MAIC

# MAIC
## Matching-Adjusted Indirect Comparisons
### Claus Thorn Ekstrøm<br>Biostatistik, KU<br>.small[<a href="mailto:ekstrom@sund.ku.dk" class="email">ekstrom@sund.ku.dk</a> ]
### 13. oktober 2021

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background-image: url(pics/ababc.png)
background-position: center center 
background-size: 50%

# Problemstilling

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## Oversigt

Network Meta-Analysis (NMA) 
-   AgD, IPD, direkte, indirekte sammenligninger, multiplicitet
-   Golden standard, fleksibilitet
-   Problemer: Lange netværk, disjunkte netværk, heterogenitet

Buchers metode
-   AgD, indirekte sammenligninger
-   Efficiens, simpel
-   Problemer: som NMA

]

Alternativer:

Matching-adjusted indirect comparisons (MAIC)
-   AgD + IPD, indirekte sammenligning
-   Kan "fixe" nogle problemer med heterogenitet, disjunkte netværk.

Simulated treatment comparisons (STC)

]

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# Indirekte sammenligninger

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# Buchers metode

Antagelser: Aggregerede resultater fra to (RCT-) studier `$AC$` og `$BC$`.

`$$\begin{array}{ll}\text{Forhold (HR, OR, RR):} &\frac{\frac{\hat{\mu}_A}{\hat{\mu}_C}}{\frac{\hat{\mu}_B}{\hat{\mu}_C}} = \frac{\hat{\mu}_A}{\hat{\mu}_B} \\ \text{Forskel (RD, Gnst):} & \underbrace{\hat{\mu}_A - \hat{\mu}_C}_\text{Fra AC} - \underbrace{(\hat{\mu}_B - \hat{\mu}_C)}_\text{Fra BC} = \hat{\mu}_A - \hat{\mu}_B\end{array}$$`

Indenfor hvert studie (ca.):

`$$\hat{\mu}_{t} = \frac{\sum_{i=1}^{N_t} Y_{it}}{N_t}$$`

???

Samme estimand?

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# Problemer med Buchers metode

Fordelingen af *mindst en* effektmodificerende variabel er forskellig i studierne for `$A$` og `$B$`.

*   Antagelser ikke opfyldte
*   Resultaterne er ikke direkte sammenlignelige
*   Forskellige estimander?

---

|    | + | - |   |
|----|---|---|---|
| A  | 80 | 20 | 0.8 |
| C  | 50 | 50 | 0.5 |

`$RR_\text{AC} = 8/5$`

|    | + | - |   |
|----|---|---|---|
| B  | 60 | 40 | 0.6 |
| C  | 50 | 50 | 0.5 |

`$RR_\text{BC} = 6/5$`

`$RR_\text{AB} = \frac{8/5}{6/5} = \frac{8}{6}$`

]

|    | + | - |   |
|----|---|---|---|
| A  | .yellow[40] | .yellow[40 +] 20 | 0.4 |
| C  | 50 | 50 | 0.5 |

`$RR_\text{AC} = 4/5$`

|    | + | - |   |
|----|---|---|---|
| B  | .yellow[30] | .yellow[30 +] 40 | 0.3 |
| C  | 50 | 50 | 0.5 |

`$RR_\text{BC} = 3/5$`

`$RR_\text{AB} = \frac{4/5}{3/5} = \frac{4}{3}$`

]

???

Kun effektivt på 50% af befolkningen, men det er det samme for begge studier

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.pull-left[
|    | + | - |   |
|----|---|---|---|
| A  | .yellow[40] | .yellow[40 +] 20 | 0.4 |
| C  | 50 | 50 | 0.5 |

`$RR_\text{AC} = 40/50$`

|    | + | - |   |
|----|---|---|---|
| B  | .yellow[48] | .yellow[12 +] 40 | 0.48 |
| C  | 50 | 50 | 0.50 |

`$RR_\text{BC} = 48/50$`

`$RR_\text{AB} = \frac{40/50}{48/50} = \frac{40}{48}$` 
]

![](maic_files/figure-html/unnamed-chunk-1-1.png)

]

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## Effektmodifiktorer?

Effektmodifikation: forskellige effekter i forskellige undergrupper/strata.

*   Bør ikke være baseret på tests. .tiny[Overmatchning, faktor 16, sample size]

*   Marginale sammenligninger kan skjule forskelle &#9758;
*   Skala - additiv / multiplikativ?

