Ukungahleliwe Kusebenza Ezivivinyweni, Ngisho Nangaphandle Kwebhalansi

yokwelapha ekuhlolweni inomkhuba omangalisayo wokulinganisa iziphambanisi namanye ama-covariate kuwo wonke amaqembu okuhlola. Lokhu kuthambekela kunikeza izici eziningi ezivumayo zokuhlaziya imiphumela yokuhlolwa nokudweba iziphetho. Nokho, randomization ijwayele ukulinganisa ama-covariates – kunjalo hhayi okuqinisekisiwe.

Kuthiwani uma i-randomization ingalingani ama-covariates? Ingabe ukungalingani kubukela phansi ukufaneleka kokuhlolwa?

Ngabhekana nalo mbuzo isikhathi eside ngaphambi kokuba ngifinyelele esiphethweni esigculisayo. Kulesi sihloko, ngizokuhambisa ngenqubo yokucabanga engiyithathile ukuze ngiqonde ukuthi ukufaneleka kokuhlola kuncike kuyo ukuzimela ama-covariates kanye nokwelashwa, hhayi ibhalansi.

Nazi izihloko eziqondile engizozihlanganisa:

• Ukungahleliwe kuvame ukulinganisa ama-covariate
• Yini ebangela ukungalingani kwe-covariate ngisho nange-randomization
• Ukufaneleka kokuhlola kumayelana nokuzimela hhayi ukulingana

Ukwenza okungahleliwe kuvame ukulinganisa ama-covariate, kodwa asikho isiqinisekiso

I-Central Limit Theorem (CLT) ibonisa ukuthi incazelo yesampula ekhethwe ngokungahleliwe ivamise ukusatshalaliswa ngenani elilingana nenani labantu kanye nokwehluka okulingana nokuhluka kwabantu okuhlukaniswa ngosayizi wesampula. Lo mqondo uyasebenza kakhulu engxoxweni yethu ngoba sithanda ibhalansi — okungukuthi, lapho kusho yamasampula ethu angahleliwe aseduze. I-CLT ihlinzeka ngokusatshalaliswa kwalezi zindlela zesampula.

Ngenxa ye-CLT, singacabanga ngencazelo yesampula ngendlela efanayo esingenza ngayo noma yikuphi okunye okuguquguqukayo okungahleliwe. Uma ukhumbula emuva emathubeni angu-101, uma kubhekwa ukusatshalaliswa kokuguquguquka okungahleliwe, singabala amathuba okuthi umuntu ngamunye awadwebe ekusabalaliseni awe phakathi kobubanzi obuthile.

Ngaphambi kokuba sibe nethiyori kakhulu, ake sigxumele esibonelweni ukuze sakhe intuition. Ithi sifuna ukwenza ucwaningo oludinga amaqembu amabili onogwaja akhethwe ngokungahleliwe. Sizothatha ngokuthi isisindo sikanogwaja ngamunye ngokuvamile sisatshalaliswa ngesilinganiso esingu-3.5 lbs kanye nokuhluka okungu-0.25 lbs.

Umsebenzi olula wePython ngezansi ubala amathuba okuthi isampula yethu engahleliwe yonogwaja iwele ebangeni elithile elinikezwe ukusatshalaliswa kwesibalo sabantu kanye nosayizi wesampula:

from scipy.stats import norm

def normal_range_prob(lower,
                      upper,
                      pop_mean,
                      pop_std,
                      sample_size):

    sample_std = pop_std/np.sqrt(sample_size)
    upper_prob = norm.cdf(upper, loc=mean, scale=sample_std)
    lower_prob = norm.cdf(lower, loc=mean, scale=sample_std)
    return upper_prob - lower_prob

Ake sithi sizocabangela izindlela ezimbili zesampula njengezibhalansi uma zombili ziwela ngaphakathi kuka-+/-0.10 lbs wenani labantu. Ukwengeza, sizoqala ngesampula kasayizi onogwaja abayi-100 ngamunye. Singakwazi ukubala amathuba okuthi isampula elilodwa lisho ukuthi liwele kulobu bubanzi sisebenzisa umsebenzi wethu onjengokuthi ngezansi:

Ngesampula kasayizi wonogwaja abayi-100, sinethuba elicishe libe ngu-95% lesampula lethu elisho ukuthi liwela ngaphakathi kwama-0.1 lbs wenani labantu. Ngoba ngokungahleliwe isampula amaqembu amabili kukhona ezimele imicimbi, singasebenzisa Umthetho Womkhiqizo, ukubala amathuba okuba amasampuli amabili abe ngaphakathi kwama-lbs angu-0.1 wesibalo sabantu asho ngokumane siphinde siphindeke samathuba okuqala. Ngakho-ke, amathuba okuthi amasampula amabili alinganiswe futhi asondele kusilinganiso sabantu angu-0.90% (0.95).²). Uma besinosayizi wamasampula amathathu, amathuba okuthi bonke balinganisele eduze kwencazelo ngu-0.95³ = 87%.

