms of chance-corrected concordance, the method achieves 44.5% in adults, 39% in children, and 23.9% in neonates. CSMF accuracy was 0.745 in adults, 0.709 in children, and 0.679 in neonates.</p> <p>Conclusions</p> <p>Verbal autopsies can be an efficient means of obtaining cause of death data, and Tariff provides an intuitive, reliable method for generating individual cause assignment and CSMFs. The method is transparent and flexible and can be readily implemented by users without training in statistics or computer science.</p

La política antidrogas: nuevos horizontes de cambio en el control de la oferta y la demanda

96 p.De acuerdo con la Organización Mundial de la Salud (OMS, 1994) una sustancia o droga psicoactiva es aquella que, al ingerirse, afecta procesos mentales, como la cognición o la memoria. El término es asemejado generalmente con el de psicotrópico y ambas expresiones refieren al grupo de sustancias, legales e ilegales, de interés para la política en materia de drogas. En general, la literatura refiere con el término psicotrópico, a medicamentos utilizados principalmente en el tratamiento de los trastornos mentales, como los ansiolíticos, sedantes, antidepresivos, anti maníacos y neurolépticos. Bajo la categoría de sustancias psicotrópicas se encuentran los estupefacientes, acepción utilizada para referirse a sustancias cuya acción sedante, analgésica, narcótica y euforizante puede conducir al acostumbramiento y a la toxicomanía, por lo cual tienen un elevado potencial de abuso y / o dependencia psíquica/física. Entre ellos, se cuentan los estimulantes -cocaína, cafeína, nicotina-, los alucinógenos -Peyote y Psilocybes, los opiáceos -morfina, heroína-, y los sedantes/hipnóticos -alcohol- (OMS, 1994).Prólogo Introducción Capítulo 1. El panorama global: evolución reciente del fenómeno del consumo de sustancias psicoactivas Capítulo 2. La junta internacional de fiscalización de estupefacientes y la eficacia de la política antidrogas: el caso colombiano Capítulo 3. Hacia nuevos horizontes del análisis de política antidrogas Conclusiones Bibliografí

Direct estimation of cause-specific mortality fractions from verbal autopsies: multisite validation study using clinical diagnostic gold standards

<p>Abstract</p> <p>Background</p> <p>Verbal autopsy (VA) is used to estimate the causes of death in areas with incomplete vital registration systems. The King and Lu method (KL) for direct estimation of cause-specific mortality fractions (CSMFs) from VA studies is an analysis technique that estimates CSMFs in a population without predicting individual-level cause of death as an intermediate step. In previous studies, KL has shown promise as an alternative to physician-certified verbal autopsy (PCVA). However, it has previously been impossible to validate KL with a large dataset of VAs for which the underlying cause of death is known to meet rigorous clinical diagnostic criteria.</p> <p>Methods</p> <p>We applied the KL method to adult, child, and neonatal VA datasets from the Population Health Metrics Research Consortium gold standard verbal autopsy validation study, a multisite sample of 12,542 VAs where gold standard cause of death was established using strict clinical diagnostic criteria. To emulate real-world populations with varying CSMFs, we evaluated the KL estimations for 500 different test datasets of varying cause distribution. We assessed the quality of these estimates in terms of CSMF accuracy as well as linear regression and compared this with the results of PCVA.</p> <p>Results</p> <p>KL performance is similar to PCVA in terms of CSMF accuracy, attaining values of 0.669, 0.698, and 0.795 for adult, child, and neonatal age groups, respectively, when health care experience (HCE) items were included. We found that the length of the cause list has a dramatic effect on KL estimation quality, with CSMF accuracy decreasing substantially as the length of the cause list increases. We found that KL is not reliant on HCE the way PCVA is, and without HCE, KL outperforms PCVA for all age groups.</p> <p>Conclusions</p> <p>Like all computer methods for VA analysis, KL is faster and cheaper than PCVA. Since it is a direct estimation technique, though, it does not produce individual-level predictions. KL estimates are of similar quality to PCVA and slightly better in most cases. Compared to other recently developed methods, however, KL would only be the preferred technique when the cause list is short and individual-level predictions are not needed.</p