# Proportional Odds Analysis for 4/29 Lancet Remdesivir Study

**URL:** <https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247>\
**Category:** general\
**Tags:** statistical-model\
**Created:** [April 30, 2020, 2:51pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247 "2020-04-30T14:51:09Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![Raj](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/raj/32/169_2.png) [@Raj](https://discourse.datamethods.org/u/Raj)\
**Post date:** [April 30, 2020, 2:51pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/1 "2020-04-30T14:51:09Z")

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Question about statistical analysis for ordinal outcomes, baseline differences, and the proportional odds assumption.

Lancet published a much awaited study on use of Remdesivir for Covid19. This was a randomized (2:1 allocation ratio), double-blind, placebo-controlled trial (n=237):  
[https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31022-9/fulltext](https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31022-9/fulltext)

**The primary outcome** was “time to clinical improvement within 28 days after randomization.” Clinical improvement was defined using a 6-point ordinal scale:

- 6 = death
- 5 = hospital admission for ECMO or mechanical ventilation
- 4 = hospital admission for non-invasive ventilation or high-flow oxygen
- 3 = hospital admission for regular oxygen therapy
- 2 = hospital admission but not requiring oxygen
- 1 = discharged or having reached discharge criteria

**The statistical analysis** , briefly, was as follows:

- “The primary efficacy analysis was done on an intention-to-treat (ITT) basis with all randomly assigned patients. Time to clinical improvement was assessed after all patients had reached day 28; no clinical improvement at day 28 or death before day 28 were considered as right censored at day 28. Time to clinical improvement was portrayed by Kaplan-Meier plot and compared with a log-rank test. The HR and 95% CI for clinical improvement and HR with 95% CI for clinical deterioration were calculated by Cox proportional hazards model.”

**Results:**

- Time to clinical improvement:  
 ![gr2](https://discourse.datamethods.org/uploads/default/original/2X/a/a7d593751778582593e4d529020a47f31db2da59.jpeg)
- Outcomes  
 ![dayall](https://discourse.datamethods.org/uploads/default/original/2X/7/70bd94aaf427e6e74a6daa0d9913f2eeb26c7922.png)
- Proportion distribution at Day 1, 7, 14, & 28:  
 ![2020-04-30 10_54_16-mmc1.pdf](https://discourse.datamethods.org/uploads/default/original/2X/c/c7efcdd86005981172a0cfe5c69de5afc494964e.png)

**Question:** (Edited)  
I am trying to understand why the outcomes appear to shift for the _worse_ at Day 7, and then for the _better_ at Day 14.

- Is this just normal “noise” that we see in data early on in a trial?
- Is it possible chance handed Remdesivir a slightly sicker group of patients at baseline?
- Does Cox proportional hazards model take into account baseline differences?
- Does this violate the proportional odds assumption?
- Does this effect the optimal choice for a statistical model?
- Is it possible the choice of outcome scale flawed?

My initial assumption is that this is just expected noise/variation in data at the early point of the study. But I thought I would ask others so they could offer expertise on how to best interpret & learn form this example.

Thanks!  
Raj

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**Author:** ![pmbrown](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/pmbrown/32/1382_2.png) [@pmbrown](https://discourse.datamethods.org/u/pmbrown)\
**Post date:** [April 30, 2020, 4:49pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/2 "2020-04-30T16:49:30Z")

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worth noting clinical improvement defined as: “a decline of two levels on a six-point ordinal scale of clinical status (from 1=discharged to 6=death) or discharged alive from hospital, whichever came first”, also phrased as: "a two-point reduction in patients’ admission status on a six-point ordinal scale, or live discharge from the hospital, whichever came first. "

i guess they mean 2 levels or more, although im not sure what decline of 2 levels means on the scale you give above

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**Author:** ![f2harrell](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/f2harrell/32/165_2.png) [@f2harrell](https://discourse.datamethods.org/u/f2harrell)\
**Post date:** [April 30, 2020, 7:10pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/3 "2020-04-30T19:10:33Z")

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Angst. There are **severe** problems with this endpoint. See [here](https://discourse.datamethods.org/t/responder-analysis-loser-x-4).

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**Author:** ![karlamoPA](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/karlamopa/32/1276_2.png) [@karlamoPA](https://discourse.datamethods.org/u/karlamoPA)\
**Post date:** [June 9, 2020, 6:53pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/4 "2020-06-09T18:53:25Z")

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One imbalance in risk factors from table 1 suggesting to me that sicker patients were in the placebo arm:  
Hospitalized, needing invasive ventilation or ECMO.  
-Remdesivir 125 (23%) | Placebo 147 (28%)

My understanding is that this risk factor is more substantially associated with death than any other.

 ![image](https://discourse.datamethods.org/uploads/default/original/2X/f/f53d5f4a3f033f571bb593bb8ade3493bf253e11.jpeg)

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**Author:** ![f2harrell](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/f2harrell/32/165_2.png) [@f2harrell](https://discourse.datamethods.org/u/f2harrell)\
**Post date:** [June 10, 2020, 2:11am UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/5 "2020-06-10T02:11:13Z")

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I don’t see how it’s valid to compare baseline distributions in a randomized study. Plus you’ll easily find counterbalancing factors.