Kunobudlelwano obubili engifuna ukubumemezela lapha – (1) uma usayizi wesampula ukhuphuka, amathuba okulinganisa ayanda futhi (2) njengoba inani lamaqembu okuhlola likhula, amathuba okuthi wonke abhalansise ehle.

Ithebula elingezansi libonisa amathuba awo wonke amaqembu okuhlola anikezwe ngokungahleliwe abhalansisa amasampula osayizi abaningi nezinombolo zeqembu lokuhlola:

Lapha sibona ukuthi ngosayizi wesampula omkhulu ngokwanele, isisindo sethu sikanogwaja esilingiswayo kungenzeka silingane, ngisho namaqembu okuhlola angu-5. Kodwa, ngenhlanganisela yosayizi abancane besampula kanye namaqembu amaningi okuhlola, lawo mathuba ayancipha.

Manje njengoba sesinokuqonda ukuthi i-randomization ivame ukulinganisa ama-covariates ezimweni ezivumayo, sizongena engxoxweni yokuthi kungani ama-covariate kwesinye isikhathi engalingani.

Qaphela: Kule ngxoxo, sicabangele kuphela ithuba lokuthi ibhalansi ye-covariate eduze nencazelo yesampula. Ngokuqagela, bangabhalansisa endaweni ekude nencazelo yesampula, kodwa lokho bekungeke kwenzeke kakhulu. Asikunakanga lokho okungenzeka lapha – kodwa bengifuna ukumemeza ukuthi likhona.

Izimbangela zokungalingani kwe-covariate naphezu kokwabiwa okungahleliwe

Engxoxweni edlule, sakhe intuition yokuthi kungani ama-covariate ejwayele ukulinganisa nesabelo esingahleliwe. Manje sizoshintshela ekuxoxeni ngokuthi yiziphi izici ezingaqhuba ukungalingani kuma-covariate kuwo wonke amaqembu okuhlola.

Ngezansi izizathu ezinhlanu engizozihlanganisa:

1. Ibhadi ekuthathweni kwesampula
2. Osayizi besampula abancane
3. Ukusabalalisa kwe-covariate okwedlulele
4. Amaqembu amaningi okuhlola
5. Ama-covariate amaningi anomthelela

Ibhadi ekuthathweni kwesampula

Ukulinganisa kwe-Covariate kuhlala kuhlotshaniswa namathuba futhi awekho neze amathuba aphelele angu-100% okulinganisa. Ngenxa yalokhu, kuhlale kunethuba – ngisho nangaphansi kwezimo ezinhle kakhulu ze-randomization – ukuthi ama-covariate ekuhlolweni ngeke alinganise.

Osayizi besampula abancane

Uma sinosayizi abancane besampula, ukuhluka kokusabalalisa kwethu kusho kukhulu. Lokhu kwehluka okukhulu kungaholela emathubeni aphezulu omehluko omkhulu kuma-covariate ethu amaphakathi kuzo zonke izixuku ezihlolwayo, okungagcina kuholele ekungalinganini kwe-covariate.

Kuze kube manje, siphinde sacabanga ukuthi amaqembu ethu okwelapha wonke anamasampula osayizi afanayo. Kunezimo eziningi lapho sizofuna ukuba namasampula osayizi abahlukene kuwo wonke amaqembu okwelapha. Ngokwesibonelo, singase sibe nomuthi esiwuthandayo weziguli ezinesifo esithile; kodwa futhi sifuna ukuhlola ukuthi umuthi omusha ungcono yini. Ukuhlola okufana nalokhu, sifuna ukugcina iziguli eziningi emithini ekhethwayo kuyilapho sinikeza ngokungahleliwe ezinye iziguli emithini engaba ngcono, kodwa engahloliwe. Ezimeni ezifana nalezi, amaqembu amancane okuhlola azoba nokusatshalaliswa okubanzi kwesilinganiso sawo sesampula futhi ngenxa yalokho abe namathuba aphezulu okuba nesampula yencazelo ngokuqhubekayo ukusuka kuncazelo yabantu futhi okungabangela ukungalingani.