]
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![](maic_files/figure-html/unnamed-chunk-2-1.png)

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class:inverse, middle, center

# MAIC

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# Ideen i MAIC

Grundidé: Udregn den effekt af `$A$`, man ville forvente at se i `$B$` populationen.

Hvordan? Lav en pseudo-population ud fra `$A$`, der ligner `$B$`-populationen så mneget som muligt.

Eksempel: køn som effektmodifikator

** `$B$` studiet **

]
--
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** `$A$` studiet**

| <svg aria-hidden="true" role="img" viewBox="0 0 256 512" style="height:1em;width:0.5em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M128 0c35.346 0 64 28.654 64 64s-28.654 64-64 64c-35.346 0-64-28.654-64-64S92.654 0 128 0m119.283 354.179l-48-192A24 24 0 0 0 176 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H80a24 24 0 0 0-23.283 18.179l-48 192C4.935 369.305 16.383 384 32 384h56v104c0 13.255 10.745 24 24 24h32c13.255 0 24-10.745 24-24V384h56c15.591 0 27.071-14.671 23.283-29.821z"/></svg> | <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg> | <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg> | <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg> | <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg> | <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg> |
| ------------- | ------------- | ----- | ----- | ----- | ----- |
| 3      | 3/5 | 3/5 | 3/5 | 3/5 | 3/5 |

]

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# Hvornår kan MAIC benyttes?

Antagelser: IPD er tilgængeligt for `$A$`, mens aggregerede data findes fra `$B$`.

*   .yellow[**kun**] forskel mellem populationerne for effektmodificerende variable eller prognostiske faktorer
*   .yellow[**ingen**] forskelle ift *opfølgning*, administration af behandling mm. .tiny[Disse forskelle kan ikke korrigeres/fikses.]
*   har tilgængelige data på *alle relevante* variable for både `$A$` og `$B$`.

Desuden antager ansøger (ofte lidt stiltiende), at

*   behandlingseffekten er nok populationsafhængig. .tiny[Alternativt antages det modsatte!]
*   den relevante population er tættere på `$B$` end på deres eget studie med `$A$`.

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# To typer sammenligninger

*   **Anchored.** Sammenligning går via en fælles komparator. Fx `$AC$` og `$BC$`.

Justér for *alle* effektmodifikatorer for at sikre balance og reducere bias.<br>
    
    <p style="font-size: 70%">Prognostiske variable "forkorter ud" i de enkelte studier, og hvis de medtages risikeres overmatching &rArr; mindre effektiv stikprøvestørrelse &rArr; større usikkerhed.</p>
    
*   **Unanchored.** Sammenligning uden fælles komparator (fx single-arm). `$A$` og `$B$`

Justér for *alle* effektmodifikatorer og *alle* prognostiske faktorer for at sikre balance, fjerne confoundere og reducere bias.

<p style="font-size: 70%">Prognostiske variable skal inkluderes for at deres effekt "fjernes"  i de enkelte studier og man så vidt muligt identificerer den konkrete behandlingseffekt. Hvis forskel i fordeling introduceres bias &rArr; hvad måler vi?</p>

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# "Fri leg"

### (Lad os alle matche)

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# ESS - effective sample size

ESS `$\approx$` antal uafhængige observationer, som den vægtede stikprøve svarer til.

Lille ESS ift den oprindelige stikprøve indikerer at vægtene varierer meget og at estimaterne kan være ustabile. Skyldes begrænset sammenfald i fordelingen af match-variable.

]
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![](maic_files/figure-html/unnamed-chunk-3-1.png)

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# MAIC vs Bucher

`$$\hat{\mu}_{t(BC)} = \frac{\sum_{i=1}^{N_{AC_t}} Y_{it} w_{it}}{\sum_{i=1}^{N_{AC_t}} w_{it}}$$`

Derefter traditionelle indirekte sammenligninger.

.pull-left[
*   Studierne ens `$\Rightarrow$` `$w_i \approx 1$`. Unbiased, men usikkerhed på vægte og reduceret ESS giver større SE.

