# Questions tagged [censoring]

The process of censoring yields data w/ only partial information. The most common example of censoring is *right censoring* in survival analysis, where the time until the event occurred is only known to be longer than some duration because the event had not occurred when the study ended.

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### How to model this odd-shaped distribution (almost a reverse-J)

My dependent variable shown below doesn't fit any stock distribution that I know of. Linear regression produces somewhat non-normal, right-skewed residuals that relate to predicted Y in an odd way (...
7k views

### ML estimate of exponential distribution (with censored data)

In Survival Analysis, you assume the survival time of a r.v. $X_i$ to be exponentially distributed. Considering now that I have $x_1,\dots,x_n$ "outcomes" of i.i.d r.v.'s $X_i$. Only some proportion ...
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### Unbiased estimation of covariance matrix for multiply censored data

Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...
4k views

### Layman's explanation of censoring in survival analysis

I have read about what censoring is and how it needs to be accounted for in survival analysis but I would like to hear a less mathematical definition of it and a more intuitive definition (pictures ...
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### What exactly are censored data?

I have read different descriptions of censored data: A) As explained in this thread, unquantified data below or above a certain threshold is censored. Unquantified means data is above or below a ...
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### Problem with informative censoring

I am reading "Monte Carlo Statistical Methods" by Robert and Cassella, and problem 1.3 asks In example 1.1, the distribution of the random variable $Z=\min(X,Y)$ was of interest. Derive the ...
768 views

### Modelling when the dependent variable has a “cut-off”

Apologies in advance if any of the terminology I use is incorrect. I'd welcome any correction. If what I describe as a "cut-off" goes by a different name, let me know and I can update the question. ...
23k views

### What is the difference between censoring and truncation?

In the book Statistical Models and Methods for Lifetime Data , it is written : Censoring: When an observation is incomplete due to some random cause. Truncation: When the incomplete nature of ...
4k views

### What is “Targeted Maximum Likelihood Expectation”?

I'm trying to understand some papers by Mark van der Laan. He's a theoretical statistician at Berkeley working on problems overlap significantly with machine learning. One problem for me (besides ...
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### How should I handle a left censored predictor variable in multiple regression?

I have a dataset (N=350) for which I would like to regress a neuropsychological test score (continuous) on age, education, symptom severity (continuous), and diagnosis (binary). Symptom severity is ...
14k views

### Difference between independent and non-informative censoring

I was wondering if I could get a third opinion to settle a discussion on the distinction between independent and non-informative censoring. My definitions: 1) In independent censoring, the event ...
24k views

### Right censoring and Left censoring

Wikipedia gives the following definitions: Right censoring: a data point is above a certain value but it is unknown by how much. Left censoring: a data point is below a certain value but it is ...
110 views

### Censored logit transform for (ad hoc) exploratory data analysis

In my work I commonly have to analyze binary composition data, expressed as a fraction $f\in[0,1]$. The data $f[x]$ is spatially distributed ($x\in\mathbb{R}^n$, $n=1,2,3$), and typically comes in the ...
169 views

### Weighted normal errors regression with censoring

I have some data which I would model via standard multiple regression except: There is censoring (left-censored, fixed but varying censoring points which are known) The errors are assumed independent ...
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### Calculate E[X] from incomplete data?

The exercise I'm doing describes the random variable $X$ as the following ...
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### Do we have a problem of “pity upvotes”?

I know, this may sound like it is off-topic, but hear me out. At Stack Overflow and here we get votes on posts, this is all stored in a tabular form. E.g.: post id voter id vote type ...
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### How should I model a continuous dependent variable in the $[0, \infty]$ range?

I have a dependent variable that can range from 0 to infinity, with 0s actually being correct observations. I understand censoring and Tobit models only apply when the actual value of $Y$ is partially ...
373 views

### If $Z_i =\min \{k_i, X_i\}$, $X_i \sim U[a_i, b_i]$, what is the distribution of $\sum_iZ_i$?

Assume the following set up: Let $Z_i = \min\{k_i, X_i\}, i=1,...,n$. Also $X_i \sim U[a_i, b_i], \; a_i, b_i >0$. Moreover $k_i = ca_i + (1-c)b_i,\;\; 0<c<1$ i.e. $k_i$ is a convex ...
328 views

### Informative censoring caused by cesarean section

I study labor and delivery as an epidemiologist. It is well established that a large fetus has a higher risk of causing maternal birth trauma. But a large baby is also likely to be delivered by ...
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### Can a Cox proportional hazards model be used on general left-censored data (i.e. non-survival data)?

A familiar problem in applied science is having censored data, in particular left-censored data arising due to an assay or piece of equipment having a lower limit of detection (LOD). Assuming a ...
320 views

### What are the mean and variance of a 0-censored multivariate normal?

Let $Z \sim \mathcal N(\mu, \Sigma)$ be in $\mathbb R^d$. What are the mean and covariance matrix of $Z_+ = \max(0, Z)$ (with the max computed elementwise)? This comes up e.g. because, if we use the ...
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### How can I estimate the time at which 50% of a binomial variable will have transitioned?

