Addressing an Idiosyncrasy in Estimating Survival Curves Using Double Sampling in the Presence of Self-Selected Right Censoring

We investigate the use of follow-up samples of individuals to estimate survival curves from studies that are subject to right censoring from two sources: (i) early termination of the study, namely, administrative censoring, or (ii) censoring due to lost data prior to administrative censoring, so-called dropout. We assume that, for the full cohort of individuals, administrative censoring times are independent of the subjects' inherent characteristics, including survival time. To address the loss to censoring due to dropout, which we allow to be possibly selective, we consider an intensive second phase of the study where a representative sample of the originally lost subjects is subsequently followed and their data recorded. As with double-sampling designs in survey methodology, the objective is to provide data on a representative subset of the dropouts. Despite assumed full response from the follow-up sample, we show that, in general in our setting, administrative censoring times are not independent of survival times within the two subgroups, nondropouts and sampled dropouts. As a result, the stratified Kaplan-Meier estimator is not appropriate for the cohort survival curve. Moreover, using the concept of potential outcomes, as opposed to observed outcomes, and thereby explicitly formulating the problem as a missing data problem, reveals and addresses these complications. We present an estimation method based on the likelihood of an easily observed subset of the data and study its properties analytically for large samples. We evaluate our method in a realistic situation by simulating data that match published margins on survival and dropout from an actual hip-replacement study. Limitations and extensions of our design and analytic method are discussed.     

Estimating the Accuracy of Anal Cytology in the Presence of an Imperfect Reference Standard

Background

The study aim is to estimate sensitivity and specificity of anal cytology for histologic HSIL in analyses adjusted for the imperfect biopsy reference standard.

Methods and Principal Findings

Retrospective cohort study of an anal dysplasia screening program for HIV infected adults. We estimated the prevalence of histologic HSIL by concurrent cytology category and the associated cytology ROC area. Cytology operating characteristics for HSIL were estimated and adjusted for the imperfect reference standard by 3 methodologies. The study cohort included 261 patients with 3 available measures: (1) referral cytology; (2) HRA cytology; and (3) HRA directed biopsy. The prevalence of biopsy HSIL varied according to the concurrent HRA cytology result: 64.5% for HSIL or ASC-H, 12.6% for LSIL, 10.9% for ASCUS, and 6.3% for no abnormality. The cytology ROC area was 0.78. The observed prevalence of HSIL was 37% (referral cytology), 24% (HRA cytology), and 24% (HRA biopsy). Unadjusted estimates of sensitivity and specificity of cytology were 0.66 and 0.90, respectively. Adjusted estimates varied from 0.47–0.89 (sensitivity) and 0.89—1.0 (specificity).

Conclusions

Analysis of a single dataset yields widely different estimates of anal cytology operating characteristics that depend on difficult to verify assumptions regarding the accuracy of the imperfect reference standard.     

Using Hierarchical Bayes to Understand Movement,Health, and Survival in the Endangered North Atlantic Right Whale

Body condition is an indicator of health, and it plays a key role in many vital processes for mammalian species. While evidence of individual body condition can be obtained, these observations provide just brief glimpses into the health state of the animal. An analytical framework is needed for understanding how health of animals changes over space and time.Through knowledge of individual health we can better understand the status of populations. This is particularly important in endangered species, where the consequences of disruption of critical biological functions can push groups of animals rapidly toward extinction. Here we built a state-space model that provides estimates of movement, health, and survival. We assimilated 30+ years of photographic evidence of body condition and three additional visual health parameters in individual North Atlantic right whales, together with survey data, to infer the true health status as it changes over space and time. We also included the effect of reproductive status and entanglement status on health. At the population level, we estimated differential movement patterns in males and females. At the individual level, we estimated the likely animal locations each month. We estimated the relationship between observed and latent health status. Observations of body condition, skin condition, cyamid infestation on the blowholes, and rake marks all provided measures of the true underlying health. The resulting time series of individual health highlight both normal variations in health status and how anthropogenic stressors can affect the health and, ultimately, the survival of individuals. This modeling approach provides information for monitoring of health in right whales, as well as a framework for integrating observational data at the level of individuals up through the health status of the population. This framework can be broadly applied to a variety of systems – terrestrial and marine – where sporadic observations of individuals exist.     

