Estimating cumulative treatment effects in the presence of nonproportional hazards

Summary .   Often in medical studies of time to an event, the treatment effect is not constant over time. In the context of Cox regression modeling, the most frequent solution is to apply a model that assumes the treatment effect is either piecewise constant or varies smoothly over time, i.e., the Cox nonproportional hazards model. This approach has at least two major limitations. First, it is generally difficult to assess whether the parametric form chosen for the treatment effect is correct. Second, in the presence of nonproportional hazards, investigators are usually more interested in the cumulative than the instantaneous treatment effect (e.g., determining if and when the survival functions cross). Therefore, we propose an estimator for the aggregate treatment effect in the presence of nonproportional hazards. Our estimator is based on the treatment-specific baseline cumulative hazards estimated under a stratified Cox model. No functional form for the nonproportionality need be assumed. Asymptotic properties of the proposed estimators are derived, and the finite-sample properties are assessed in simulation studies. Pointwise and simultaneous confidence bands of the estimator can be computed. The proposed method is applied to data from a national organ failure registry.     

Are Statistical Contributions to Medicine Undervalued?

Econometricians Daniel McFadden and James Heckman won the 2000 Nobel Prize in economics for their work on discrete choice models and selection bias. Statisticians and epidemiologists have made similar contributions to medicine with their work on case-control studies, analysis of incomplete data, and causal inference. In spite of repeated nominations of such eminent figures as Bradford Hill and Richard Doll, however, the Nobel Prize in physiology and medicine has never been awarded for work in biostatistics or epidemiology. (The "exception who proves the rule" is Ronald Ross, who, in 1902, won the second medical Nobel for his discovery that the mosquito was the vector for malaria. Ross then went on to develop the mathematics of epidemic theory--which he considered his most important scientific contribution-and applied his insights to malaria control programs.) The low esteem accorded epidemiology and biostatistics in some medical circles, and increasingly among the public, correlates highly with the contradictory results from observational studies that are displayed so prominently in the lay press. In spite of its demonstrated efficacy in saving lives, the "black box" approach of risk factor epidemiology is not well respected. To correct these unfortunate perceptions, statisticians would do well to follow more closely their own teachings: conduct larger, fewer studies designed to test specific hypotheses, follow strict protocols for study design and analysis, better integrate statistical findings with those from the laboratory, and exercise greater caution in promoting apparently positive results.     

Propensity score matching with time-dependent covariates

In observational studies with a time-dependent treatment and time-dependent covariates, it is desirable to balance the distribution of the covariates at every time point. A time-dependent propensity score based on the Cox proportional hazards model is proposed and used in risk set matching. Matching on this propensity score is shown to achieve a balanced distribution of the covariates in both treated and control groups. Optimal matching with various designs is conducted and compared in a study of a surgical treatment, cystoscopy and hydrodistention, given in response to a chronic bladder disease, interstitial cystitis. Simulation studies also suggest that the statistical analysis after matching outperforms the analysis without matching in terms of both point and interval estimations.     

Attributable effects in case2-studies

Summary In an effort to determine whether a particular treatment causes a particular outcome event, data are obtained from a database system that records events when they occur, and for such events, the system records exposure to the treatment. That is, the system records information about cases. The system provides no information about events that might have occurred but did not, that is, about units which are not cases. Roughly speaking, we know the number of successes for two proportions, treated and control, but not the numbers of trials or units for these proportions; indeed, the concept of a “trial” may be somewhat vague. With no further information, the situation is quite hopeless. However, an interesting strategy that is sometimes used entails identifying two types of cases whose origin is entirely different so that it is known the cases of the second type were definitely not affected by the treatment under study. This strategy—the case–case or case²‐study—seems to have been reinvented independently many times, and has recently been offered as a general strategy for infectious disease epidemiology by McCarthy and Giesecke (1999, International Journal of Epidemiology 28, 764–768). Can this strategy permit estimation of the number of cases caused by the treatment? Using attributable effects in a new way, a method of exact inference is proposed, along with a large sample approximation. Two examples are discussed: one concerning the effects of daytime running lights (DRLs) on the risk of multivehicle accidents; the other concerning the origin of a Salmonella infection. A counterexample with superficially similar appearance is also discussed concerning suicide rates following the publication of Final Exit; here, the treatment may alter the outcome, or it may alter the type, and the attributable effect cannot be estimated.     

