23-BIOSTATICS, FORMULAE

categorical/qualitative data-percentage% freq of occurrence(comparision of magnitude) bar diagram pie chart/sector diagram

pictogram map diagram/spot mapquanTitative data-mean±SD(unskew), median(range)(skew) distribution(not related to time) hisTogram

freq polygon freq curve line diag(time trend) scatter plot(study relation b/n 2variable)

measure of central tendency outlier, skewed, extreme most affected-mean least affect-mode most preferred-median

geometric mean=(n)√(x1×x2×…xn)harmonic mean=1/(1/x1+1/x2+…1/xn)

meas of dispersion/deviation/variation range=max–min mean deviation=|mean–x|/n SD=√[Σ(|mean–x|)²/n] SD(<30)=√[Σ(|mean–x|)²/(n–1)] variance=SD² CV=(SD/mean)×100 SE=SD/√n precision=1/SE=√n/SD for bimodal data mode=3median–2mean z score/relative deviate/critical ratio z=|mean–x|/SD

(quant)SE=SD/√n

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(qualit)SE=√(PQ/n)(quant)95%CI=mean±2.5SE(qualit)95%CI=proportion±2.5SE(quant)sample size=Z²SE²/L²(qualit)sample size=Z²PQ/L² Z²=4, P=prevalence, Q=1–P, L=100-CI

probability p(event)=n(experiment)/n(total event) odds=n(event occur)/n(event not occur) Poisson distribution-discrete probability distribution for random event

+ve/rt skew mean>median>mode–ve/lt skew mean<median<mode(Hint-arrange in alphabetical order and look at the direction where the (<,>) is pointing)Pearson skewness coefficient=(mean–mode)/SD

std normal curve area=1 mean=mode=median=0 SD=1 mean±1SD=68.27% mean±2SD=95.45% mean±3SD=99.73%

test for pRecision(Reliability, Reproducibility, Repeatability) Range chart R chart CRonbachαtest for accuracy mean chart LJ(Levy Jenning) chart Shewart control chart

कम ह तैो कर दोnull hypothesis( reject ) rejected-p value<0.05-p value significant accepted-p value>0.05-p value insignificant

p value=prob of declaring diff when actually not=prob rejecting null hypothesis when true

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p value 0.01-difference 99%signif↑→ ↓ CI level of signif

type I error-false +ve type II error-false –ve

epidemiologic hypothesis specify population, expected outcome, sp cause, dose response relationship, time response relationship

epidemiological study cohort(AIR)-Attributable risk, Incidence, Relative risk-natural h/o ds, Hawthorn effect-behaviour change when being observed case control-Odds ratio cross sectional-prevalence ecological(best)-group characteristics-unit-population

observational study descriptive analytical ecological-correlation-polpulation cross sectional-prevalence-individual case control-case reference-individual cohort-follow up-individual prospective-Framingham heart study, Doll&Hills study on smoking&ca lung nested case control study

retrospective-effect of fetal monitoring on neonatal death, PVC exposure& angiosarcoma liver

COmbine-COurt Brown&Doll study on radiation therapy

experimental study randomised control trial-clinical trial-pt field trial-healthy people, introduce vacc for 1y old&see its efficacy community trial-community intervention study-community

randomised control trial-dropout not excluded fr study

accuracy to test association b/n risk factor&ds systematic review& metaanalysis> randomised control trial> retrospective cohort> prospective cohort> case cohort> cross sectional>

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ecological

yield=new case d/t screening→ screen time=time(1st possible Dx final critical Dx)

→ lead time=time(1st possibl Dx usual time Dx)→ serial interval=time(prim case sec case)

→ generation time=time(receipt of inf by host max infectivity) T interval=no. of d bed of hosp remain vacant incubat period≈generation time

RR/risk ratio=incid(exposed)/incid(non exposed) AR=[incid(exposed)–incid(non exposed)]/incid(expos) popul AR=[incid(population)–incid(not exposed)]/incid(population)

type of bias-technique selection-randomisation surveillance/detection Neyman survival/incidence prevalence referral/volunteer response Berkesonian(hosp admission)

recall(memory) bias d/t confounding-matching, multivariate analysis information-single blinding interviewer/observer-double blinding statician-triple blinding

sensitivity=(true+ve/all ds)×100 specificity=(true–ve/all not ds)×100 +ve predictive value=(true+ve/all+ve)×100–ve predictive value=(true–ve/all–ve)×100