Fitting Survival Data to a Piecewise Linear Hazard Rate in the Presence of Covariates

This paper extends the work of KODLIN (1967), who proposed a method for analyzing patient survival data wherein the hazard rate was linearly related to the survival time. The present paper extends Kodlin's model to permit maximum likelihood estimation of the parameters so that covariate effects are included and the slope and intercept parameters are allowed to change over fixed intervals of the time domain of study. An illustration of the method using multiple myeloma data is given and the results are compared with those of Kodlin's model, the Feigl-Zelen, Zippin-Armitage model, the exponential model, and Cox's proportional hazards model.     

A Note on Correction of Information Time in a Survival Trial Using an Alpha Spending Function

Spending functions allow flexible monitoring of a clinical trial in that neither the number nor timing of the interim analyses need be pre-specified. Instead, we specify a function dictating the amount of alpha to be spent by different fractions of information. With a survival outcome, information is proportional to the number of patients who will have an event by the end of the trial. If the initial estimate of the number of events is incorrect, then we will spend an undesirable amount of alpha at interim looks. This note shows that for the most popular spending functions, which spend very little alpha early, we can fix an underestimate of the final information with very little effect on the boundaries.     

The Presence in tRNA Molecule Sequences of the Double Hairpin,an Evolutionary Stage Through Which the Origin of this Molecule is Thought to have Passed

We analyse 6,810 tRNAs, calculating the free energy of the corresponding double hairpin and ‘cigar’ secondary structures, for which we find a high thermodynamic and statistical significance. We also analyse these tRNAs for similarity and complementarity of their 5′ and 3′ halves or segments of them in intra-and inter-molecular comparisons. We find very clear signs that the two halves of tRNAs had an evident evolutionary relationship, although it is not totally clear whether this was a relationship of homology or complementarity between the 5′ and 3′ halves of tRNAs, even if there is strong evidence in favour of the homology hypothesis. Overall, these data favour models for the origin of the tRNA molecule postulating that a duplication event involving a hairpin structure as a precursor was involved in the origin of this molecule. Moreover, we interpret these results and favour the hypothesis that sees the assembly of two hairpin structures sharing a homology relationship as the intermediate evolutionary stage preceding the appearance of the cloverleaf structure of tRNA.     

Estimating Treatment Effects for Recurrent Events in the Presence of Rescue Medications: An Application to the Immune Thrombocytopenia Study

In many clinical studies, patients may experience the same type of event of interest repeatedly over time. However, the assessment of treatment effects is often complicated by the rescue medication uses due to ethical reasons. For example, in the motivating trial in studying the Immune Thrombocytopenia (ITP), when the interest lies in evaluating the treatment benefit of investigational product (IP) on reducing patient’s repeated bleeding, rescue medication such as platelet transfusions may be allowed to raise platelet counts. Both the intention-to-treat analysis and treating the intermediate rescue medication as covariate tend to attenuate the treatment benefit, and the estimates can be biased if interpreted as causal. In this paper, we propose a general causal framework when intermediate rescue medications are informative. We adopt the inverse weighted estimation approach to estimate the treatment effect, where weights are constructed to reflect time-dependent medication use probabilities. The proposed estimators are shown to be asymptotically normal and are demonstrated to perform well in small-sample simulation studies. The application to the ITP studies reveals a stronger benefit of using IP in reducing bleeding.     

