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7

You are right that this is a very common scenario in medical research. "I should note that these studies are not meant to invent a new method of treatment or change protocols, they are used to see what variables are of interest for future research." OK, I take this to mean that you are interested in causal inference, not in prediction. And from the ...

0

I assume you have some independent variables (predictors/covariates might be other terms you use) in which case a multivariable regression (likely a proportional hazards/Cox model) would be best. This however assumes you actually have time to event for each patient (i.e. censored at day 45, deceased at day 19, alive at 3 month follow up). To really give a ...

0

Use a standard Kaplan-Meier analysis to find the fraction of patients surviving to 3 months. The other methods described do not use all the data or misrepresent censored subjects. If you need to regress, consider a Cox regression and then fitting curves.

0

Does this mean that the score has a higher validity than the binary variables on their own? Precision and validity are not the same thing. I can estimate something very precisely and have it be invalid. You'll need to determine what your hypothesis actually is before you select a regression model. Are you interested in how the composite score affects the ...

8

Another issue is that the relationship between the IV and the DV (here, BP and heart attack risk) might not be linear. I would think this sort of nonlinearity would be quite common in medical fields. Indeed, this is sometimes given as a reason for categorizing the continuous variable (albeit into more than two categories). But this isn't good. A better ...

14

Dichotomizing a continuous covariate is ill-advised, as has been noted by other users. One strategy I employ is to rescale the predictor to something more reasonable. 1 mmHg may not be a very meaningful scale on which to interpret changes in BP. But, if you rescale the predictor so that a difference of 1 unit represents say a difference 10 mmHg then ...

12

Similar to EdM's answer, a marginal effects plot is a useful way to showcase the relationship between a clinical measurement and outcome while holding other variables constant. These plots are helpful because they show the relationship between the predictor and outcome, so if the outcome is nonlinear, physicians can easily see this and interpret it ...

9

For digestibility, use examples from representative situations: in your example, maybe comparing risks at BP of 160 versus BP of 120. For an approach that can take into account the multiple predictors typically important in clinical studies, use a nomogram. It provides a graphical tool to show how predictor values affect outcomes. The rms package in R ...

0

You are not the only one to have thought correlation useless! John Tukey also had such ideas, see the paper John Tukey and the correlation coefficient by David Brillinger. The paper has many quotes (with refs), but trying to copy quotes here only results in chinese ... so not. Have a look at the paper! Tukey's reason for disliking correlations did not have ...

1

So here is my answer. This is by no means the best answer. Rather it is just a basic general framework that is used. When I fit a model I typically like to decide the "best fit" by splitting my data into a training set and a validation set. The training set is used to actually fit the model and the validation set is used to test the model's accuracy. The ...

0

The implication seems to be that the grades are made into noisy predictors by the order of the grading, so what is the correlation between the "denoised" grades and the job prediction? But I don't quite know how one would model the way the grades receive that noise, and even if you do make such a model, I believe you need the actual data on job performance ...

0

For biomedical studies, a general rule of thumb to avoid overfitting in an unpenalized logistic regression model is to have on the order of 10-20 minority-class cases per evaluated predictor. You have 11 cases in the minority class, so without penalization should only be evaluating 1 predictor. That predictor would need to be pre-selected based on your ...

0

"The relationship should be calculated from adjusted values using a model that controls for intervention administration (outliers), otherwise the intervention effects are taken to be Gaussian noise, underestimating the actual correlation effect" This was pointed out by @Adamo in one of his posts on time series data Interrupted Time Series Analysis - ...

3

Regression can't do everything rank correlation does. If you are talking about simple linear regression on the raw data then Regression makes assumptions that Spearman's does not. Regression results are in terms of the units, Spearman's is not. Regression posits that one variable is dependent and the other is independent. Spearman's does not. Regression ...

0

You perform a Bonferoni correction to avoid an inflation of the Type 1 error rate (rejecting the Nullhypothesis although it is true). The Chance of making a Type 1 Error when you do a single test for example a t-test is your alpha level, usually 0.05. However, when you perform a second test then the chance that you get at least one Type 1 Error increases to ...

-1

Explanatory model has also been used in medicine and the health area as well, with a very different meaning. Basically what people have as internal beliefs or meanings can be quite different from accepted explanations. For example a religious person may have an explanatory model that an illness was due to punishment or karma for a past behaviour along with ...

2

You could do all this with a GAM and allow the model to identify the shape of the deterministic relationship, then answer your questions using the posterior distribution of the model. You can use a cyclic cubic regression spline to constrain the end points of 0 and 24 to be the same. For example: knots <- list(ToD = c(0, 24)) m <- gam(y ~ s(ToD, bs = ...

2

The thing that strikes me about your example data is the low proportion (about 4%) of Fractures. That may very well be legitimate, but it does mean your data contains very little information. In the example data there are only 25 persons with a fracture. With such a tiny sample size it is no surprise that the model becomes highly unstable, especially in a ...

1

If you're comparing your models to some observed reference, then it's a problem of measuring similarities of the two matrices. A matrix that assigns a scalar value to every single point in some area is, in other words, a really, really simple vector fields. What do you know, calculating differences between vector fields has been something centuries of ...

2

You ask a couple of questions here so let's unpack. 1.) "If you have a variable you want to investigate but you realize you should probably control for a number of variables, is it okay to do this for every variable you find interesting?" Normally, you would use the literature to determine which variables you should examine that need to be controlled for. ...