diagnostic test-predictive value false+ve%=(FP/total not ds)×100=1–sPecificity false–ve%=(FN/total ds)×100=1–seNsitivity efficiency(accuracy)=all true/all pt likelihood ratio for +ve test=sensitivity/(1–specificity) likelihood ratio –ve test=(1–sensitivity)/specificity pretest probability=prevalence+clinical assessm posttest probability=pretest probability×likelihood ratio↑ ↑ ↓ sensitivity- TP- PPV↑ ↑ ↓ specificity- TN- NPV

sensitivity,specificity-criterion validity

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multiple Dx test↓ ↑ ↑ series- sensitivity, specificity, PPV↑ ↓ ↑ parallel- sensitivity, specificity, NPV

best test to compare new&old test-Bland&Altman analysis

sampling random/probability/nonpurposive-chance of being selected-same&known simple systematic stratified(heterogenous) multistage Cluster(homogenous-Cost effective)

nonrandom/nonprobability/purposive convenient quota/targetted snowball/network judgement

PQLI=IMR+life expectancy at age 1y+literacy rate, range=0-100, India=65(rank-63) measure social, economic, politic policies does not measure economic growth

HDI=GNI per capita+ life expectancy at birth+ (mean y of school, expected y of school), range0-1, India=0.545(rank-136) top-Norway, Australia, USA bottom-Congo, Nigeria

human poverty index1=long&healthy life(probability at birth not surviving 40y)+ knowledge(adult literacy rate)+ std of living(%of populat using improved H2O source+ %child underwt for age), India=31.3%

DALY(Disability Adjusted Life Y)=y of life lost+y lost to disability burden of ds in populat effectiveness of intervention

DFLE(Disability Free Life Expectancy)/active life expectancy=no. of y expected free of disability if current pattern of mortality& disability continue to apply

HALE(Health Adjusted Life Expectancy)=life expectancy–time spent in poor health

QALY(Quality Adjusted Life Y)=no. of y added to life by intervention

type of data(NOIR)

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Nominal(mode)-mal/fem, black/white, rural/urban Ordinal(median)-1st,2nd, very satisfied,satisfied,dissatisfied Interval(mean)-90°C,100°C,110°C Ratio(mean)-pulse rate 90,100,110/min

correlation graph-scatter plot(correlation diagram) +ve-change in same direction–ve-change in opposite direction

r(Piersen correlation coefficient) r=+1-perfect +ve r=–1-perfect –ve r=0-no correlation

–1≤r≤+1 r²=coeff of determination 0≤r²≤1 r<0.3-very weak r=0.3-0.49-weak r=0.5-0.89-strong r≥0.9-very strong

type of regression simple linear-y=a+bx multiple linear-y=a+bx1+cx2+dx3 simple curvilinear-y=a+bx³ multiple curvilinear-y=a+bx1³+cx2³+dx3³

test of significance quantitative 2group related(before-after)-paired t test unrelated-unpaired t test

>2group ANOVA(F) test qualitative/categorical Pearson chi² test/Fisher exact test/Yate correction

obesity BMI(Quetlet index)=wt(kg)/ht(m²) Brocca index-ideal wt(kg)=ht(cm)–100 corpulence index-actual wt/desirable wt≤1.2 Lorentz formula-ideal wt(kg)= ht(cm)–100–[{ht(cm)–150}/2(fem),4(mal)}] skinfold thickn(MC meth)

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midtriceps(best)+biceps+subscapular+suprailiac ≥50mm(fem),≥40mm(mal) midtriceps≥18mm(mal), ≥32mm(fem) waist circumf(cm) World≥102(mal), ≥88(fem) India≥90(mal), ≥80(fem)

waist/hip ratio>1.0(mal), >0.85(fem) waist/ht ratio(best CVS ds risk)≥0.5

contracept effectiveness Pearl index potency of contraception=(total accident preg/no. of pt observed×mth of use)×1200 life table analysis-best

prot quality assessm digestibilty coefficient=(N2 absorbed/N2 intake)×100 biological value=(N2 retained/N2 absorbed)×100 net protein utilization=(N2 retained/N2 intake)×100=(biological value×digestibility coefficient)/100 protein efficiency ratio=wt gain(g)/prot intake(g) AA(chemical) score=[{(no. of AA/g prot)}/{(no. of same AA/g egg prot)}]×100prot quantity assessm prot energy ratio=(energy fr prot/total energy fr diet)×100 1g prot=6.25g N2 norm NPU=50-80

relative humidity=H2O vapour content/H2O vapour capacity

Box Whisker plot quartile

forest plot represent result in systematic review& metaanalysis(best study design)

funnel plot assess publication bias

Kaplan Meier curve/product limit estimation survival fn fr lifetime data-#pt living for certain time after Rx X-time, Y-%of survival cox-proportion hazard model to control confounding factor in survival analysis