Estimating the time to extinction in an island population of song sparrows

We estimated and modelled how uncertainties in stochastic population dynamics and biases in parameter estimates affect the accuracy of the projections of a small island population of song sparrows which was enumerated every spring for 24 years. The estimate of the density regulation in a theta-logistic model (theta = 1.09 suggests that the dynamics are nearly logistic, with specific growth rate r1 = 0.99 and carrying capacity K = 41.54. The song sparrow population was strongly influenced by demographic (ŝigma2(d) = 0.66) and environmental (ŝigma2(d) = 0.41) stochasticity. Bootstrap replicates of the different parameters revealed that the uncertainties in the estimates of the specific growth rate r1 and the density regulation theta were larger than the uncertainties in the environmental variance sigma2(e) and the carrying capacity K. We introduce the concept of the population prediction interval (PPI), which is a stochastic interval which includes the unknown population size with probability (1 - alpha). The width of the PPI increased rapidly with time because of uncertainties in the estimates of density regulation as well as demographic and environmental variance in the stochastic population dynamics. Accepting a 10% probability of extinction within 100 years, neglecting uncertainties in the parameters will lead to a 33% overestimation of the time it takes for the extinction barrier (population size X = 1) to be included into the PPI. This study shows that ignoring uncertainties in population dynamics produces a substantial underestimation of the extinction risk.     

gfp-Tagged Cells as a Useful Tool to Study the Survival of Escherichia coli in the Presence of the River Microbial Community

We have used an Escherichia coli strain DH5a containing pGreenTIR to study the survival of this bacterium in river water. As green fluorescence was maintained throughout survival both in dark and illuminated conditions, gfp-tagged E. coli cells were clearly distinguished from the microbial community of the river Butrón. gfp-tagged E. coli cells were monitored to estimate total density as well as the density of the culturable and viable (active electron transport system, CTC+) cells. Our results indicate that autochthonous bacteria and introduced E. coli are predated by flagellates. The autochthonous bacterial community behaves as predation-escaping prey, showing a tendency to cellular miniaturization and so maintaining the density of the population. In contrast, introduced E. coli behaves as predation-non-escaping prey, so E. coli was eliminated from the system. When comparing the elimination by predation of heat-treated and non-heated gfp-tagged E. coli cells we deduce that the flagellates do not discriminate between live and heat-treated cells. Finally, in the presence of the river microbial community, the E. coli cells appeared to be ingested before cellular deterioration could occur. Thus predation reduces the quantitative importance of the viable but nonculturable (VBNC) population of E. coli in the aquatic systems.     

Accurate and Precise DNA Quantification in the Presence of Different Amplification Efficiencies Using an Improved Cy0 Method

Quantitative real-time PCR represents a highly sensitive and powerful technology for the quantification of DNA. Although real-time PCR is well accepted as the gold standard in nucleic acid quantification, there is a largely unexplored area of experimental conditions that limit the application of the Ct method. As an alternative, our research team has recently proposed the Cy0 method, which can compensate for small amplification variations among the samples being compared. However, when there is a marked decrease in amplification efficiency, the Cy0 is impaired, hence determining reaction efficiency is essential to achieve a reliable quantification. The proposed improvement in Cy0 is based on the use of the kinetic parameters calculated in the curve inflection point to compensate for efficiency variations. Three experimental models were used: inhibition of primer extension, non-optimal primer annealing and a very small biological sample. In all these models, the improved Cy0 method increased quantification accuracy up to about 500% without affecting precision. Furthermore, the stability of this procedure was enhanced integrating it with the SOD method. In short, the improved Cy0 method represents a simple yet powerful approach for reliable DNA quantification even in the presence of marked efficiency variations.     

Greater Activity in the Frontal Cortex on Left Curves: A Vector-Based fNIRS Study of Left and Right Curve Driving

ObjectivesIn the brain, the mechanisms of attention to the left and the right are known to be different. It is possible that brain activity when driving also differs with different horizontal road alignments (left or right curves), but little is known about this. We found driver brain activity to be different when driving on left and right curves, in an experiment using a large-scale driving simulator and functional near-infrared spectroscopy (fNIRS).ResultsUnder driving conditions, there were no sites where cerebral oxygen exchange increased significantly more during right curves than during left curves (p > 0.05), but cerebral oxygen exchange increased significantly more during left curves (p < 0.05) in the right premotor cortex, the right frontal eye field and the bilateral prefrontal cortex. Under non-driving conditions, increases were significantly greater during left curves (p < 0.05) only in the right frontal eye field.ConclusionsLeft curve driving was thus found to require more brain activity at multiple sites, suggesting that left curve driving may require more visual attention than right curve driving. The right frontal eye field was activated under both driving and non-driving conditions.     