1

Ok, so this was fun. Luckily I have the book on hand and so if you follow some equations of Section 3.3.1 then (I think) it becomes quite easy. Let's write a class to do all the stuff we need. import numpy as np import matplotlib.pyplot as plt def make_design(x, s=0.1, p = 9): design = np.zeros(shape = (x.size, p)) design[:,0] = 1 for i in ...

1

I will be working backwards from the plot you are supposed to generate. The plot on page 157 of Bishops book on pattern recognition is a plot with the values of the input $x$ on the 1st axis and $t$ on the 2nd axis. The model for the data generating proces is $$t = sin(2\pi x) + \epsilon,$$ with $x \in [0,1]$ and $\epsilon \sim \mathcal N(0,\sigma^2)$ ...

0

What if you look at the partial explained variance. For example run first the intial regression. And then run a regression adding the effect of grading order. I guess you could say something about the change in explained variance

0

To build a predictive model, you must select the most relevant features in the model else if you have large number of features then your model will not converge. So will not get the right results from the model. As you rightly mention that if features are highly correlated then the variables coefficients will be inflated. For predictive model my suggestion ...

0

Considering you're comfortable with the idea of making subjective assumptions, and it's not a model that will determine if someone lives or dies, I would suggest a Bayesian model might be a good option. This would allow you to state your assumptions explicitly and visualize them in a graph, so it can be audited and interpreted in a fairly straightforward ...

2

The approach that is currently used is wrong for many reasons, see Algorithms for automatic model selection for a nice summary. As for alternatives, there are two (three) main ones, depending on your goal: As you suggested, use domain knowledge to filter the data and then run one model, in which case inference holds and can be reported for all variables. ...

3

The intercept $\beta_0$ is interpreted as the predicted value of $y$ when $x$ is zero. The p-value corresponds to the test of $H_0: \beta_0 = 0$. Sometimes this is an interesting test, and other times it isn't. In general, you might ask the question, "For a given value of $x$, does the predicted value for $y$ differ from zero?". The test of $\beta_0$ answers ...

2

The standard error, p-value, and confidence intervals about regression constants represent the uncertainty in the estimated value of the constant. Let's take bivariate OLS linear regression as an example. One of the primary questions we answer with linear regression is what straight line* best predicts the trend in mean values of $y$ over values of $x$? ...

1

This is a "rule of thumb" (English usage: a rough guide, in this case a guide to study design and initial modeling), not a strict "rule" that by itself ensures a lack of overfitting. Harrell's course notes and book provide (in their 4th Chapters) references to several studies that evaluated the sample sizes necessary to avoid overfitting in low signal-to-...

5

A bit late to the party but I wanted to clarify that the intercepts in your models have different interpretations, as follows. model1 <- lm(Totalpoints~m400 + m1500 + m100 + m110hurdles, data = samp1) The intercept for model1 represents the total points predicted by the model for a randomly selected athlete from your target population of athletes for ...

6

Linear regression is $$y = \text{intercept} + \text{coefficients} \times \text{features} + \varepsilon$$ If $\text{coefficients} \times \text{features}$ is high, then the intercept would need to be low enough to align the result with the predicted values, and if $\text{coefficients} \times \text{features}$ is small, the intercept would need to be bigger. ...

5

Logistic regression is used when modelling the probability of an event happening, which will usually mean that the response variable is binary. The model provides odds ratios for the exposure. It can be used in both prospective and retrospective studies. Logistic regression can also be used as a predictive model for classification where the target variable ...

5

This is not the main difference. Cox regression deals with time-to-event data, especially where there is censoring. So, with Cox regression, you are interested in how long it takes for something to happen. Logistic regression deals with whether something happens at all and does not account for censoring so if you have censored data, you will be looking at "...

1

Mixed models are used to account for the correlations in an outcome variable in grouped or clustered data. Like in your case, scores coming from the same participant will be correlated. However, there may also be other sources of correlations, e.g., scores from the same location could also be correlated. Mixed models do allow for such complex correlation ...

1

Note that different accuracy measures (such as the MAPE or the RMSE) are minimized in expectation by different functionals of the unknown future distribution. See Kolassa (2020, International Journal of Forecasting) for an explanation. The MAPE in particular rewards a biased forecast: What are the shortcomings of the Mean Absolute Percentage Error (MAPE)? ...

2

In 1961 James and Stein published an article called "Estimation with Quadratic Loss" https://projecteuclid.org/download/pdf_1/euclid.bsmsp/1200512173 . While it doesn't specifically coin the term shrinkage, they discuss minimax estimators for high dimensional (actually even for a 3 parameter location) statistics that have less risk (expected loss) than the ...

3

Counterexample: imagine you want to learn to predict human income given some other data. You train your model on the data on billionaires vs people who live for \$1 per day. Those two populations do not have much in common with vast majority of general population. Additionally, if you're using something like squared errors (including$R^2$), correctly ... 3 Your manual calculation is correct in terms of the coefficients, but you lose precision by either rounding incorrectly (i.e. the coefficient of the interaction) or by just not using enough numbers after the decimal point. Here is the manual calculation using 5 significant digits:$\$ \mathrm{logit}(y) = -13.609 + 0.018344\cdot 380 + 3.6522\cdot 3.61 - 1.3435\...

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