Semiparametric estimation and variable selection under length-biased sampling with heavy censoring
Bibliographic record
Abstract
Semiparametric estimation procedures under Cox proportional hazards model and lengthbiased sampling have been developed using the weighted estimating equation method and the likelihood-based approaches over the past decade (Shen et al., 2017).The common feature of the procedures is that they are driven by risk sets just prior to failure times.Under length-biased sampling, however, censoring is informative and failing to incorporate the information on censored data into the estimation mechanism can lead to a substantial loss of efficiency when length-biased data are subject to heavy censoring; i.e. more than 50% of the data are censored.We compute the likelihood contribution for uncensored and censored data separately and propose maximum approximate partial likelihood estimation (MAPLE).The procedure is further improved by exploiting the additional information for uncensored data under length-biased sampling.We call this procedure maximum approximate composite partial likelihood estimation (C-MAPLE).The asymptotic properties of the estimator from C-MAPLE are established using the functional delta method.It is shown in a simulation study that C-MAPLE and MAPLE outperform other procedures under the Cox proportional hazards model and length-biased sampling with heavy censoring.We also apply the proposed procedures to the International Stroke Trial (IST) data collected in Argentina.We next develop a unified class of penalized estimating functions which encompasses any estimation procedure under the Cox proportional hazards model and length-biased sampling.We solve the penalized estimating function by slightly perturbing the penalty function in the Minorize-Maximization algorithm (Hunter and Li, 2005).We then investigate the asymptotic properties of the penalized estimators.It is shown that the penalized estimators are n-consistent and with a proper choice of the tuning parameter and the penalty function, they possess the same asymptotic properties as if the true model were known a priori which is termed as the oracle property.Two simulation studies are conducted to compare the performance of the penalized estimators and confirm our theoretical results.The procedure is also used for variable selection under the Cox proportional hazards model for the IST data collected in Argentina.We further study tuning parameter selections in the penalized List of Figures2.1 Positions of variables in a prevalent cohort study . . . . . . . . . . . . . . . .2.2 Standard Error (Left) and Mean Square Error (Right) of 1 from different procedures versus rates of censoring. . . . . . . . . . . . . . . . . . . . . . .2.3 Histograms of ( 1 , 2 ) from C-MAPLE (Upper) and MAPLE (Lower). . . . .2.4 Estimated cumulative distribution function of the truncation times (Left), Kaplan-Meier estimates for the survival functions of the backward and forward recurrence times (Right). . . . . . . . . . . . . . . . . .
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".