Using the Lives Saved Tool (LiST) to Model mHealth Impact on Neonatal Survival in Resource-Limited Settings

While the importance of mHealth scale-up has been broadly emphasized in the mHealth community, it is necessary to guide scale up efforts and investment in ways to help achieve the mortality reduction targets set by global calls to action such as the Millennium Development Goals, not merely to expand programs. We used the Lives Saved Tool (LiST)–an evidence-based modeling software–to identify priority areas for maternal and neonatal health services, by formulating six individual and combined interventions scenarios for two countries, Bangladesh and Uganda. Our findings show that skilled birth attendance and increased facility delivery as targets for mHealth strategies are likely to provide the biggest mortality impact relative to other intervention scenarios. Although further validation of this model is desirable, tools such as LiST can help us leverage the benefit of mHealth by articulating the most appropriate delivery points in the continuum of care to save lives.     

Using Geostatistical Analysis to Evaluate the Presence of Rotylenchulus reniformis in Cotton Crops in Brazil: Economic Implications

In recent years, the productivity of cotton in Brazil has been progressively decreasing, often the result of the reniform nematode Rotylenchulus reniformis. This species can reduce crop productivity by up to 40%. Nematodes can be controlled by nematicides but, because of expense and toxicity, application of nematicides to large crop areas may be undesirable. In this work, a methodology using geostatistics for quantifying the risk of nematicide application to small crop areas is proposed. This risk, in economic terms, can be compared to nematicide cost to develop an optimal strategy for Precision Farming. Soil (300 cm³) was sampled in a regular network from a R. reniformis-infested area that was a cotton monoculture for 20 years. The number of nematodes in each sample was counted. The nematode number per volume of soil was characterized using geostatistics, and 100 conditional simulations were conducted. Based on the simulations, risk maps were plotted showing the areas where nematicide should be applied in a Precision Farming context. The methodology developed can be applied to farming in countries that are highly dependent on agriculture, with useful economic implications.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.     

On the Validity of Using Increases in 5-Year Survival Rates to Measure Success in the Fight against Cancer

Background

The 5-year survival rate of cancer patients is the most commonly used statistic to reflect improvements in the war against cancer. This idea, however, was refuted based on an analysis showing that changes in 5-year survival over time bear no relationship with changes in cancer mortality.

Methods

Here we show that progress in the fight against cancer can be evaluated by analyzing the association between 5-year survival rates and mortality rates normalized by the incidence (mortality over incidence, MOI). Changes in mortality rates are caused by improved clinical management as well as changing incidence rates, and since the latter can mask the effects of the former, it can also mask the correlation between survival and mortality rates. However, MOI is a more robust quantity and reflects improvements in cancer outcomes by overcoming the masking effect of changing incidence rates. Using population-based statistics for the US and the European Nordic countries, we determined the association of changes in 5-year survival rates and MOI.

Results

We observed a strong correlation between changes in 5-year survival rates of cancer patients and changes in the MOI for all the countries tested. This finding demonstrates that there is no reason to assume that the improvements in 5-year survival rates are artificial. We obtained consistent results when examining the subset of cancer types whose incidence did not increase, suggesting that over-diagnosis does not obscure the results.

Conclusions

We have demonstrated, via the negative correlation between changes in 5-year survival rates and changes in MOI, that increases in 5-year survival rates reflect real improvements over time made in the clinical management of cancer. Furthermore, we found that increases in 5-year survival rates are not predominantly artificial byproducts of lead-time bias, as implied in the literature. The survival measure alone can therefore be used for a rough approximation of the amount of progress in the clinical management of cancer, but should ideally be used with other measures.