]
.pull-right[
| EM |  Justering  |  Bucher  |  MAIC |
|:----------------:| --------------------- | --------  | -------- |
| Ja  | Nej | <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:red;overflow:visible;position:relative;"><path d="M256 8C119 8 8 119 8 256s111 248 248 248 248-111 248-248S393 8 256 8zM124 296c-6.6 0-12-5.4-12-12v-56c0-6.6 5.4-12 12-12h264c6.6 0 12 5.4 12 12v56c0 6.6-5.4 12-12 12H124z"/></svg>  = | <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:red;overflow:visible;position:relative;"><path d="M256 8C119 8 8 119 8 256s111 248 248 248 248-111 248-248S393 8 256 8zM124 296c-6.6 0-12-5.4-12-12v-56c0-6.6 5.4-12 12-12h264c6.6 0 12 5.4 12 12v56c0 6.6-5.4 12-12 12H124z"/></svg> |
|     | Ja  |  | <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:green;overflow:visible;position:relative;"><path d="M173.898 439.404l-166.4-166.4c-9.997-9.997-9.997-26.206 0-36.204l36.203-36.204c9.997-9.998 26.207-9.998 36.204 0L192 312.69 432.095 72.596c9.997-9.997 26.207-9.997 36.204 0l36.203 36.204c9.997 9.997 9.997 26.206 0 36.204l-294.4 294.401c-9.998 9.997-26.207 9.997-36.204-.001z"/></svg> |
| Nej | Nej | <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:green;overflow:visible;position:relative;"><path d="M173.898 439.404l-166.4-166.4c-9.997-9.997-9.997-26.206 0-36.204l36.203-36.204c9.997-9.998 26.207-9.998 36.204 0L192 312.69 432.095 72.596c9.997-9.997 26.207-9.997 36.204 0l36.203 36.204c9.997 9.997 9.997 26.206 0 36.204l-294.4 294.401c-9.998 9.997-26.207 9.997-36.204-.001z"/></svg>  = | <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:green;overflow:visible;position:relative;"><path d="M173.898 439.404l-166.4-166.4c-9.997-9.997-9.997-26.206 0-36.204l36.203-36.204c9.997-9.998 26.207-9.998 36.204 0L192 312.69 432.095 72.596c9.997-9.997 26.207-9.997 36.204 0l36.203 36.204c9.997 9.997 9.997 26.206 0 36.204l-294.4 294.401c-9.998 9.997-26.207 9.997-36.204-.001z"/></svg> |
|     | Ja  |  | <svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:orange;overflow:visible;position:relative;"><path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z"/></svg> |
]

---

# Generelle problemer med vægtede analyser

*   Observationerne er ikke længere uafhængige / den effektive stikprøvestørrelse reduceres.
*   Vægtene er estimerede og ikke kendte. .tiny[Robuste SEs]

Hvad sker der, hvis man vægter med noget, som ikke er en effektmodifikator?

Uheldige fordelinger:

.pull-left[
|   |  A  |  B  |
|:-------------:| ------------- | ----- |
| <svg aria-hidden="true" role="img" viewBox="0 0 256 512" style="height:1em;width:0.5em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M128 0c35.346 0 64 28.654 64 64s-28.654 64-64 64c-35.346 0-64-28.654-64-64S92.654 0 128 0m119.283 354.179l-48-192A24 24 0 0 0 176 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H80a24 24 0 0 0-23.283 18.179l-48 192C4.935 369.305 16.383 384 32 384h56v104c0 13.255 10.745 24 24 24h32c13.255 0 24-10.745 24-24V384h56c15.591 0 27.071-14.671 23.283-29.821z"/></svg> | 33% | 15% |
| <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg>  | 33% | 0% |
| <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M327.1 96c-89.97 0-168.54 54.77-212.27 101.63L27.5 131.58c-12.13-9.18-30.24.6-27.14 14.66L24.54 256 .35 365.77c-3.1 14.06 15.01 23.83 27.14 14.66l87.33-66.05C158.55 361.23 237.13 416 327.1 416 464.56 416 576 288 576 256S464.56 96 327.1 96zm87.43 184c-13.25 0-24-10.75-24-24 0-13.26 10.75-24 24-24 13.26 0 24 10.74 24 24 0 13.25-10.75 24-24 24z"/></svg>  | 34% | 85% |

