# What statistical test is suitable to summarise patient time in hospital with health condition

I am working on a dataset in which I am trying to summarise patient time in hospital by age and any health condition(e.g Cancer, Deprivatin, Depression or any). In my case it's Deprivatin. Patient time contains number of days spent by a patient in hospital. Age contains the actual age of a patient. Health condition contain score from 1 to 5 (1 is low and 5 is highest). I also made some graphs and correlated the dataset but I can't make a strong statistical decision based on the graphs because the data is very close. Below are the graphs generated from the data and first five entries of the dataset. Total number of entries in the dataset is 5000. With the given dataset and graphs, what would be the best statistical test for such data, from which a user can summarise patient time in hospital by age and health condition, and make a strong conclusion based on the result of statistical test. Thanks

Based on the feedback I got from different answers and comments, I applied MLR and got the following results.

    Residuals:
Min      1Q  Median      3Q     Max
-8.4344 -3.1339 -0.5236  2.5612 22.7393

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)              2.513551   0.199057   12.49  < 2e-15
data$$dep 0.423002 0.058672 7.21 3.09e-14 data$$age                 0.044427   0.002494   18.91  < 2e-15

(Intercept)              ***
data$$dep *** data$$age                 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.221 on 5130 degrees of freedom
Multiple R-squared:  0.07203,   Adjusted R-squared:  0.07166
F-statistic: 199.1 on 2 and 5130 DF,  p-value: < 2.2e-15

• From what I understand, you want to evaluate the factors contributing to the length of stay of patients in Hospital. From the correlation data, apparently there are no strong correlation between your variables (a moderate correlation between age and dependent). So I can suggest a multivariate regression if the assumptions are met. However, there is no guarantee of a strong conclusion. Jun 29 at 3:51
• @The_old_man Looking at to the correlation plot, what assumption can be made ? Jun 29 at 8:05
• @The_old_man. I have added the results of MLR in my question. What can be concluded from the results ? thanks Jun 29 at 15:00
• Why is days on the right hand side in the model formula? Isn't the goal to predict hospital stay (in days)? Jun 29 at 15:19
• @dipetkov. Sorry that was my mistake. Is it fine now ? I paste the new results. Thanks Jun 29 at 15:51

A regression analysis could be useful in this case. You can estimate a multivariate linear regression model.

Patient time in the hospital will be your dependent variable. Age and health condition (deprivation) will be the independent variables. The estimated coefficients will give you some insights into how age and deprivation are affecting patient time. If both your coefficients for age and deprivation are significant, you can say that they have a strong effect on patient time in the hospital.

You must ensure that your model is reliable before interpreting the results. Make sure there is no heteroscedasticity and the error terms are normally distributed. Check for multicollinearity as well, although it doesn't seem like it should be a problem in your case.

• I have added the results of MLR in my question. Can we conclude something from it ? Thanks Jun 29 at 14:59
• Both variables show a positive relationship with patient time. This means that an increase in deprivation and age increases patient time in hospital. An increase in deprivation by 1 point increases patient time in hospital by 0.423 days (approx. 10 hours) on average. With an increase in the age of the patient by 1 year, patient time increases by 0.044 days (approx. 1 hour) on average. However, you should further check into how the model is performing and how it fits. Adding some more important variables or a different approach might improve your results. Jun 30 at 4:44

Your model seem to indicate that age and health condition are significantly associated with the number of days in the hospital. While interpretation of the age is easy (the older the patients, the longer they stay in hospital), your other variable needs more investigation.

I suggest you try dummy coding (google it, many available resources) for your health condition variable, and then investigate each condition separately.

However, last but not least, always check for assumptions of the linear model. Here is a link for you.