Crude incidence in two-phase designs in the presence of competing risks.

BackgroundIn many studies, some information might not be available for the whole cohort, some covariates, or even the outcome, might be ascertained in selected subsamples. These studies are part of a broad category termed two-phase studies. Common examples include the nested case-control and the case-cohort designs. For two-phase studies, appropriate weighted survival estimates have been derived; however, no estimator of cumulative incidence accounting for competing events has been proposed. This is relevant in the presence of multiple types of events, where estimation of event type specific quantities are needed for evaluating outcome.MethodsWe develop a non parametric estimator of the cumulative incidence function of events accounting for possible competing events. It handles a general sampling design by weights derived from the sampling probabilities. The variance is derived from the influence function of the subdistribution hazard.ResultsThe proposed method shows good performance in simulations. It is applied to estimate the crude incidence of relapse in childhood acute lymphoblastic leukemia in groups defined by a genotype not available for everyone in a cohort of nearly 2000 patients, where death due to toxicity acted as a competing event. In a second example the aim was to estimate engagement in care of a cohort of HIV patients in resource limited setting, where for some patients the outcome itself was missing due to lost to follow-up. A sampling based approach was used to identify outcome in a subsample of lost patients and to obtain a valid estimate of connection to care.ConclusionsA valid estimator for cumulative incidence of events accounting for competing risks under a general sampling design from an infinite target population is derived

A perfect correlate does not a surrogate make

BACKGROUND: There is common belief among some medical researchers that if a potential surrogate endpoint is highly correlated with a true endpoint, then a positive (or negative) difference in potential surrogate endpoints between randomization groups would imply a positive (or negative) difference in unobserved true endpoints between randomization groups. We investigate this belief when the potential surrogate and unobserved true endpoints are perfectly correlated within each randomization group. METHODS: We use a graphical approach. The vertical axis is the unobserved true endpoint and the horizontal axis is the potential surrogate endpoint. Perfect correlation within each randomization group implies that, for each randomization group, potential surrogate and true endpoints are related by a straight line. In this scenario the investigator does not know the slopes or intercepts. We consider a plausible example where the slope of the line is higher for the experimental group than for the control group. RESULTS: In our example with unknown lines, a decrease in mean potential surrogate endpoints from control to experimental groups corresponds to an increase in mean true endpoint from control to experimental groups. Thus the potential surrogate endpoints give the wrong inference. Similar results hold for binary potential surrogate and true outcomes (although the notion of correlation does not apply). The potential surrogate endpointwould give the correct inference if either (i) the unknown lines for the two group coincided, which means that the distribution of true endpoint conditional on potential surrogate endpoint does not depend on treatment group, which is called the Prentice Criterion or (ii) if one could accurately predict the lines based on data from prior studies. CONCLUSION: Perfect correlation between potential surrogate and unobserved true outcomes within randomized groups does not guarantee correct inference based on a potential surrogate endpoint. Even in early phase trials, investigators should not base conclusions on potential surrogate endpoints in which the only validation is high correlation with the true endpoint within a group

Simple estimators of the intensity of seasonal occurrence

<p>Abstract</p> <p>Background</p> <p>Edwards's method is a widely used approach for fitting a sine curve to a time-series of monthly frequencies. From this fitted curve, estimates of the seasonal intensity of occurrence (i.e., peak-to-low ratio of the fitted curve) can be generated.</p> <p>Methods</p> <p>We discuss various approaches to the estimation of seasonal intensity assuming Edwards's periodic model, including maximum likelihood estimation (MLE), least squares, weighted least squares, and a new closed-form estimator based on a second-order moment statistic and non-transformed data. Through an extensive Monte Carlo simulation study, we compare the finite sample performance characteristics of the estimators discussed in this paper. Finally, all estimators and confidence interval procedures discussed are compared in a re-analysis of data on the seasonality of monocytic leukemia.</p> <p>Results</p> <p>We find that Edwards's estimator is substantially biased, particularly for small numbers of events and very large or small amounts of seasonality. For the common setting of rare events and moderate seasonality, the new estimator proposed in this paper yields less finite sample bias and better mean squared error than either the MLE or weighted least squares. For large studies and strong seasonality, MLE or weighted least squares appears to be the optimal analytic method among those considered.</p> <p>Conclusion</p> <p>Edwards's estimator of the seasonal relative risk can exhibit substantial finite sample bias. The alternative estimators considered in this paper should be preferred.</p