.tiny[Dele af A udelukkes]
]
.pull-right[
|   |  A  |  B  |
|:-------------:| ------------- | ----- |
| <svg aria-hidden="true" role="img" viewBox="0 0 256 512" style="height:1em;width:0.5em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M128 0c35.346 0 64 28.654 64 64s-28.654 64-64 64c-35.346 0-64-28.654-64-64S92.654 0 128 0m119.283 354.179l-48-192A24 24 0 0 0 176 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H80a24 24 0 0 0-23.283 18.179l-48 192C4.935 369.305 16.383 384 32 384h56v104c0 13.255 10.745 24 24 24h32c13.255 0 24-10.745 24-24V384h56c15.591 0 27.071-14.671 23.283-29.821z"/></svg> | 55% | 15% |
| <svg aria-hidden="true" role="img" viewBox="0 0 192 512" style="height:1em;width:0.38em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M96 0c35.346 0 64 28.654 64 64s-28.654 64-64 64-64-28.654-64-64S60.654 0 96 0m48 144h-11.36c-22.711 10.443-49.59 10.894-73.28 0H48c-26.51 0-48 21.49-48 48v136c0 13.255 10.745 24 24 24h16v136c0 13.255 10.745 24 24 24h64c13.255 0 24-10.745 24-24V352h16c13.255 0 24-10.745 24-24V192c0-26.51-21.49-48-48-48z"/></svg>  | 45% | 5% |
| <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M327.1 96c-89.97 0-168.54 54.77-212.27 101.63L27.5 131.58c-12.13-9.18-30.24.6-27.14 14.66L24.54 256 .35 365.77c-3.1 14.06 15.01 23.83 27.14 14.66l87.33-66.05C158.55 361.23 237.13 416 327.1 416 464.56 416 576 288 576 256S464.56 96 327.1 96zm87.43 184c-13.25 0-24-10.75-24-24 0-13.26 10.75-24 24-24 13.26 0 24 10.74 24 24 0 13.25-10.75 24-24 24z"/></svg>  | 0% | 80% |

.tiny[A og B vil ikke være sammenlignelige, medmindre der findes subgrupperesultater fra B uden <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:dodgerblue;overflow:visible;position:relative;"><path d="M327.1 96c-89.97 0-168.54 54.77-212.27 101.63L27.5 131.58c-12.13-9.18-30.24.6-27.14 14.66L24.54 256 .35 365.77c-3.1 14.06 15.01 23.83 27.14 14.66l87.33-66.05C158.55 361.23 237.13 416 327.1 416 464.56 416 576 288 576 256S464.56 96 327.1 96zm87.43 184c-13.25 0-24-10.75-24-24 0-13.26 10.75-24 24-24 13.26 0 24 10.74 24 24 0 13.25-10.75 24-24 24z"/></svg>.

]

---

# MAIC i evidenshierarkiet

*   Rangerer lavere end direkte sammenlignende RCT'ere.<br>
    Ingen kausale konklusioner (kræver massevis af utestbare antagelser)

*   Usikkert hvordan MAIC indgår i evidenshierarkiet		
    *   Hvis matching/propensity scoring er suboptimal kan det introducere/ikke fjerne bias. <p style="font-size: 70%">F.eks. bør der justeres for alle kendte effektmodifikatorer.</p>
*   Bedre (= reducerer bias) end indirekte sammenligning uden justering for forskelle i population/effect modifiers, hvis gennemført korrekt.

---

# Rapportering af MAIC analyser

*   Hvilke variable er blevet vurderet som potentielt effektmodificerende? Prognostiske faktorer? 
    Argumentation! Hvilke er siet fra – og hvorfor?
    
*   Fordeling af vægte for hvert effektmål (gennemsnit, minimum, 25 percentil, median 75 percentil og maximum) – gerne visualiseret med histogrammer.

*   Effektiv sample size (ESS) for `$A$` studiet efter vægtning – er der en betydelig reduktion i studiets styrke? Hvor mange i `$A$` studiet vægtes til 0?

*   Ujusterede resultater fra `$A$` studiet

*   De justerede resultater fra `$A$` studiet

---

# Referencer

Phillippo, D.M., Ades, A.E., *et al.* (2018) *Methods for Population-Adjusted Indirect Comparisons in Health Technology Appraisal*. Medical Decision Making, 38, 200-211.

Vehtari, Gelman, Hill (2021). *Regression and Other Stories*, Ch 16.4

Signorovitch, J. E., Wu, E. Q., *et al.* (2010). *Comparative effectiveness without head-to-head trials*. Pharmacoeconomics 28 935–945.

Signorovitch, J. E., Sikirica, V., *et al.* (2012). *Matching-adjusted indirect comparisons: a new tool for timely comparative effectiveness research*. Value in Health 15 940–947.

Cheng, D., Ayyagari, R., and Signorovitch, J. E. (2020) *The Statistical Performance of Matching-Adjusted Indirect Comparisons*. [arXiv 1910.06449v2](https://arxiv.org/pdf/1910.06449.pdf)
]