Ukusabalalisa kwe-covariate okwedlulele

I-CLT ikhomba kahle ukuthi isampuli isho ukuthi noma yikuphi ukusatshalaliswa kuvame ukusatshalaliswa ngosayizi wesampula owanele. Nokho, usayizi wesampula owanele akufani kukho konke ukusatshalaliswa. Ukusabalalisa okudlulele kudinga usayizi wesampula owengeziwe ukuze isampula isho ukuthi isatshalaliswe ngokujwayelekile. Uma inani labantu linama-covariate anokusabalalisa okudlulele, amasampuli amakhulu azodingeka ukuze isampula lisho ukuthi liziphathe kahle. Uma amasayizi amasampula emakhulu ngokuqhathaniswa, kodwa emancane kakhulu ukunxephezela ukusatshalaliswa okwedlulele, ungase ubhekane nenkinga kasayizi wesampula encane esixoxile ngayo esigabeni sangaphambilini nakuba ungase ube nosayizi wesampula omkhulu.

Amaqembu amaningi okuhlola

Ngokufanelekile, sifuna wonke amaqembu okuhlola abe nama-covariate abhalansi. Njengoba inani lamaqembu okuhlola likhula, lokho kuba mancane kakhulu amathuba. Ngisho nasezimeni ezimbi kakhulu lapho iqembu elilodwa lokuhlola linamathuba angama-99% okuba seduze nenani labantu, ukuba namaqembu ayi-100 kusho ukuthi kufanele silindele ukuthi okungenani elilodwa liwele ngaphandle kwalolo hlu.

Ngenkathi amaqembu okuhlola ayikhulu abonakala eqisa kakhulu. Akuvamile umkhuba ukuba namaqembu amaningi okuhlola. Imiklamo evamile yokuhlola ihlanganisa izici eziningi okufanele zihlolwe, ngayinye inamazinga ahlukahlukene. Cabanga nje sihlola ukusebenza kwemisoco yezitshalo ezahlukene ekukhuleni kwezitshalo. Singase sifune ukuhlola imisoco emi-4 ehlukene kanye namazinga ama-3 ahlukene okugxilisa ingqondo. Uma lokhu kuhlolwa bekusezingeni eligcwele (sakha iqembu lokuhlola lenhlanganisela ngayinye yokwelashwa okungenzeka kube khona), besizodala 81 (3⁴) amaqembu okuhlola.

Ama-covariate amaningi anomthelela

Esibonelweni sethu sokuhlola onogwaja, sixoxe nge-covariate eyodwa kuphela. Empeleni, sifuna wonke ama-covariate anomthelela alinganisele. Uma kukhona ama-covariate anomthelela kakhulu, mancane amathuba okuba kufinyelelwe ibhalansi ephelele. Ngokufana nenkinga yamaqembu amaningi okuhlola, i-covariate ngayinye inethuba lokungalingani – ama-covariate amaningi, mancane amathuba okuthi wonke azobhalansi. Akufanele sicabangele kuphela ama-covariate esaziyo ukuthi abalulekile, kodwa futhi nalawo angenakulinganiswa esingawalandeli noma esiwazi ngisho nawo. Sifuna labo babhalanse nabo.

Lezi yizizathu ezinhlanu zokuthi singase singaboni ibhalansi kuma-covariate ethu. Akulona uhlu oluphelele, kodwa kwanele ukuba siqonde kahle lapho inkinga ivame ukuvela khona. Manje sisesimweni esihle sokuqala ukukhuluma ngokuthi kungani ukuhlola kuvumelekile ngisho noma ama-covariate engalingani.

Ukufaneleka kokuhlolwa kumayelana nokuzimela, hhayi ibhalansi

Ama-covariate abhalansile anezinzuzo lapho ehlaziya imiphumela yokuhlolwa, kodwa awadingeki ukuze abe semthethweni. Kulesi sigaba, sizohlola ukuthi kungani ibhalansi inenzuzo, kodwa ingadingeki ekuhloleni okuvumelekile.

Izinzuzo zama-covariate alinganiselayo

Uma ibhalansi ye-covariates kuwo wonke amaqembu okuhlola, izilinganiso zomphumela wokwelashwa zivame ukunemba kakhudlwana, ngokuhluka okuphansi kusampula yokuhlola.