I have the following data, representing the binary state of four subjects at four times, note that it is only possible for each subject to transition $0\to 1$ but not $1\to 0$: ...
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### Simple case of MNAR missing data

I believe I have a very simple problem with missing data, but I'm a bit lost because all the materials I read seem to be focused on much more complicated cases. I have a random variable $X$ which has ...
323 views

### Estimating right-censored data

I am VERY new to stats. I have a large amount of life-time data (delay in arrival since start of experiment) from repeat experiments. Some data is missing, but essentially represents a delay longer ...
114 views

### Deriving the distribution of the sum of censored variables

I want to be able to calculate the distribution of $$Y = \sum_{i=1}^n\max\{0,X_i\}$$ where the random variable $X_i\sim N(\mu_i,\sigma_i)$. Is the calculation of $f_Y(y)$ possible and if so what is ...
198 views

### Learning a continuous model from binned data

A very similar question has been asked before, but it didn't get a real answer. Background I would like to develop a probability model for a continuous, ratio-scale random variable $Y$. Let's say it ...
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### How to get R squared/goodness of fit for Tobit model in R?

I do a Tobit regression to analyze censored data. To measure the goodness of fit the authors of these papers use Efron's $R^2$. So my idea is to use this one as well. To realize my Tobit regression, ...
701 views

### LASSO or other regularized regression with censored (missing) data

Here is my problem. I am looking at various time series curves. Let's call them total spend aggregated over all customers on various products versus time. At any given time, I want to predict the ...
573 views

### Statistics for rounded data

I wonder about the existence of "standard" statistical procedures for rounded (log)normal data. Indeed, in my work I often encounter rounded data which potentially cause some problems: "awful" qqplots,...
3k views

### Fit a Weibull distribution to…right-censored data?

Premise: I know next to nothing about survival analysis, I just started. I have a vector of failure times for some machines. Most of the machines (3362 vs 2694) are still running today, so I know they ...
872 views

### Inference with only left-censored data

Suppose I have a data set that is only left-censored data, ex: <5, <5, <5, <10, <10, <10 A technique to handle left-censored data is the Kaplan Meier estimate, see page 5 of this ...
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### How to estimate parameters of a distribution with left-truncated and right-censored data?

I have been trying to find the best way of estimating parameters for a known pdf from a data-set that is left-truncated and right-censored. More precisely, I have lifetimes for a system where there ...
162 views

### Should one use a censored survival model when an event is only observed at death?

A colleague of mine is trying to estimate how neutron radiation exposure changes cancer incidence rates (in mice). He has autopsy data that reports whether a cancer was observed at the time of death, ...
37 views

### Poisson regression on devices that fail during observation period?

I am observing N devices over a period of time $[0,T]$ and counting the number of certain events $y_j$, for each device, during that period of time. I also have some specifications $x_j$ for each ...
590 views

### Right-censored independent variable in Cox/logistic regression

I have a right-censored continuous independent variable that I want to include in a Cox regression. The variable is a physiologic test which is capped at a certain time, say 120 seconds, due to safety ...
61 views

### Inference for a distribution with different number of samples due to censoring

I have the following problem in case someone has an idea about how to solve this. Assume three experiments that refer to the same population for a random variable $X$. In the first experiment, I ...
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### Method for fitting censored data in R

I have 320 data points - each has a redshift and a turnover-frequency, and I want to fit a correlation between them (a linear fit). However, 120 of the turnover-frequency values are upper limits. As ...
253 views

### Version of Mann-Whitney U test, for right-censored data

Is there an equivalent of the Mann-Whitney U test, but for right-censored data? I have right-censored numerical data from two different groups. The mean for one group is higher than the other. I'd ...
445 views

### Poisson regression for ordered variables

I have three waves of data, and I am trying to estimate group-based trajectories of binge drinking across the three waves. The question asked (at all three waves was): “Over/During the past 12 months, ...
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### Best way to handle na values in regression predictor variable

I am running a multinomial logistic regression model in R (using the multinom function from the nnet package) with a set of 12 ...
281 views

### Likelihood of censored data

Let $X_1,X_2,\ldots, X_{n_1}$ be IID with PDF $f(x-\theta)$, for $-\infty<x<\infty$ and $-\infty<\theta<\infty$. Denote the CDF of $X_i$ by $F(x-\theta)$. Let $Z_1,Z_2, \ldots, Z_{n_2}$ ...
210 views

### Time-to-event data with low censoring

I have data on individuals, consisting of an individual identifier column, starting date column and length date column. This indicates an individual being in financial distress for a specific period ...