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**Author:** ![karlamoPA](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/karlamopa/32/1276_2.png) [@karlamoPA](https://discourse.datamethods.org/u/karlamoPA)\
**Post date:** [June 11, 2020, 8:48am UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/6 "2020-06-11T08:48:49Z")

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Highlighting the source that prompts my concern for persons requiring mechanical ventilation: “_Of those receiving mechanical ventilation, 17% (276/1658) were discharged alive, 37% (618/1658) died, and 46% (764/1658) remained in hospital._”

Features of 20 133 UK patients in hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: prospective observational cohort study [https://www.bmj.com/content/369/bmj.m1985](https://www.bmj.com/content/369/bmj.m1985)

Results The median age of patients admitted to hospital with covid-19, or with a diagnosis of covid-19 made in hospital, was 73 years (interquartile range 58-82, range 0-104). More men were admitted than women (men 60%, n=12 068; women 40%, n=8065). The median duration of symptoms before admission was 4 days (interquartile range 1-8). The commonest comorbidities were chronic cardiac disease (31%, 5469/17 702), uncomplicated diabetes (21%, 3650/17 599), non-asthmatic chronic pulmonary disease (18%, 3128/17 634), and chronic kidney disease (16%, 2830/17 506); 23% (4161/18 525) had no reported major comorbidity.

Overall, 41% (8199/20 133) of patients were discharged alive, 26% (5165/20 133) died, and 34% (6769/20 133) continued to receive care at the reporting date.

17% (3001/18 183) required admission to high dependency or intensive care units; of these, 28% (826/3001) were discharged alive, 32% (958/3001) died, and 41% (1217/3001) continued to receive care at the reporting date.

_Of those receiving mechanical ventilation, 17% (276/1658) were discharged alive, 37% (618/1658) died, and 46% (764/1658) remained in hospital._

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**Author:** ![yetanotherpatel](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/yetanotherpatel/32/1909_2.png) [@yetanotherpatel](https://discourse.datamethods.org/u/yetanotherpatel)\
**Post date:** [December 3, 2020, 6:57pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/7 "2020-12-03T18:57:40Z")

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I had a question regarding the clinical interpretation of the common odds ratio. This is a segment of Table 3, with the results of the ordinal scale at day 28:

 ![image](https://discourse.datamethods.org/uploads/default/original/2X/b/bb02d252f1591739d3535ad56d740fd12275ec37.png)

I realize that the CI for the common odds ratio is very wide, but let’s just assume the point estimate is valid for argument purposes. I think I would interpret it as follows:

- If a patient started treatment requiring supplemental oxygen (3 on the scale), he has a 1.15x higher odds of being at a 2 on the scale 28 days later (being hospitalized, but not requiring supplemental oxygen).

How would the common OR change if I wanted to estimate the odds of a patient improving by \> 1 point on the scale? Taking the example above, what are the odds the patient goes from a 3 to a 1 (discharged from the hospital)?

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**Author:** ![yetanotherpatel](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/yetanotherpatel/32/1909_2.png) [@yetanotherpatel](https://discourse.datamethods.org/u/yetanotherpatel)\
**Post date:** [December 3, 2020, 7:00pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/8 "2020-12-03T19:00:32Z")

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Also, @f2harrell mentioned how there is a major problem with the primary endpoint of **clinical improvement**.

This seems to be the main problem with ACTT-1 study as well right? The difference being that the common odds ratio in that study showed a significant benefit in favor of remdesivir.

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**Author:** ![f2harrell](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/f2harrell/32/165_2.png) [@f2harrell](https://discourse.datamethods.org/u/f2harrell)\
**Post date:** [December 3, 2020, 8:33pm UTC](https://discourse.datamethods.org/t/proportional-odds-analysis-for-4-29-lancet-remdesivir-study/3247/9 "2020-12-03T20:33:33Z")

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> [@yetanotherpatel](#):
>
> - If a patient started treatment requiring supplemental oxygen (3 on the scale), he has a 1.15x higher odds of being at a 2 on the scale 28 days later (being hospitalized, but not requiring supplemental oxygen).
> 
> How would the common OR change if I wanted to estimate the odds of a patient improving by \> 1 point on the scale? Taking the example above, what are the odds the patient goes from a 3 to a 1 (discharged from the hospital)?

As an aside note that only using the 28d result results in a power loss.

The OR doesn’t have to do with within-patient changes. If the OR is not covariate adjusted for initial ordinal state, then the interpretation is the ratio of odds for treatment B : A of being in outcome category y or worse, for any y other than the first. If it is covariate adjusted, then the OR responses the same ratio of odds but for a subject on treatment B with initial state x being compared to a subject on treatment A who is in the same initial state x.