Ngokuvamile kuwumqondo omuhle ukufaka ama-covariate ekuhlaziyweni kokuhlolwa. Lapho ibhalansi ye-covariates, imiphumela yokwelashwa elinganiselwe ayizweli kancane ekufakweni nasekucacisweni kwama-covariates ekuhlaziyweni. Uma ama-covariate engalingani, kokubili ubukhulu nokutolikwa komthelela wokwelashwa olinganiselwe kungancika kakhulu ekutheni yiziphi ama-covariate afakiwe nokuthi amodelwa kanjani.

Kungani ibhalansi ingadingeki esivivinyweni esivumelekile

Nakuba ibhalansi ilungile, ayidingeki ekuhlolweni okuvumelekile. Ukufaneleka kokuhlolwa kumayelana nokuphula ukuncika kokwelashwa kunoma iyiphi i-covariate. Uma lokho kwephukile, khona-ke ukuhlola kuvumelekile – ukwenza okungahleliwe okulungile njalo kwephula ubudlelwano obuhlelekile phakathi kokwelashwa nawo wonke ama-covariate.

Ake sibuyele esibonelweni sethu sikanogwaja futhi. Uma sivumele onogwaja ukuthi bazikhethele ukudla, kungase kube nezinto ezithinta kokubili ukuzuza isisindo kanye nokukhetha ukudla. Mhlawumbe onogwaja abancane bathanda ukudla okunamafutha amaningi kanti onogwaja abancane banamathuba amaningi okuthi bakhuluphale njengoba bekhula. Noma mhlawumbe kunophawu lwezakhi zofuzo okwenza onogwaja bakhuluphale futhi bathande ukudla okunamafutha amaningi. Ukuzikhetha kungabangela zonke izinhlobo zezinkinga ezididayo esiphethweni sokuhlaziya kwethu.

Uma esikhundleni salokho, senze okungahleliwe, ubudlelwano obuhlelekile phakathi kokukhetha ukudla (ukwelashwa) kanye neminyaka noma izakhi zofuzo (izihlanganisi) buyaphulwa futhi inqubo yethu yokuhlola izosebenza. Ngenxa yalokho, noma yikuphi ukuhlangana okusele phakathi kokwelashwa kanye nama-covariates kungenxa ithuba esikhundleni sokukhetha, futhi okucatshangelwayo okuyimbangela okuvela ekuhlolweni kuyasebenza.

Ngenkathi i-randomization iphula isixhumanisi phakathi kwama-confounders nokwelashwa futhi yenza inqubo yokuhlola isebenze. Akuqinisekisi ukuthi ukuhlola kwethu ngeke kufike esiphethweni esingalungile.

Cabanga ngokuhlolwa okulula kwe-hypothesis kusuka kusingeniso sakho kuya esifundweni sezibalo. Sidweba ngokungahleliwe isampula kubantu ukuze sinqume ukuthi inani labantu lisho ukuthi lihlukile noma alihlukile ukusuka kunani elinikeziwe. Le nqubo ivumelekile — okusho ukuthi inamazinga amaphutha achazwe kahle, kodwa ishwa kusampula eyodwa engahleliwe ingabangela amaphutha ohlobo I noma uhlobo II. Ngamanye amazwi, indlela yokwenza inengqondo, nakuba ingaqinisekisi isiphetho esifanele ngaso sonke isikhathi.

Ukungahleliwe ekuhloleni kusebenza ngendlela efanayo. Kuyindlela evumelekile yokucabanga okuyimbangela, kodwa lokho akusho ukuthi zonke izivivinyo ezingahleliwe zizoletha isiphetho esifanele. Ukungalingani kwamathuba kanye nokwehluka kwamasampula kusengathinta imiphumela kunoma yikuphi ukuhlola ngakunye. Ukuba nokwenzeka kweziphetho eziyiphutha akuyenzi indlela yokwenza.

Eyisonga

Ukungahleliwe kuvame ukulinganisa ama-covariate kuwo wonke amaqembu okwelapha, kodwa akuqinisekisi ibhalansi kunoma yikuphi ukuhlola okukodwa. Lokho okuqinisekisa i-randomization ukufaneleka. Ubudlelwano obuhlelekile phakathi kwesabelo sokwelashwa kanye nama-covariate buphulwa ngokuklama. Ibhalansi ye-Covariate ithuthukisa ukunemba, kodwa akuyona imfuneko yokuqagela okuvumelekile kwembangela. Lapho ukungalingani kwenzeka, ukulungiswa kwe-covariate kunganciphisa imiphumela yako. Okubalulekile okuthathwayo ukuthi ibhalansi iyafiseleka futhi iyasiza, kodwa i-randomization (hhayi ibhalansi) yikho okwenza ukuhlola kusebenze.