Sampling-Based Approaches to Improve Estimation of Mortality among Patient Dropouts: Experience from a Large PEPFAR-Funded Program in Western Kenya

Monitoring and evaluation (M&E) of HIV care and treatment programs is impacted by losses to follow-up (LTFU) in the patient population. The severity of this effect is undeniable but its extent unknown. Tracing all lost patients addresses this but census methods are not feasible in programs involving rapid scale-up of HIV treatment in the developing world. Sampling-based approaches and statistical adjustment are the only scaleable methods permitting accurate estimation of M&E indices.In a large antiretroviral therapy (ART) program in western Kenya, we assessed the impact of LTFU on estimating patient mortality among 8,977 adult clients of whom, 3,624 were LTFU. Overall, dropouts were more likely male (36.8% versus 33.7%; p = 0.003), and younger than non-dropouts (35.3 versus 35.7 years old; p = 0.020), with lower median CD4 count at enrollment (160 versus 189 cells/ml; p<0.001) and WHO stage 3-4 disease (47.5% versus 41.1%; p<0.001). Urban clinic clients were 75.0% of non-dropouts but 70.3% of dropouts (p<0.001). Of the 3,624 dropouts, 1,143 were sought and 621 had their vital status ascertained. Statistical techniques were used to adjust mortality estimates based on information obtained from located LTFU patients. Observed mortality estimates one year after enrollment were 1.7% (95% CI 1.3%-2.0%), revised to 2.8% (2.3%-3.1%) when deaths discovered through outreach were added and adjusted to 9.2% (7.8%-10.6%) and 9.9% (8.4%-11.5%) through statistical modeling depending on the method used. The estimates 12 months after ART initiation were 1.7% (1.3%-2.2%), 3.4% (2.9%-4.0%), 10.5% (8.7%-12.3%) and 10.7% (8.9%-12.6%) respectively. CONCLUSIONS/SIGNIFICANCE ABSTRACT: Assessment of the impact of LTFU is critical in program M&E as estimated mortality based on passive monitoring may underestimate true mortality by up to 80%. This bias can be ameliorated by tracing a sample of dropouts and statistically adjust the mortality estimates to properly evaluate and guide large HIV care and treatment programs

Effects of growth rate, size, and light availability on tree survival across life stages: a demographic analysis accounting for missing values and small sample sizes.

The data set supporting the results of this article is available in the Dryad repository, http://dx.doi.org/10.5061/dryad.6f4qs. Moustakas, A. and Evans, M. R. (2015) Effects of growth rate, size, and light availability on tree survival across life stages: a demographic analysis accounting for missing values.Plant survival is a key factor in forest dynamics and survival probabilities often vary across life stages. Studies specifically aimed at assessing tree survival are unusual and so data initially designed for other purposes often need to be used; such data are more likely to contain errors than data collected for this specific purpose

Outcome based subgroup analysis: a neglected concern

A subgroup of clinical trial subjects identified by baseline characteristics is a proper subgroup while a subgroup determined by post randomization events or measures is an improper subgroup. Both types of subgroups are often analyzed in clinical trial papers. Yet, the extensive scrutiny of subgroup analyses has almost exclusively attended to the former. The analysis of improper subgroups thereby not only flourishes in numerous disguised ways but also does so without a corresponding awareness of its pitfalls. Comparisons of the grade of angina in a heart disease trial, for example, usually include only the survivors. This paper highlights some of the distinct ways in which outcome based subgroup analysis occurs, describes the hazards associated with it, and proposes a simple alternative approach to counter its analytic bias. Data from six published trials show that outcome based subgroup analysis, like proper subgroup analysis, may be performed in a post-hoc fashion, overdone, selectively reported, and over interpreted. Six hypothetical trial scenarios illustrate the forms of hidden bias related to it. That bias can, however, be addressed by assigning clinically appropriate scores to the usually excluded subjects and performing an analysis that includes all the randomized subjects. A greater level of awareness about the practice and pitfalls of outcome based subgroup analysis is needed. When required, such an analysis should maintain the integrity of randomization. This issue needs greater practical and methodologic attention than has been accorded to it thus far

Comparison of Methods to Correct Survival Estimates and Survival Regression Analysis on a Large HIV African Cohort