Statistical issues arising in the Women's Health Initiative

A brief overview of the design of the Women's Health Initiative (WHI) clinical trial and observational study is provided along with a summary of results from the postmenopausal hormone therapy clinical trial components. Since its inception in 1992, the WHI has encountered a number of statistical issues where further methodology developments are needed. These include measurement error modeling and analysis procedures for dietary and physical activity assessment; clinical trial monitoring methods when treatments may affect multiple clinical outcomes, either beneficially or adversely; study design and analysis procedures for high-dimensional genomic and proteomic data; and failure time data analysis procedures when treatment group hazard ratios are time dependent. This final topic seems important in resolving the discrepancy between WHI clinical trial and observational study results on postmenopausal hormone therapy and cardiovascular disease.     

Prognostic value of epidermal growth factor receptor in patients with gastric cancer: A meta-analysis

Background

The epidermal growth factor receptor (EGFR) plays important roles in the development of gastric cancer. This study aims to analyze the prognostic value of EGFR in patients with gastric cancer.

Methods

A meta-analysis is performed by searching Cochrane Library, PubMed, EMBASE and Science Direct databases from Jan 1970 to May 2013. Data are extracted from studies evaluating the survival of gastric cancer patients with either positive or negative EGFR expression. Pooled hazard ratios (HRs) and 95% confidence intervals (CIs) are calculated.

Results

Totally 1600 cases of gastric cancer patients from five studies are subjected to final analysis. The HR of post-operational survival of patients with positive EGFR expression is 1.16 (95% CI: 0.94–1.43) as compared with those with negative expression, indicating that positive EGFR expression does not significantly predict the poor survival of gastric cancer.

Conclusions

EGFR expression is not an independent predictor for the survival of gastric cancer patients.     

Confidence intervals for uncommon but dramatic responses to treatment

A small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment. The ranks used in these tests are very different from conventional ranks, being relatively flat for low responses and then rising steeply, and the associated tests are much more powerful than conventional rank tests when, indeed, only a small fraction of treated subjects exhibit dramatic responses. Because the tests are derived from considerations of local power, they do not yield a plausible family of models for effect, and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests. There is a similarity between these tests and another family of tests, originally motivated by different considerations involving peak performance in small subsets. Exploiting this similarity, a method for obtaining confidence statements is proposed. In the case of observational studies, sensitivity to unobserved bias from nonrandom assignment of treatments is also examined. Two examples are used as illustrations: (i) a study of smoking during pregnancy and its effects on birth weight, in which smokers are matched to six controls, and (ii) a matched pair study of damage to DNA among workers at aluminum production plants.     

Simple testing procedures for the Holling type II model

In this paper, we consider predator–prey data that can be viewed as solutions to a planar system of ordinary differential equations (ODE) observed with random error. The ODE system admits a limit cycle, while the random error is supposed to act additively in the log-scale. One of the oldest such systems is Holling’s type II model. In spite of its simplicity, it is still very popular in data analyses, although more sophisticated models have been introduced in the literature. We propose a simple way of deciding whether a set of predator–prey pairs is indicative or not of a departure from this basic model by exploiting the geometric properties of the solution in the phase plane. To illustrate our method, we use simulated and real data.     

The impact of left common pulmonary vein on cryoballoon ablation of atrial fibrillation. A meta-analysis

IntroductionConflicting results regarding the impact of left common pulmonary vein (LCPV) on clinical outcome of atrial fibrillation (AF) ablation with cryoballoon technology have been reported.MethodsWe systematically searched PubMed and Cochrane library for articles that compared the arrhythmia recurrence rate after cryoballoon ablation between patients with normal pattern PVs and patients with LCPV. Studies of first ablation for persistent and paroxysmal AF using the 28 mm Arctic Front Advance, Medtronic cryoballoon (CB-A) reporting clinical success rates at a mean follow-up of ≥12 months were included. Data were analyzed by applying a random effects model.ResultsA total of 5 studies with a total of 1178 patients met our predefined inclusion criteria. After a mean follow-up of 18.4 months, the overall success rate of CB-A ablation among patients with persistent and paroxysmal AF was 57%; in the LCPV group the success rate was 46% and in the normal anatomical pattern group it was 61%. No significant heterogeneity was noted among the studies (I² = 35.8%; Q (df = 3) = 6.23 p-value = 0.18). Arrhythmia recurrence after CB-A ablation was not statistically significant between the two groups (LogOR 0.24; 95% CI [-0.16-0.63]; p-value = 0.23). No significant difference in PNI was observed between the two groups (p-value = 0.693).ConclusionThe presence of LCPV does not affect the long-term outcome of paroxysmal and persistent atrial fibrillation ablation with 28 mm CB-A compared to normal left PVs pattern.