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1. Combining Deep Learning With Optical Coherence Tomography Imaging to Determine Scalp Hair and Follicle Counts

   https://doi.org/10.1002/lsm.23324  

   Urban, Gregor ; Feil, Nate ; Csuka, Ella ; Hashemi, Kiana ; Ekelem, Chloe ; Choi, Franchesca ; Mesinkovska, Natasha A. ; Baldi, Pierre ( September 2020 , Lasers in Surgery and Medicine)

   One of the challenges in developing effective hair loss therapies is the lack of reliable methods to monitor treatment response or alopecia progression. In this study, we propose the use of optical coherence tomography (OCT) and automated deep learning to non‐invasively evaluate hair and follicle counts that may be used to monitor the success of hair growth therapy more accurately and efficiently.

   We collected 70 OCT scans from 14 patients with alopecia and trained a convolutional neural network (CNN) to automatically count all follicles present in the scans. The model is based on a dual approach of both detecting hair follicles and estimating the local hair density in order to give accurate counts even for cases where two or more adjacent hairs are in close proximity to each other.

   We evaluate our system on 70 OCT manually labeled scans taken at different scalp locations from 14 patients, with 20 of those redundantly labeled by two human expert OCT operators. When comparing the individual human predictions and considering the exact locations of hair and follicle predictions, we find that the two human raters disagree with each other on approximately 22% of hairs and follicles. Overall, the deep learning (DL) system predicts the number of follicles with an error rate of 11.8% and the number of hairs with an error rate of 18.7% on average on the 70 scans. The OCT system can capture one scalp location in three seconds, and the DL model can make all predictions in less than a second after processing the scan, which takes half a minute using an unoptimized implementation.

   This approach is well‐positioned to become the standard for non‐invasive evaluation of hair growth treatment progress in patients, saving significant amounts of time and effort compared with manual evaluation.

   Lasers Surg. Med. © 2020 Wiley Periodicals, Inc.

    

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2. Sublinear Algorithms and Lower Bounds for Metric TSP Cost Estimation

   https://doi.org/10.4230/LIPIcs.ICALP.2020.30  

   Chen, Yu ; Kannan, Sampath ; Khanna, Sanjeev ( April 2020 , Leibniz international proceedings in informatics)

   We consider the problem of designing sublinear time algorithms for estimating the cost of minimum] metric traveling salesman (TSP) tour. Specifically, given access to a n × n distance matrix D that specifies pairwise distances between n points, the goal is to estimate the TSP cost by performing only sublinear (in the size of D) queries. For the closely related problem of estimating the weight of a metric minimum spanning tree (MST), it is known that for any epsilon > 0, there exists an O^~(n/epsilon^O(1))-time algorithm that returns a (1+epsilon)-approximate estimate of the MST cost. This result immediately implies an O^~(n/epsilon^O(1)) time algorithm to estimate the TSP cost to within a (2 + epsilon) factor for any epsilon > 0. However, no o(n^2)-time algorithms are known to approximate metric TSP to a factor that is strictly better than 2. On the other hand, there were also no known barriers that rule out existence of (1 + epsilon)-approximate estimation algorithms for metric TSP with O^~ (n) time for any fixed epsilon > 0. In this paper, we make progress on both algorithms and lower bounds for estimating metric TSP cost. On the algorithmic side, we first consider the graphic TSP problem where the metric D corresponds to shortest path distances in a connected unweighted undirected graph. We show that there exists an O^~(n) time algorithm that estimates the cost of graphic TSP to within a factor of (2 − epsilon_0) for some epsilon_0 > 0. This is the first sublinear cost estimation algorithm for graphic TSP that achieves an approximation factor less than 2. We also consider another well-studied special case of metric TSP, namely, (1, 2)-TSP where all distances are either 1 or 2, and give an O^~(n ^ 1.5) time algorithm to estimate optimal cost to within a factor of 1.625. Our estimation algorithms for graphic TSP as well as for (1, 2)-TSP naturally lend themselves to O^~(n) space streaming algorithms that give an 11/6-approximation for graphic TSP and a 1.625-approximation for (1, 2)-TSP. These results motivate the natural question if analogously to metric MST, for any epsilon > 0, (1 + epsilon)-approximate estimates can be obtained for graphic TSP and (1, 2)-TSP using O^~ (n) queries. We answer this question in the negative – there exists an epsilon_0 > 0, such that any algorithm that estimates the cost of graphic TSP ((1, 2)-TSP) to within a (1 + epsilon_0)-factor, necessarily requires (n^2) queries. This lower bound result highlights a sharp separation between the metric MST and metric TSP problems. Similarly to many classical approximation algorithms for TSP, our sublinear time estimation algorithms utilize subroutines for estimating the size of a maximum matching in the underlying graph. We show that this is not merely an artifact of our approach, and that for any epsilon > 0, any algorithm that estimates the cost of graphic TSP or (1, 2)-TSP to within a (1 + epsilon)-factor, can also be used to estimate the size of a maximum matching in a bipartite graph to within an epsilon n additive error. This connection allows us to translate known lower bounds for matching size estimation in various models to similar lower bounds for metric TSP cost estimation. 

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3. Counterfactual Sensitivity and Robustness

   https://doi.org/10.3982/ECTA17232  

   Christensen, Timothy ; Connault, Benjamin ( January 2023 , Econometrica)

   We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models. 

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4. Sensitivity analysis for unmeasured confounding in coarse Structural Nested Mean Models

   https://doi.org/10.5705/ss.202016.0133  

   Yang S. ; Lok J.J. ( October 2018 , Statistica sinica)

   Coarse Structural Nested Mean Models (SNMMs, Robins (2000)) and G-estimation can be used to estimate the causal effect of a time-varying treatment from longitudinal observational studies. However, they rely on an untestable assumption of no unmeasured confounding. In the presence of unmeasured confounders, the unobserved potential outcomes are not missing at random, and standard G-estimation leads to biased effect estimates. To remedy this, we investigate the sensitivity of G-estimators of coarse SNMMs to unmeasured confounding, assuming a nonidentifiable bias function which quantifies the impact of unmeasured confounding on the average potential outcome. We present adjusted G-estimators of coarse SNMM parameters and prove their consistency, under the bias modeling for unmeasured confounding. We apply this to a sensitivity analysis for the effect of the ART initiation time on the mean CD4 count at year 2 after infection in HIV-positive patients, based on the prospective Acute and Early Disease Research Program. 

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5. Semiparametric estimation of structural nested mean models with irregularly spaced longitudinal observations

   https://doi.org/10.1111/biom.13471  

   Yang, Shu ( April 2021 , Biometrics)

   Structural nested mean models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at prefixed time points for all subjects, which, however, may be restrictive in practice. To deal with irregularly spaced observations, we assume a class of continuous‐time SNMMs and a martingale condition of no unmeasured confounding (NUC) to identify the causal parameters. We develop the semiparametric efficiency theory and locally efficient estimators for continuous‐time SNMMs. This task is nontrivial due to the restrictions from the NUC assumption imposed on the SNMM parameter. In the presence of ignorable censoring, we show that the complete‐case estimator is optimal among a class of weighting estimators including the inverse probability of censoring weighting estimator, and it achieves a double robustness feature in that it is consistent if at least one of the models for the potential outcome mean function and the treatment process is correctly specified. The new framework allows us to conduct causal analysis respecting the underlying continuous‐time nature of data processes. The simulation study shows that the proposed estimator outperforms existing approaches. We estimate the effect of time to initiate highly active antiretroviral therapy on the CD4 count at year 2 from the observational Acute Infection and Early Disease Research Program database.

    

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