We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

The Analysis of Variance.

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual scores are averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the mean squared error. I demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched. Effective point forecasting requires that the scoring function be specified ex ante, or that the forecaster receives a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. If the scoring function is specified ex ante, the forecaster can issue the optimal point forecast, namely, the Bayes rule. If the forecaster receives a directive in the form of a functional, it is critical that the scoring function be consistent for it, in the sense that t...

https://amstat.tandfonline.com/doi/pdf/10.1198/jasa.2011.r10138

Making and Evaluating Point Forecasts

https://escholarship.org/content/qt1p2685jh/qt1p2685jh.pdf?t=o9h7xo

A 17-gene Assay to Predict Prostate Cancer Aggressiveness in the Context of Gleason Grade Heterogeneity, Tumor Multifocality, and Biopsy Undersampling

Insights into end-stage renal disease have emerged from many investigations but less is known about the epidemiology of chronic renal insufficiency (CRI) and its relationship to cardiovascular disease (CVD). The Chronic Renal Insufficiency Cohort (CRIC) Study was established to examine risk factors for progression of CRI and CVD among CRI patients and develop models to identify high-risk subgroups, informing future treatment trials, and increasing application of preventive therapies. CRIC will enroll approximately 3000 individuals at seven sites and follow participants for up to 5 yr. CRIC will include a racially and ethnically diverse group of adults aged 21 to 74 yr with a broad spectrum of renal disease severity, half of whom have diagnosed diabetes mellitus. CRIC will exclude subjects with polycystic kidney disease and those on active immunosuppression for glomerulonephritis. Subjects will undergo extensive clinical evaluation at baseline and at annual clinic visits and via telephone at 6 mo intervals. Data on quality of life, dietary assessment, physical activity, health behaviors, depression, cognitive function, health care resource utilization, as well as blood and urine specimens will be collected annually. (125)I-iothalamate clearances and CVD evaluations including a 12-lead surface electrocardiogram, an echocardiogram, and coronary electron beam or spiral CT will be performed serially. Analyses planned in CRIC will provide important information on potential risk factors for progressive CRI and CVD. Insights from CRIC should lead to the formulation of hypotheses regarding therapy that will serve as the basis for targeted interventional trials focused on reducing the burden of CRI and CVD.

The Chronic Renal Insufficiency Cohort (CRIC) Study: Design and Methods

SUMMARY A unified estimation procedure is proposed for the analysis of censored data using linear transformation models, which include the proportional hazards model and the proportional odds model as special cases. This procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable. The estimator is the same as the Cox partial likelihood estimator in the case of the proportional hazards model. Moreover, the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug-in rules. The method is illustrated by simulation and is applied to the Veterans' Administration lung cancer data.

/pdf/semiparametric-analysis-of-transformation-models-with-6r84j9npfz.pdf

Semiparametric analysis of transformation models with censored data

Prentice (1986) proposed the case-cohort design and studied a pseudolikelihood estimator of regression parameters in Cox's model. We derive a class of estimating equations for case-cohort sampling, each depending on a different estimator of the population distribution, which lead naturally to simple estimators that improve on Prentice's pseudolikelihood estimator. We also discuss an equivalence between case-control and case-cohort sampling in terms of the estimation of regression parameters in Cox's model.

Case-cohort and case-control analysis with Cox's model

Strong consistency for maximum quasi-likelihood estimators of regression parameters in generalized linear regression models is studied. Results parallel to the elegant work of Lai, Robbins and Wei and Lai and Wei on least squares estimation under both fixed and adaptive designs are obtained. Let $y_1,\dots, y_n$ and $x_1,\dots, x_n$ be the observed responses and their corresponding design points ($p \times 1$ vectors), respectively. For fixed designs, it is shown that if the minimum eigenvalue of $\Sigma x_i x^\prime_i$ goes to infinity, then the maximum quasi-likelihood estimator for the regression parameter vector is strongly consistent. For adaptive designs, it is shown that a sufficient condition for strong consistency to hold is that the ratio of the minimum eigenvalue of $\Sigma x_i \x^\prime_i$ to the logarithm of the maximum eigenvalues goes to infinity. Use of the results for the adaptive design case in quantal response experiments is also discussed.

/pdf/strong-consistency-of-maximum-quasi-likelihood-estimators-in-f9kdwzu4pq.pdf

Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs

A class of cohort sampling designs, including nested case–control, case–cohort and classical case–control designs involving survival data, is studied through a unified approach using Cox’s proportional hazards model. By finding an optimal sample reuse method via local averaging, a closed form estimating function is obtained, leading directly to the estimators of the regression parameters that are relatively easy to compute and are more efficient than some commonly used estimators in case–cohort and nested case–control studies. A semiparametric efficient estimator can also be found with some further computation. In addition, the class of sampling designs in this study provides a variety of sampling options and relaxes the restrictions of sampling schemes that are currently available.

Generalized case–cohort sampling

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical applications, especially in treating, for example, stock price data, the size of relative error, rather than that of error itself, is the central concern of the practitioners. This paper offers an alternative to the traditional estimation methods by considering minimizing the least absolute relative errors for multiplicative regression models. We prove consistency and asymptotic normality and provide an inference approach via random weighting. We also specify the error distribution, with which the proposed least absolute relative errors estimatio...

/pdf/least-absolute-relative-error-estimation-2ce9b9rrh1.pdf

Kani Chen

Papers

Semiparametric analysis of transformation models with censored data

Case-cohort and case-control analysis with Cox's model

Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs

Generalized case–cohort sampling

Least Absolute Relative Error Estimation