The evaluation of HIV treatment programs is generally based on an estimation of survival among patients receiving antiretroviral treatment (ART). In large HIV programs, loss to follow-up (LFU) rates remain high despite active patient tracing, which is likely to bias survival estimates and survival regression analyses

Retention in Care and Connection to Care among HIV-Infected Patients on Antiretroviral Therapy in Africa: Estimation via a Sampling-Based Approach

Current estimates of retention among HIV-infected patients on antiretroviral therapy (ART) in Africa consider patients who are lost to follow-up (LTF) as well as those who die shortly after their last clinic visit to be no longer in care and to represent limitations in access to care. Yet many lost patients may have "silently" transferred and deaths shortly after the last clinic visit more likely represent limitations in clinical care rather than access to care after initial linkage.We evaluated HIV-infected adults initiating ART from 1/1/2004 to 9/30/2007 at a clinic in rural Uganda. A representative sample of lost patients was tracked in the community to obtain updated information about care at other ART sites. Updated outcomes were incorporated with probability weights to obtain "corrected" estimates of retention for the entire clinic population. We used the competing risks approach to estimate "connection to care"--the percentage of patients accessing care over time (including those who died while in care).Among 3,628 patients, 829 became lost, 128 were tracked and in 111, updated information was obtained. Of 111, 79 (71%) were alive and 35/48 (73%) of patients interviewed in person were in care and on ART. Patient retention for the clinic population assuming lost patients were not in care was 82.3%, 68.9%, and 60.1% at 1, 2 and 3 years. Incorporating updated care information from the sample of lost patients increased estimates of patient retention to 85.8% to 90.9%, 78.9% to 86.2% and 75.8% to 84.7% at the same time points.Accounting for "silent transfers" and early deaths increased estimates of patient retention and connection to care substantially. Deaths soon after the last clinic visit (potentially reflecting limitations in clinical effectiveness) and disconnection from care among patient who were alive each accounted for approximately half of failures of retention

A Novel Method to Adjust Efficacy Estimates for Uptake of Other Active Treatments in Long-Term Clinical Trials

BACKGROUND: When rates of uptake of other drugs differ between treatment arms in long-term trials, the true benefit or harm of the treatment may be underestimated. Methods to allow for such contamination have often been limited by failing to preserve the randomization comparisons. In the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) study, patients were randomized to fenofibrate or placebo, but during the trial many started additional drugs, particularly statins, more so in the placebo group. The effects of fenofibrate estimated by intention-to-treat were likely to have been attenuated. We aimed to quantify this effect and to develop a method for use in other long-term trials. METHODOLOGY/PRINCIPAL FINDINGS: We applied efficacies of statins and other cardiovascular drugs from meta-analyses of randomized trials to adjust the effect of fenofibrate in a penalized Cox model. We assumed that future cardiovascular disease events were reduced by an average of 24% by statins, and 20% by a first other major cardiovascular drug. We applied these estimates to each patient who took these drugs for the period they were on them. We also adjusted the analysis by the rate of discontinuing fenofibrate. Among 4,900 placebo patients, average statin use was 16% over five years. Among 4,895 assigned fenofibrate, statin use was 8% and nonuse of fenofibrate was 10%. In placebo patients, use of cardiovascular drugs was 1% to 3% higher. Before adjustment, fenofibrate was associated with an 11% reduction in coronary events (coronary heart disease death or myocardial infarction) (P = 0.16) and an 11% reduction in cardiovascular disease events (P = 0.04). After adjustment, the effects of fenofibrate on coronary events and cardiovascular disease events were 16% (P = 0.06) and 15% (P = 0.008), respectively. CONCLUSIONS/SIGNIFICANCE: This novel application of a penalized Cox model for adjustment of a trial estimate of treatment efficacy incorporates evidence-based estimates for other therapies, preserves comparisons between the randomized groups, and is applicable to other long-term trials. In the FIELD study example, the effects of fenofibrate on the risks of coronary heart disease and cardiovascular disease events were underestimated by up to one-third in the original analysis. TRIAL REGISTRATION: Controlled-Trials.com ISRCTN64783481

Correcting Mortality for Loss to Follow-Up: A Nomogram Applied to Antiretroviral Treatment Programmes in Sub-Saharan Africa

Matthias Egger and colleagues present a nomogram and a web-based calculator to correct estimates of program-level mortality for loss to follow-up, for use in antiretroviral treatment programs