Levy Jenning chart accuracy, quality monitoring

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rate-numerator part of denominator, time is taken IMR, incidence

ratio-numerator not part of denominator std mortality rate, risk ratio, sex ratio, dependency ratio, coefficient of variance, abortion ratio

PRoportion-% case fatality rate, PRevalence

abortion ratio=no. of abortion performed/no. of live birth age sp death rate=(death age grp/MYP of same age grp)×1000 case fatality rate(CFR)=(death d/t ds/total case)×100 child sex ratio=no. of fem(0-6y)/no. of mal(0-6y) child survival rate=(1000–under5 mortality rate)/10 crude birth rate=(8×TFR)+1 crude death rate=(no. of death during 1y/MYP)×1000 dependency ratio=[(0-14y+>65y)/(15- 65y)]×100 general fertilty rate=(no. of child born/reproductive women)×1000 gross reprod/fertility rate=no. of girl born/reproduct fem(no mortality) incidence rate(I)=(no. of new case during a period/population at risk)×1000 maternal mortality RATE=(maternal death/reprod women)×1000 maternal mortality RATIO=(mat death/live birth)×1lac net reproduct rate=no. of girl born/reproductive women(fix age sp fertility& mortality) 1-4y mortality(child death) rate=(death 1-4y/total childr1-4y)×1000 prevalenc ratio(P)=(total no. of all case/population at risk) P=I×duration of ds(time) proportional mortality rate=(death d/t ds/total death)×100 sp death rate d/t caus=(no. of death d/t cause/MYP)×1000 standardised mortality ratio=(observed death/expected death)×100 survival rate=1–CFR total fertilty rate=no. of child born/reproductive women(fix age sp fertility rate) under5(child) mortality rate=(death<5y/live birth)×100

best indicator health status of community, effectiven of MCH service, level of living-IMR socioeconomic status-under5(child) mortality rate>IMR

malaria Annual Parasite Incidence(API) =(confirm case in 1y/populat)×1000 Annual Bld Examinat Rate(ABER)

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=(no. slide examin/populat)×100 MPO≥10% spleen rate=(no. child2-10y with enlarged spleen/total child2-10y)×100 Infant Parasite Index(most sensitive) =(infant with +ve PS/total infant)×100 IPI=0×3consec y

plague total flea index =no. flea/no. rat all sp cheopis/specif flea index =no. X cheopis/no. rat

>1-potential explosive plague outbreak specif% flea =(sp of flea/no. rat)×100

burrow index =free living flea per species per rodent burrow

Abbreviations a-artery, AA-amino acid, abtc-antibiotic, AI-autoimmune bef-before, bel-below, b/l-bilateral, bld-blood, b/n-between, bn-benign, br-branch, Bx-biopsy ca-carcinoma, carb-carbohydrate, c/i-contraindication, c/l-contralateral, conc-concentration, cong-congenital, Cx-cervix d-day, def-deficient, ds-disease, d/t-due to, Dx-diagnosis E-estrogen fem-female, fr-from gld-gland, glu-glucose h-hormone idiop-idiopathic, i/l-ipsilateral, inf-infection, inj-injury lig-ligament, LL-lower limb, l/t-leading to m-muscle, maj-major, mal-male, MC-most common, met-metastasis, min-minor, mtx-methotrexate, Mx-management n-nerve, norm-normal P-progesterone, pl-plasma, prot-protein, pt-patient Rx-treatment SCC-squamous cell carcinoma, sr-serum, Sx-surgery, sz-seizure tm-tumour, ts-tissue UL-upper limb, u/l-unilateral vag-vagina, VC-vocal cord, vel-velocity, vert-vertebra, vit-vitamin, vol-volume w-week, wt-weight Xr-X ray y-year #-fracture °-degree

THESE NOTES ARE ONLY FOR THE PURPOSE OF GUIDANCE AND HELP TO PG ASPIRANTS, NOT FOR COMMERCIAL OR OTHER PURPOSE. REFERENCE

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HAS BEEN TAKEN FROM VARIOUS STANDARD TEXTBOOKS.

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