# Univariate non-significant results becoming significant on multivariate analysis---X-ray waiting times

I'm having a look at x-ray waiting times in an emergency department and how these relate to the day of the week and the time of day that requests are ordered. (Want to know if patients have to wait longer for their x-rays on weekends and at night compared with day shifts).

The waiting times have a significant right skew when plotted on a histogram. I divided the continuous variable "waiting times" into 5 categories (0-30 mins being the reference category). I also dummy coded the 6 days of the week and the "time of day" (which was divided into the 3 shifts of the day) into 0-the day in question and 1-the rest of the days of the week.

I performed univariate multinomial regression with waiting times as the dependent variable and each independent dummy variable in turn (omitting Saturday and Night shift from the analysis to act as "reference").

when I entered each variable independently, not one of them showed a significant relationship with x-ray waiting times. On multivariable multinomial regression, I found four variables were demonstrating p values less than 0.05, particularly with the waiting time category of 61-90 mins.

I wondered if anyone knew why this was? If there's a plausible explanation or whether I've made a mistake somewhere? Please help if you have any suggestions as I'm a complete stats amateur ...

You don't really have more than one independent variable. You have multiple levels of a single categorical independent variable. You'll want to read threads like this one and the one linked at the bottom of that page, where the conversation is picked up in more detail. (btw, on that first page, I'd give more weight to @Frank's comment than to my answer.)

In addition to the main question you ask (for which see the thread mentioned by @rolando2), I would not categorize waiting time. You might consider transforming it - for variables that are very skewed to the right, log often works nicely.

But, if you do categorize it as you did, then you don't really have multinomial logistic, you have ordinal logistic

• Not that I'm asking you to quantify this exactly, but how much difference does it make in practice whether one uses ordinal or multinomial? – rolando2 Apr 7 '12 at 13:56
• Unfortunately I'm new to stats, so was unsure how to interpret the estimates produced by ordinal logistic as spss doesn't convert them into odds ratios. Any pointers in this direction? – Elena love Apr 7 '12 at 21:26
• @rolando I don't think that's answerable in general; you have to take it on a case-by-case basis – Peter Flom Apr 8 '12 at 12:06
• @Elenalove If you use SAS, see a paper I wrote – Peter Flom Apr 8 '12 at 12:08
• The statement "you don't really have multinomial logistic, you have ordinal logistic" doesn't make sense. The ordinal logistic model is a submodel of the multinomial logistic. What you've said is like saying "You don't have a polygon, you have a square". – Macro Apr 9 '12 at 22:33

First, I want to say that this is a classic Survival Analysis situation. It's called by different names in different disciplines; while SA is most common, 'Time to Event Analysis' may be more intuitive in your situation. SA can be done in SPSS, although it's been a while since I've had access to SPSS, so I can't advise on the mechanics of performing the analysis, unfortunately. Googling SA SPSS yielded this pdf, which looks like it may be helpful in that regard. I would recommend you use a Cox Proportional Hazard model for this analysis, as you are primarily interested in the effect of your covariates, rather than the baseline hazard rate. These things having been said, I should acknowledge that if a transformation (such as taking the log) sufficiently normalizes your response variable, multiple linear regression should be acceptable. If you are totally unfamiliar with SA, are unlikely to have to work with similar situations in the future, and/or are not in a position to pick up new techniques right now, the costs of trying to learn about SA would outweigh the benefits, and multiple regression would probably be your best bet.